Metrics for Toniolo and Linder, Equation (7)

analyze320.0ms (1.8%)

Memory

20.3MiB live, 525.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
0%	0%	99.9%	0.1%	0%	0%	0%	7
0%	0%	74.9%	0.1%	0%	25%	0%	8
4.2%	3.1%	71.8%	0.1%	0%	25%	0%	9
6.3%	4.7%	70.2%	0.1%	0%	25%	0%	10
11.3%	7%	55.4%	0.1%	0%	37.4%	0%	11
16.9%	10.5%	51.9%	0.1%	0%	37.4%	0%	12

Compiler

Compiled 29 to 20 computations (31% saved)

sample2.9s (15.6%)

Memory

-17.3MiB live, 3 718.4MiB allocated

Samples

905.0ms	5 432×	0	valid
529.0ms	2 622×	1	valid
374.0ms	2 857×	0	invalid
341.0ms	1 615×	1	invalid
59.0ms	202×	2	valid
22.0ms	85×	2	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-mult: 676.0ms (38.1% of total)

ival-div: 285.0ms (16.1% of total)

ival-sqrt: 239.0ms (13.5% of total)

ival-sub: 205.0ms (11.6% of total)

ival-add: 175.0ms (9.9% of total)

adjust: 166.0ms (9.4% of total)

exact: 13.0ms (0.7% of total)

ival-true: 9.0ms (0.5% of total)

ival-assert: 5.0ms (0.3% of total)

Bogosity

preprocess689.0ms (3.8%)

Memory

-29.6MiB live, 688.9MiB allocated

Algorithm

1×	egg-herbie

Rules

25 302×	`lower-fma.f64`
25 302×	`lower-fma.f32`
4 556×	`lower-*.f32`
4 546×	`lower-*.f64`
2 076×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	250
1	221	248
2	650	246
3	2219	246
4	7024	246
0	18	27
0	31	27
1	58	27
2	113	27
3	212	27
4	437	27
5	990	27
6	2266	27
7	5077	27
0	8183	26

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

Outputs

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (*.f64 t t) (*.f64 l l)) (+.f64 x #s(literal -1 binary64))) (*.f64 l (neg.f64 l)))))

Symmetry

(abs l)

(negabs t)

explain443.0ms (2.4%)

Memory

15.8MiB live, 382.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	3	(1.1538598438748657e+212 6.679114410415179e-50 4.837590714817483e-236)	`(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))`
91	-	0	-	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`
0	-	0	-	`(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))`
0	-	0	-	`(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`t`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 t t))`
0	-	0	-	`(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)`
0	-	0	-	`(+.f64 x #s(literal 1 binary64))`
0	-	0	-	`(*.f64 l l)`
0	-	0	-	`(sqrt.f64 #s(literal 2 binary64))`
0	-	0	-	`(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))`
0	-	0	-	`(*.f64 t t)`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(-.f64 x #s(literal 1 binary64))`
0	-	0	-	`l`
0	-	0	-	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))`	oflow-rescue	97	0
↳	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`	overflow	97
↳	`(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))`	overflow	116
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	overflow	79
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	overflow	116
↳	`(*.f64 t t)`	overflow	79
↳	`(*.f64 l l)`	overflow	118
`-.f64`	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`	nan-rescue	59	0
↳	`(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))`	overflow	116
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	overflow	79
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	overflow	116
↳	`(*.f64 t t)`	overflow	79
↳	`(*.f64 l l)`	overflow	59
↳	`(*.f64 l l)`	overflow	59
`-.f64`	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`	cancellation	32	0
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))`	uflow-rescue	25	0
↳	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`	underflow	25
↳	`(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))`	underflow	17
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	underflow	54
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	underflow	17
↳	`(*.f64 t t)`	underflow	54
↳	`(*.f64 l l)`	underflow	136

Confusion

	Predicted +	Predicted -
+	172	1
-	1	82

Precision

0.9942196531791907

Recall

0.9942196531791907

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	172	0	1
-	1	0	82

Precision?

0.9942196531791907

Recall?

0.9942196531791907

Freqs

test

number	freq
0	83
1	133
2	40

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

76.0ms	334×	0	valid
36.0ms	166×	1	valid
4.0ms	12×	2	valid

Compiler

Compiled 326 to 76 computations (76.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-mult: 49.0ms (56% of total)

ival-sub: 9.0ms (10.3% of total)

ival-div: 8.0ms (9.1% of total)

ival-sqrt: 8.0ms (9.1% of total)

ival-add: 7.0ms (8% of total)

adjust: 6.0ms (6.9% of total)

exact: 1.0ms (1.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	33.7%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))

Status

Accuracy

Program

▶

33.7%

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

Compiler

Compiled 30 to 18 computations (40% saved)

simplify689.0ms (3.8%)

Memory

-1.6MiB live, 523.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
✓	cost-diff	128	(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))

Rules

25 302×	`lower-fma.f64`
25 302×	`lower-fma.f32`
4 556×	`lower-*.f32`
4 546×	`lower-*.f64`
2 076×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	131
0	31	131
1	58	131
2	113	131
3	212	131
4	437	131
5	990	131
6	2266	131
7	5077	131
0	8183	126

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))
(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))
(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))
(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(-.f64 x #s(literal 1 binary64))
(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))
(*.f64 l l)
l
(.f64 #s(literal 2 binary64) (.f64 t t))
(*.f64 t t)

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l (neg.f64 l)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))
(sqrt.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (*.f64 l (neg.f64 l))))
(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (*.f64 l (neg.f64 l)))
(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))
(/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(-.f64 x #s(literal 1 binary64))
(+.f64 x #s(literal -1 binary64))
(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))
(fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))
(*.f64 l l)
l
(.f64 #s(literal 2 binary64) (.f64 t t))
(*.f64 t t)

localize128.0ms (0.7%)

Memory

-36.6MiB live, 86.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
✓	accuracy	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	accuracy	69.3%	(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))
✓	accuracy	55.1%	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))

Samples

51.0ms	167×	0	valid
30.0ms	83×	1	valid
2.0ms	6×	2	valid

Compiler

Compiled 133 to 20 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 7.0ms (28% of total)

ival-div: 4.0ms (16% of total)

ival-sqrt: 4.0ms (16% of total)

ival-sub: 3.0ms (12% of total)

adjust: 3.0ms (12% of total)

ival-add: 3.0ms (12% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series78.0ms (0.4%)

Memory

12.9MiB live, 52.1MiB allocated

Counts

6 → 144

Calls

Call 1

Inputs
#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l)))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))) (patch (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l)) (patch (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l)) #<representation binary64>) () ())

Outputs
#s(alt (* 2 (pow t 2)) (taylor 0 l) (#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (pow t 2)) (pow l 2)) (taylor 0 l) (#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (pow t 2)) (pow l 2)) (taylor 0 l) (#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (pow t 2)) (pow l 2)) (taylor 0 l) (#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())) ())
#s(alt (pow l 2) (taylor inf l) (#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())) ())
#s(alt (* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2))))) (taylor inf l) (#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())) ())
#s(alt (* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2))))) (taylor inf l) (#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())) ())
#s(alt (* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2))))) (taylor inf l) (#s(alt (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) (patch (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))) #<representation binary64>) () ())) ())
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Calls

36 calls:

Time	Variable		Point	Expression
24.0ms	x	@	0	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
5.0ms	x	@	0	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
4.0ms	x	@	-inf	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
4.0ms	t	@	0	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
4.0ms	x	@	inf	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

simplify3.4s (18.4%)

Memory

18.3MiB live, 651.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 416×	`lower-fma.f64`
10 416×	`lower-fma.f32`
9 668×	`lower-*.f64`
9 668×	`lower-*.f32`
3 974×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	676	10349
1	2332	9162
0	8701	8754

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(* 2 (pow t 2))
(+ (* 2 (pow t 2)) (pow l 2))
(+ (* 2 (pow t 2)) (pow l 2))
(+ (* 2 (pow t 2)) (pow l 2))
(pow l 2)
(* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2)))))
(* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2)))))
(* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2)))))
(pow l 2)
(* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2)))))
(* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2)))))
(* (pow l 2) (+ 1 (* 2 (/ (pow t 2) (pow l 2)))))
(pow l 2)
(+ (* 2 (pow t 2)) (pow l 2))
(+ (* 2 (pow t 2)) (pow l 2))
(+ (* 2 (pow t 2)) (pow l 2))
(* 2 (pow t 2))
(* (pow t 2) (+ 2 (/ (pow l 2) (pow t 2))))
(* (pow t 2) (+ 2 (/ (pow l 2) (pow t 2))))
(* (pow t 2) (+ 2 (/ (pow l 2) (pow t 2))))
(* 2 (pow t 2))
(* (pow t 2) (+ 2 (/ (pow l 2) (pow t 2))))
(* (pow t 2) (+ 2 (/ (pow l 2) (pow t 2))))
(* (pow t 2) (+ 2 (/ (pow l 2) (pow t 2))))
(* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))
(* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (pow t 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* 8 (/ (pow (+ 1 x) 3) (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 4)))) (/ (* (+ 1 x) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))))
(* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))
(+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))
(+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))))
(+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/2 (* (/ (* (sqrt 2) (+ (* 1/16 (/ (* (pow (- x 1) 4) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)) (pow (+ 1 x) 4))) (* 1/8 (/ (* (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))) (* (pow (sqrt 1/2) 2) (+ 1 x)))))) (* (pow t 6) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))))
(* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (+ (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* 1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1)))))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (+ (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (* 1/2 (* (/ (* (sqrt 2) (+ (* 1/16 (/ (* (pow (- x 1) 4) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)) (pow (+ 1 x) 4))) (* 1/8 (/ (* (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))) (* (pow (sqrt 1/2) 2) (+ 1 x)))))) (* (pow t 6) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))))))
(* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))
(+ (* 1/2 (* (* t (* x (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))
(+ (* x (+ (* 1/2 (* (* t (* x (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* 1/4 (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) (pow (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))) 2))) (/ (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))) (* 1/2 (* (* t (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))
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(* (sqrt 1/2) (sqrt 2))
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Outputs
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))))
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(fma.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 (*.f64 l l) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(+ (* 2 (/ (* (pow t 2) (+ 1 x)) (- x 1))) (* (pow l 2) (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(fma.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 (*.f64 l l) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(+ (* 2 (/ (* (pow t 2) (+ 1 x)) (- x 1))) (* (pow l 2) (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(fma.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 (*.f64 l l) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* (pow l 2) (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))
(.f64 (.f64 l l) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1)))) (+ (/ 1 (- x 1)) (/ x (- x 1)))) 1))
(.f64 (.f64 l l) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 l (.f64 l (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1)))) (+ (/ 1 (- x 1)) (/ x (- x 1)))) 1))
(.f64 (.f64 l l) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 l (.f64 l (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1)))) (+ (/ 1 (- x 1)) (/ x (- x 1)))) 1))
(.f64 (.f64 l l) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 l (.f64 l (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* (pow l 2) (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))
(.f64 (.f64 l l) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1)))) (+ (/ 1 (- x 1)) (/ x (- x 1)))) 1))
(.f64 (.f64 l l) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 l (.f64 l (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1)))) (+ (/ 1 (- x 1)) (/ x (- x 1)))) 1))
(.f64 (.f64 l l) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 l (.f64 l (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1)))) (+ (/ 1 (- x 1)) (/ x (- x 1)))) 1))
(.f64 (.f64 l l) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 l (.f64 l (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))
(fma.f64 (.f64 l l) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l)))
(- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (- x 1))) (pow l 2))
(-.f64 (fma.f64 (.f64 l l) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))) (.f64 l l))
(- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (- x 1))) (pow l 2))
(-.f64 (fma.f64 (.f64 l l) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))) (.f64 l l))
(- (+ (* 2 (/ (* (pow t 2) (+ 1 x)) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (- x 1))) (pow l 2))
(-.f64 (fma.f64 (.f64 l l) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))) (.f64 l l))
(* 2 (/ (* (pow t 2) (+ 1 x)) (- x 1)))
(.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
(* (pow t 2) (- (+ (* 2 (/ (+ 1 x) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (* (pow t 2) (- x 1)))) (/ (pow l 2) (pow t 2))))
(.f64 (.f64 t t) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 l l) (.f64 t t))) (/.f64 (.f64 l l) (neg.f64 (.f64 t t)))))
(* (pow t 2) (- (+ (* 2 (/ (+ 1 x) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (* (pow t 2) (- x 1)))) (/ (pow l 2) (pow t 2))))
(.f64 (.f64 t t) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 l l) (.f64 t t))) (/.f64 (.f64 l l) (neg.f64 (.f64 t t)))))
(* (pow t 2) (- (+ (* 2 (/ (+ 1 x) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (* (pow t 2) (- x 1)))) (/ (pow l 2) (pow t 2))))
(.f64 (.f64 t t) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 l l) (.f64 t t))) (/.f64 (.f64 l l) (neg.f64 (.f64 t t)))))
(* 2 (/ (* (pow t 2) (+ 1 x)) (- x 1)))
(.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
(* (pow t 2) (- (+ (* 2 (/ (+ 1 x) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (* (pow t 2) (- x 1)))) (/ (pow l 2) (pow t 2))))
(.f64 (.f64 t t) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 l l) (.f64 t t))) (/.f64 (.f64 l l) (neg.f64 (.f64 t t)))))
(* (pow t 2) (- (+ (* 2 (/ (+ 1 x) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (* (pow t 2) (- x 1)))) (/ (pow l 2) (pow t 2))))
(.f64 (.f64 t t) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 l l) (.f64 t t))) (/.f64 (.f64 l l) (neg.f64 (.f64 t t)))))
(* (pow t 2) (- (+ (* 2 (/ (+ 1 x) (- x 1))) (/ (* (pow l 2) (+ 1 x)) (* (pow t 2) (- x 1)))) (/ (pow l 2) (pow t 2))))
(.f64 (.f64 t t) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 l l) (.f64 t t))) (/.f64 (.f64 l l) (neg.f64 (.f64 t t)))))

rewrite726.0ms (4%)

Memory

-14.2MiB live, 665.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

13 380×	`lower-fma.f64`
13 380×	`lower-fma.f32`
6 638×	`lower-*.f32`
6 628×	`lower-*.f64`
3 164×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	85
0	31	85
1	116	85
2	928	84
0	8797	80

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

6 → 417

Calls

Call 1

Inputs
(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))
(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))

Outputs
(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (*.f64 l l))
(+.f64 (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (*.f64 t #s(literal -2 binary64)))))))
(-.f64 (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (*.f64 t #s(literal -2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l))) (/.f64 (.f64 l (.f64 l (.f64 l l))) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (*.f64 l l))))
(fma.f64 l l (.f64 #s(literal 2 binary64) (.f64 t t)))
(fma.f64 l (.f64 l #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (*.f64 t t)))
(fma.f64 (.f64 l l) #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 t t)))
(fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))
(fma.f64 #s(literal 2 binary64) (.f64 (.f64 t t) #s(literal 1 binary64)) (*.f64 l l))
(fma.f64 t (.f64 #s(literal 2 binary64) t) (.f64 l l))
(fma.f64 t (.f64 (.f64 #s(literal 2 binary64) t) #s(literal 1 binary64)) (*.f64 l l))
(fma.f64 (.f64 t t) #s(literal 2 binary64) (.f64 l l))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) #s(literal 1 binary64) (*.f64 l l))
(fma.f64 #s(literal 1 binary64) (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 t t)) (*.f64 l l))
(fma.f64 (.f64 l (.f64 l (.f64 l l))) (/.f64 #s(literal 1 binary64) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (*.f64 t #s(literal -2 binary64)))))))
(fma.f64 (.f64 #s(literal 2 binary64) t) t (.f64 l l))
(fma.f64 (.f64 #s(literal 2 binary64) t) (.f64 t #s(literal 1 binary64)) (*.f64 l l))
(fma.f64 (exp.f64 (log.f64 l)) (exp.f64 (log.f64 l)) (.f64 #s(literal 2 binary64) (.f64 t t)))
(fma.f64 (.f64 #s(literal 1 binary64) l) l (.f64 #s(literal 2 binary64) (*.f64 t t)))
(fma.f64 (.f64 #s(literal 1 binary64) t) (.f64 #s(literal 2 binary64) t) (*.f64 l l))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 t t)) #s(literal 2 binary64) (*.f64 l l))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) t)) t (*.f64 l l))
(neg.f64 (/.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 t t) (.f64 t (.f64 t (.f64 t t)))) (.f64 (.f64 l (.f64 l l)) (.f64 l (.f64 l l)))) (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 t t) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l))) (.f64 l (.f64 l (.f64 l l)))))))
(neg.f64 (/.f64 (fma.f64 l (.f64 l (.f64 l l)) (.f64 (.f64 t (.f64 t (.f64 t t))) #s(literal -4 binary64))) (neg.f64 (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64)))))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 t t) (.f64 t (.f64 t (.f64 t t)))) (.f64 (.f64 l (.f64 l l)) (.f64 l (.f64 l l))))) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 t t) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l))) (.f64 l (.f64 l (.f64 l l))))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 l (.f64 l (.f64 l l)) (.f64 (.f64 t (.f64 t (.f64 t t))) #s(literal -4 binary64)))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 t (.f64 t (.f64 (.f64 t t) #s(literal 4 binary64))) (.f64 (.f64 l l) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64)))))) (fma.f64 #s(literal 8 binary64) (.f64 (.f64 t t) (.f64 t (.f64 t (.f64 t t)))) (.f64 (.f64 l (.f64 l l)) (.f64 l (*.f64 l l))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l)) (-.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (.f64 l (.f64 l (.f64 l l))))))
(/.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 t t) (.f64 t (.f64 t (.f64 t t)))) (.f64 (.f64 l (.f64 l l)) (.f64 l (.f64 l l)))) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 t t) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l))) (.f64 l (.f64 l (.f64 l l)))))
(/.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 t t) (.f64 t (.f64 t (.f64 t t)))) (.f64 (.f64 l (.f64 l l)) (.f64 l (.f64 l l)))) (fma.f64 t (.f64 t (.f64 (.f64 t t) #s(literal 4 binary64))) (.f64 (.f64 l l) (fma.f64 l l (.f64 t (*.f64 t #s(literal -2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))
(/.f64 (fma.f64 l (.f64 l (.f64 l l)) (.f64 (.f64 t (.f64 t (.f64 t t))) #s(literal -4 binary64))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 t t) (.f64 t (.f64 t (.f64 t t)))) (.f64 (.f64 l (.f64 l l)) (.f64 l (.f64 l l))))) (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 t t) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l))) (.f64 l (.f64 l (.f64 l l))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 t t) (.f64 t (.f64 t (.f64 t t)))) (.f64 (.f64 l (.f64 l l)) (.f64 l (.f64 l l))))) (neg.f64 (fma.f64 t (.f64 t (.f64 (.f64 t t) #s(literal 4 binary64))) (.f64 (.f64 l l) (fma.f64 l l (.f64 t (*.f64 t #s(literal -2 binary64))))))))
(/.f64 (neg.f64 (fma.f64 l (.f64 l (.f64 l l)) (.f64 (.f64 t (.f64 t (.f64 t t))) #s(literal -4 binary64)))) (neg.f64 (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (.f64 l (.f64 l (.f64 l l)))) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l)))
(/.f64 (-.f64 (.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (.f64 (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64)))) (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))))) (.f64 (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64)))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 t t) (.f64 t (.f64 t (.f64 t t)))) (.f64 (.f64 l (.f64 l l)) (.f64 l (.f64 l l)))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 t t) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l))) (.f64 l (.f64 l (.f64 l l)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 l (.f64 l (.f64 l l)) (.f64 (.f64 t (.f64 t (.f64 t t))) #s(literal -4 binary64))))) (neg.f64 (neg.f64 (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (.f64 l (.f64 l (.f64 l l))))) (neg.f64 (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (.f64 l l))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (fma.f64 (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (.f64 (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (*.f64 t #s(literal -2 binary64)))))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64)))))) (.f64 (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))))) (+.f64 (/.f64 (.f64 l (.f64 l (.f64 l l))) (fma.f64 l l (.f64 t (.f64 t #s(literal -2 binary64))))) (/.f64 (.f64 (.f64 t t) (.f64 (.f64 t t) #s(literal 4 binary64))) (fma.f64 l l (.f64 t (*.f64 t #s(literal -2 binary64)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) #s(literal -1 binary64))
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(.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (*.f64 l l)))))
(.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (neg.f64 (.f64 (.f64 l (.f64 l l)) (.f64 l (.f64 l l)))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 l (.f64 l (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 l l))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(.f64 (+.f64 (neg.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (.f64 l (.f64 l (.f64 l l)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (*.f64 l l)))))

eval139.0ms (0.8%)

Memory: 19.9MiB live, 130.7MiB allocated
Compiler: Compiled 33 915 to 2 339 computations (93.1% saved)

prune122.0ms (0.7%)

Memory

4.8MiB live, 246.3MiB allocated

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	541	20	561
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	542	20	562

Accuracy

89.6%

Counts

562 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	16.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
	29.3%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) (neg.f64 (.f64 l l)))))
	33.4%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 l (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (/.f64 l (+.f64 x #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
	23.3%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
	33.2%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 l (.f64 l (+.f64 x #s(literal 1 binary64)))) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
	33.9%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) l) l (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l))))))
▶	28.8%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))
	2.7%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
	50.2%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (/.f64 (-.f64 (-.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) #s(literal -2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x)) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 t t) x) (/.f64 (.f64 l l) x))) (neg.f64 x))))))
	50.0%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (+.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 t t) x) (.f64 t t)) (/.f64 (.f64 l l) x)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) x)))))
	37.2%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
	50.4%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64))))))
▶	75.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))
	73.8%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64)))))
	5.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	33.6%	(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
	5.0%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	73.9%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)))))
▶	6.3%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
▶	72.7%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))

Compiler

Compiled 1 146 to 672 computations (41.4% saved)

simplify350.0ms (1.9%)

Memory

13.0MiB live, 653.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
✓	cost-diff	704	(fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l)))
✓	cost-diff	0	(sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))
✓	cost-diff	0	(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))))
✓	cost-diff	0	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
✓	cost-diff	320	(/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))
✓	cost-diff	640	(-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
✓	cost-diff	0	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))

Rules

19 110×	`lower-fma.f32`
19 100×	`lower-fma.f64`
3 718×	`lower-*.f32`
3 698×	`lower-*.f64`
2 698×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	585
0	97	566
1	185	566
2	386	556
3	1050	546
4	3575	538
5	7959	538
0	8448	533

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
t
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))
(/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))
#s(literal 1 binary64)
(-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))
(fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t)))
l
(neg.f64 l)
(.f64 #s(literal -2 binary64) (.f64 t t))
#s(literal -2 binary64)
(*.f64 t t)
(*.f64 l l)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
(sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))
(neg.f64 l)
l
(/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))
(*.f64 t t)
(*.f64 l l)
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
(sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l))))
(fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l)))
(/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))
(*.f64 t t)
(*.f64 l l)
l
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
(neg.f64 (*.f64 l l))

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))
(sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
x
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 t t (*.f64 l l))))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 t t (*.f64 l l)))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
t
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))
(sqrt.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 t t (*.f64 l l))))
(/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))
(/.f64 #s(literal -1/2 binary64) (fma.f64 t t (*.f64 l l)))
#s(literal 1 binary64)
(-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))
(.f64 #s(literal -2 binary64) (fma.f64 t t (.f64 l l)))
(fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t)))
(-.f64 (.f64 t (.f64 t #s(literal -2 binary64))) (*.f64 l l))
l
(neg.f64 l)
(.f64 #s(literal -2 binary64) (.f64 t t))
(.f64 t (.f64 t #s(literal -2 binary64)))
#s(literal -2 binary64)
(*.f64 t t)
(*.f64 l l)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (*.f64 l l))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
(sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))
(sqrt.f64 (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (.f64 l l)))
(fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (.f64 l l))
(neg.f64 l)
l
(/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))
(*.f64 t t)
(*.f64 l l)
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (*.f64 l l))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
(sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l))))
(sqrt.f64 (-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (.f64 l l)))
(fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l)))
(-.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (.f64 l l))
(/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))
(*.f64 t t)
(*.f64 l l)
l
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
(neg.f64 (*.f64 l l))

localize204.0ms (1.1%)

Memory

-38.5MiB live, 404.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 l l)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 (*.f64 l l))
✓	accuracy	100.0%	(*.f64 l l)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 l)
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 l)
✓	accuracy	100.0%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
✓	accuracy	100.0%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))

Samples

95.0ms

256×

invalid

Compiler

Compiled 558 to 55 computations (90.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-mult: 23.0ms (35.4% of total)

ival-add: 12.0ms (18.5% of total)

ival-sqrt: 12.0ms (18.5% of total)

ival-div: 11.0ms (16.9% of total)

ival-sub: 3.0ms (4.6% of total)

ival-neg: 2.0ms (3.1% of total)

exact: 1.0ms (1.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series142.0ms (0.8%)

Memory

22.5MiB live, 175.1MiB allocated

Counts

22 → 492

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))) (patch #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (/ ( (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l)) (patch (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l))) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l)))))) (patch #s(approx (/ ( (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l))))) (patch (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l))))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))) (patch (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l))) (patch (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 t (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 t (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (neg.f64 l) (patch (neg.f64 l) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (.f64 l l)))) #<representation binary64>) () ())
#s(alt (.f64 l l) (patch (.f64 l l) #<representation binary64>) () ())
#s(alt (neg.f64 (.f64 l l)) (patch (neg.f64 (.f64 l l)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l)))) (patch (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l)))) #<representation binary64>) () ())

Outputs
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Calls

123 calls:

Time	Variable		Point	Expression
13.0ms	x	@	-inf	(+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l)))
8.0ms	x	@	0	(/ (* (sqrt 2) t) (sqrt (+ (* (neg l) l) (/ (* (+ (* 2 (* t t)) (* l l)) (+ x 1)) (+ x -1)))))
5.0ms	t	@	-inf	(/ (* (sqrt 2) t) (sqrt (+ (* (neg l) l) (/ (* (+ (* 2 (* t t)) (* l l)) (+ x 1)) (+ x -1)))))
5.0ms	l	@	0	(sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))
5.0ms	x	@	inf	(/ (* (sqrt 2) t) (sqrt (+ (* (neg l) l) (/ (* (+ (* 2 (* t t)) (* l l)) (+ x 1)) (+ x -1)))))

simplify456.0ms (2.5%)

Memory

-0.8MiB live, 666.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 494×	`lower-*.f64`
6 494×	`lower-*.f32`
4 422×	`lower-fma.f64`
4 422×	`lower-fma.f32`
2 872×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1904	43885
1	6784	42850
0	8185	39928

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

Inputs
(* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))
(* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (pow t 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* 8 (/ (pow (+ 1 x) 3) (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 4)))) (/ (* (+ 1 x) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))))
(* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))
(+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))
(+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))))
(+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/2 (* (/ (* (sqrt 2) (+ (* 1/16 (/ (* (pow (- x 1) 4) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)) (pow (+ 1 x) 4))) (* 1/8 (/ (* (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))) (* (pow (sqrt 1/2) 2) (+ 1 x)))))) (* (pow t 6) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))))
(* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))))
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(* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)))
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(* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)))
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(* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)))
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(* (pow l 2) (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1)))) (/ (pow (+ 1 x) 2) (- (pow x 2) 1))) 1))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1)))) (/ (pow (+ 1 x) 2) (- (pow x 2) 1))) 1))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1)))) (/ (pow (+ 1 x) 2) (- (pow x 2) 1))) 1))
(* (pow l 2) (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1)))) (/ (pow (+ 1 x) 2) (- (pow x 2) 1))) 1))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1)))) (/ (pow (+ 1 x) 2) (- (pow x 2) 1))) 1))
(* (pow l 2) (- (+ (* 2 (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1)))) (/ (pow (+ 1 x) 2) (- (pow x 2) 1))) 1))
(- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))
(- (+ (* -2 (* x (+ (* 2 (pow t 2)) (pow l 2)))) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (pow l 2))
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(* 2 (pow t 2))
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(* 2 (pow t 2))
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(* (/ (* (sqrt 1/2) (sqrt 2)) (+ 1 x)) (sqrt (- (pow x 2) 1)))
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(* (/ (* t (sqrt 2)) l) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))))
(/ (+ (* -1 (* (/ (* (pow t 3) (* (sqrt 2) (pow (+ 1 x) 2))) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))))) l)
(/ (+ (* -1 (* (/ (* (pow t 3) (* (sqrt 2) (pow (+ 1 x) 2))) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (+ (* -1/2 (* (/ (* t (* (sqrt 2) (+ (* -4 (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3) (pow (- (pow x 2) 1) 2)))) (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3) (pow (- (pow x 2) 1) 2)))))) (pow l 4)) (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))))) l)
(/ (+ (* -1 (* (/ (* (pow t 3) (* (sqrt 2) (pow (+ 1 x) 2))) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (+ (* -1/2 (* (/ (* t (* (sqrt 2) (+ (* -4 (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3) (pow (- (pow x 2) 1) 2)))) (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3) (pow (- (pow x 2) 1) 2)))))) (pow l 4)) (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))) (+ (* -1/2 (* (/ (* t (* (sqrt 2) (+ (* 8 (/ (* (pow t 6) (pow (+ 1 x) 6)) (* (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 4) (pow (- (pow x 2) 1) 3)))) (/ (* (pow t 2) (* (pow (+ 1 x) 2) (+ (* -4 (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3) (pow (- (pow x 2) 1) 2)))) (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3) (pow (- (pow x 2) 1) 2)))))) (* (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) (- (pow x 2) 1)))))) (pow l 6)) (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))))))) l)
(* -1 (* (/ (* t (sqrt 2)) l) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))))
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(sqrt -1)
(+ (sqrt -1) (* -1 (/ x (sqrt -1))))
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1
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(+ 1 (+ (/ 1/2 (pow x 2)) (/ 1 x)))
(+ 1 (+ (/ 1/2 (pow x 2)) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 3))))))
(pow (sqrt -1) 2)
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(* t (sqrt 2))
(* t (sqrt 2))
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(* t (sqrt 2))
(* t (sqrt 2))
(* t (sqrt 2))
(* t (sqrt 2))
(* t (sqrt 2))
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(* -1 l)
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(* -1 l)
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(* -1 l)
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(/ (sqrt -1/2) l)
(/ (+ (sqrt -1/2) (* 1/4 (/ (pow t 2) (* (pow l 2) (sqrt -1/2))))) l)
(/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* 1/16 (/ (pow t 4) (pow (sqrt -1/2) 2))) (* 1/2 (pow t 4))) (* (pow l 4) (sqrt -1/2)))) (* 1/4 (/ (pow t 2) (* (pow l 2) (sqrt -1/2)))))) l)
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(/ (sqrt -1/2) t)
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(/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* 1/64 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow (sqrt -1/2) 2))) (* 1/8 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (* (pow t 4) (sqrt -1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (pow (- (* -1 (pow l 2)) (pow l 2)) 3)) (* 1/8 (/ (* (+ (* 1/64 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow (sqrt -1/2) 2))) (* 1/8 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (- (* -1 (pow l 2)) (pow l 2))) (pow (sqrt -1/2) 2)))) (* (pow t 6) (sqrt -1/2)))) (* -1/8 (/ (- (* -1 (pow l 2)) (pow l 2)) (* (pow t 2) (sqrt -1/2))))))) t)
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(* (* t (* (sqrt 2) (+ 1 x))) (sqrt (/ 1 (- (pow x 2) 1))))
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(* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) 2) (* (pow t 4) (* (pow (sqrt 2) 3) (pow (+ 1 x) 3)))) (sqrt (pow (- (pow x 2) 1) 3)))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) (* (pow t 2) (* (sqrt 2) (+ 1 x)))) (sqrt (- (pow x 2) 1)))) (* (* (sqrt 2) (+ 1 x)) (sqrt (/ 1 (- (pow x 2) 1)))))))
(* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) 2) (* (pow t 4) (* (pow (sqrt 2) 3) (pow (+ 1 x) 3)))) (sqrt (pow (- (pow x 2) 1) 3)))) (+ (* 1/16 (* (/ (pow (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) 3) (* (pow t 6) (* (pow (sqrt 2) 5) (pow (+ 1 x) 5)))) (sqrt (pow (- (pow x 2) 1) 5)))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) (* (pow t 2) (* (sqrt 2) (+ 1 x)))) (sqrt (- (pow x 2) 1)))) (* (* (sqrt 2) (+ 1 x)) (sqrt (/ 1 (- (pow x 2) 1))))))))
(* -1 (* (* t (* (sqrt 2) (+ 1 x))) (sqrt (/ 1 (- (pow x 2) 1)))))
(* -1 (* t (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) (* (pow t 2) (* (sqrt 2) (+ 1 x)))) (sqrt (- (pow x 2) 1)))) (* (* (sqrt 2) (+ 1 x)) (sqrt (/ 1 (- (pow x 2) 1)))))))
(* -1 (* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) 2) (* (pow t 4) (* (pow (sqrt 2) 3) (pow (+ 1 x) 3)))) (sqrt (pow (- (pow x 2) 1) 3)))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) (* (pow t 2) (* (sqrt 2) (+ 1 x)))) (sqrt (- (pow x 2) 1)))) (* (* (sqrt 2) (+ 1 x)) (sqrt (/ 1 (- (pow x 2) 1))))))))
(* -1 (* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) 2) (* (pow t 4) (* (pow (sqrt 2) 3) (pow (+ 1 x) 3)))) (sqrt (pow (- (pow x 2) 1) 3)))) (+ (* 1/16 (* (/ (pow (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) 3) (* (pow t 6) (* (pow (sqrt 2) 5) (pow (+ 1 x) 5)))) (sqrt (pow (- (pow x 2) 1) 5)))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (pow (+ 1 x) 2)) (- (pow x 2) 1)) (pow l 2)) (* (pow t 2) (* (sqrt 2) (+ 1 x)))) (sqrt (- (pow x 2) 1)))) (* (* (sqrt 2) (+ 1 x)) (sqrt (/ 1 (- (pow x 2) 1)))))))))
(* (* t (* (sqrt 2) (+ 1 x))) (sqrt (/ 1 (- (pow x 2) 1))))
(+ (* 1/2 (* (/ (* (pow l 2) (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (* t (* (sqrt 2) (+ 1 x)))) (sqrt (- (pow x 2) 1)))) (* (* t (* (sqrt 2) (+ 1 x))) (sqrt (/ 1 (- (pow x 2) 1)))))
(+ (* (* t (* (sqrt 2) (+ 1 x))) (sqrt (/ 1 (- (pow x 2) 1)))) (* (pow l 2) (+ (* -1/8 (* (/ (* (pow l 2) (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 2)) (* (pow t 3) (* (pow (sqrt 2) 3) (pow (+ 1 x) 3)))) (sqrt (pow (- (pow x 2) 1) 3)))) (* 1/2 (* (/ (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) (* t (* (sqrt 2) (+ 1 x)))) (sqrt (- (pow x 2) 1)))))))
(+ (* (* t (* (sqrt 2) (+ 1 x))) (sqrt (/ 1 (- (pow x 2) 1)))) (* (pow l 2) (+ (* 1/2 (* (/ (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) (* t (* (sqrt 2) (+ 1 x)))) (sqrt (- (pow x 2) 1)))) (* (pow l 2) (+ (* -1/8 (* (/ (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 2) (* (pow t 3) (* (pow (sqrt 2) 3) (pow (+ 1 x) 3)))) (sqrt (pow (- (pow x 2) 1) 3)))) (* 1/16 (* (/ (* (pow l 2) (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3)) (* (pow t 5) (* (pow (sqrt 2) 5) (pow (+ 1 x) 5)))) (sqrt (pow (- (pow x 2) 1) 5)))))))))
(* l (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))
(* l (+ (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))))))
(* l (+ (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow l 4) (pow (- (pow x 2) 1) 2))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))))))
(* l (+ (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow l 4) (pow (- (pow x 2) 1) 2))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 6)) (* (pow l 6) (pow (- (pow x 2) 1) 3))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 5))))) (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))))))))
(* -1 (* l (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))))
(* -1 (* l (+ (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))))))
(* -1 (* l (+ (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow l 4) (pow (- (pow x 2) 1) 2))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))))))))
(* -1 (* l (+ (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow l 4) (pow (- (pow x 2) 1) 2))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 6)) (* (pow l 6) (pow (- (pow x 2) 1) 3))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 5))))) (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))))))))
(sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))
(+ (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (* -1 (* (* x (+ (* 2 (pow t 2)) (pow l 2))) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))))
(+ (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (* x (+ (* -1 (* (+ (* 2 (pow t 2)) (pow l 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))) (* 1/2 (* (* x (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (+ (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (pow l 2))))) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))))))
(+ (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (* x (+ (* -1 (* (+ (* 2 (pow t 2)) (pow l 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))) (* x (+ (* -1/2 (* (* x (+ (* -1 (/ (* (+ (* 2 (pow t 2)) (pow l 2)) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (+ (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (pow l 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))) (* 2 (+ (* 2 (pow t 2)) (pow l 2))))) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))) (* 1/2 (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (+ (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (pow l 2)))) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))))))))
(* t (sqrt 2))
(+ (* 2 (/ t (* x (sqrt 2)))) (+ (* t (sqrt 2)) (/ (pow l 2) (* t (* x (sqrt 2))))))
(+ (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* (pow x 2) (sqrt 2))))) (+ (* 2 (/ t (* x (sqrt 2)))) (+ (* t (sqrt 2)) (/ (pow l 2) (* t (* x (sqrt 2)))))))
(+ (* -1/2 (/ (+ (* -2 (+ (* 2 (pow t 2)) (pow l 2))) (/ (* (+ (* 2 (pow t 2)) (pow l 2)) (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2)))))) (* (pow t 2) (pow (sqrt 2) 2)))) (* t (* (pow x 3) (sqrt 2))))) (+ (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* (pow x 2) (sqrt 2))))) (+ (* 2 (/ t (* x (sqrt 2)))) (+ (* t (sqrt 2)) (/ (pow l 2) (* t (* x (sqrt 2))))))))
(* t (sqrt 2))
(+ (* 2 (/ t (* x (sqrt 2)))) (+ (* t (sqrt 2)) (/ (pow l 2) (* t (* x (sqrt 2))))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (* t (sqrt 2)))) (* -1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* x (sqrt 2)))))) x)) (* t (sqrt 2)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (+ (* -1 (/ (* (+ (* 2 (pow t 2)) (pow l 2)) (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2)))))) (* (pow t 2) (pow (sqrt 2) 2)))) (* 2 (+ (* 2 (pow t 2)) (pow l 2)))) (* t (* x (sqrt 2))))) (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (sqrt 2))))) x)) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (* t (sqrt 2))))) x)) (* t (sqrt 2)))

Outputs
(* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))
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(* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))
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(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))
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(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (pow t 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* 8 (/ (pow (+ 1 x) 3) (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 4)))) (/ (* (+ 1 x) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))))
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(* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))
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(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))))
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(sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))
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(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (/ (* (pow t 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))
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(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (+ (* -1/2 (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (pow (- x 1) 2)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (/ (+ 1 x) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))))
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(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (+ (* (/ (+ 1 x) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1/2 (* (/ (pow (+ 1 x) 2) (pow (- x 1) 2)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* 1/2 (* (/ (* (pow t 2) (pow (+ 1 x) 3)) (pow (- x 1) 3)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 5))))))))))
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(* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1))))
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(* t (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1))))))
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(* -1 (* l (+ (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow l 4) (pow (- (pow x 2) 1) 2))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1))))))))
(.f64 (neg.f64 l) (+.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 t #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 4 binary64))) (.f64 (pow.f64 l #s(literal 4 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))))) (.f64 (/.f64 (.f64 (.f64 t t) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 l l) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))))
(* -1 (* l (+ (sqrt (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 4)) (* (pow l 4) (pow (- (pow x 2) 1) 2))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 6)) (* (pow l 6) (pow (- (pow x 2) 1) 3))) (sqrt (/ 1 (pow (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1) 5))))) (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (* (pow l 2) (- (pow x 2) 1))) (sqrt (/ 1 (- (/ (pow (+ 1 x) 2) (- (pow x 2) 1)) 1)))))))))
(.f64 (neg.f64 l) (+.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))))) (/.f64 (.f64 (pow.f64 t #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 4 binary64))) (.f64 (pow.f64 l #s(literal 4 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 t #s(literal 6 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 6 binary64))) (.f64 (pow.f64 l #s(literal 6 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 5 binary64)))) (.f64 (/.f64 (.f64 (.f64 t t) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 l l) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))))))))
(sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))
(sqrt.f64 (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))
(+ (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (* -1 (* (* x (+ (* 2 (pow t 2)) (pow l 2))) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))))
(-.f64 (sqrt.f64 (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))) (.f64 x (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))
(+ (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (* x (+ (* -1 (* (+ (* 2 (pow t 2)) (pow l 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))) (* 1/2 (* (* x (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (+ (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (pow l 2))))) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))))))) (.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))))) (sqrt.f64 (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l))))))
(+ (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (* x (+ (* -1 (* (+ (* 2 (pow t 2)) (pow l 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))) (* x (+ (* -1/2 (* (* x (+ (* -1 (/ (* (+ (* 2 (pow t 2)) (pow l 2)) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (+ (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (pow l 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))) (* 2 (+ (* 2 (pow t 2)) (pow l 2))))) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))) (* 1/2 (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (+ (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (pow l 2)))) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))))))))
(fma.f64 x (-.f64 (.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 x (.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (/.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))))) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))))))))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))))) (sqrt.f64 (neg.f64 (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l))))))
(* t (sqrt 2))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
(+ (* 2 (/ t (* x (sqrt 2)))) (+ (* t (sqrt 2)) (/ (pow l 2) (* t (* x (sqrt 2))))))
(fma.f64 #s(literal 2 binary64) (/.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 t (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x)))))
(+ (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* (pow x 2) (sqrt 2))))) (+ (* 2 (/ t (* x (sqrt 2)))) (+ (* t (sqrt 2)) (/ (pow l 2) (* t (* x (sqrt 2)))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 (.f64 t (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 2 binary64) (/.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 t (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 l l) (.f64 t (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))))))
(+ (* -1/2 (/ (+ (* -2 (+ (* 2 (pow t 2)) (pow l 2))) (/ (* (+ (* 2 (pow t 2)) (pow l 2)) (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2)))))) (* (pow t 2) (pow (sqrt 2) 2)))) (* t (* (pow x 3) (sqrt 2))))) (+ (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* (pow x 2) (sqrt 2))))) (+ (* 2 (/ t (* x (sqrt 2)))) (+ (* t (sqrt 2)) (/ (pow l 2) (* t (* x (sqrt 2))))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 #s(literal 2 binary64) (.f64 t t))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) #s(literal -2 binary64))) (.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 (.f64 t (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 2 binary64) (/.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 t (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x)))))))
(* t (sqrt 2))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
(+ (* 2 (/ t (* x (sqrt 2)))) (+ (* t (sqrt 2)) (/ (pow l 2) (* t (* x (sqrt 2))))))
(fma.f64 #s(literal 2 binary64) (/.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 t (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 l l) (.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x)))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (* t (sqrt 2)))) (* -1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* x (sqrt 2)))))) x)) (* t (sqrt 2)))
(-.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 t (sqrt.f64 #s(literal 2 binary64))))) x))
(+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (+ (* -1 (/ (* (+ (* 2 (pow t 2)) (pow l 2)) (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2)))))) (* (pow t 2) (pow (sqrt 2) 2)))) (* 2 (+ (* 2 (pow t 2)) (pow l 2)))) (* t (* x (sqrt 2))))) (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (+ (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (/ (pow (+ (* 2 (pow t 2)) (pow l 2)) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (sqrt 2))))) x)) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (* t (sqrt 2))))) x)) (* t (sqrt 2)))
(-.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 t (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 #s(literal 2 binary64) (.f64 t t))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 t (sqrt.f64 #s(literal 2 binary64)))))) x)) x))

rewrite334.0ms (1.8%)

Memory

40.4MiB live, 470.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 906×	`lower-*.f32`
5 888×	`lower-*.f64`
4 360×	`lower-/.f32`
4 348×	`lower-/.f64`
4 122×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	387
0	97	363
1	399	353
2	3370	347
0	10002	347

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

22 → 397

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))
(/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))
(sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l)))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 l)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))
(*.f64 l l)
(neg.f64 (*.f64 l l))
(sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (.f64 l l))))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t))) #s(literal -1 binary64)))
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(pow.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l))) (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l))))) #s(literal 1/2 binary64))
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(.f64 (sqrt.f64 (fma.f64 (.f64 l l) (.f64 (.f64 l l) (.f64 l l)) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 l l)) (.f64 (.f64 l l) (*.f64 l l)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 l l) (.f64 (.f64 l l) (.f64 l l)) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 l l) (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 l l)) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 l l) (.f64 (.f64 l l) (.f64 l l)) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 l (neg.f64 l)) (-.f64 #s(literal 0 binary64) (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 l l))) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
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(.f64 (sqrt.f64 (fma.f64 (.f64 l l) (.f64 (.f64 l l) (.f64 l l)) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 l l) (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 l l)) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 l l) (.f64 l l)) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (*.f64 l l)))) #s(literal 1/2 binary64)))
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(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (.f64 l l) (.f64 l l)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (*.f64 l l))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (.f64 l l) (.f64 l l)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (*.f64 l l)))))
(.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l))) #s(literal 1/4 binary64)))

eval165.0ms (0.9%)

Memory: 8.4MiB live, 240.5MiB allocated
Compiler: Compiled 78 399 to 2 994 computations (96.2% saved)

prune211.0ms (1.2%)

Memory

7.9MiB live, 278.7MiB allocated

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	1 031	14	1 045
Fresh	10	5	15
Picked	3	2	5
Done	0	0	0
Total	1 044	21	1 065

Accuracy

91.0%

Counts

1 065 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	2.7%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
	50.2%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (-.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) #s(literal -2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) x)) x)))))
	50.0%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t))))))
✓	75.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))
▶	74.5%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
▶	75.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
▶	5.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	11.7%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	3.6%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l)))) (.f64 l (sqrt.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))
	74.9%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t))
	74.8%	(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
	74.7%	(.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))))
	33.6%	(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
	5.0%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	73.9%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)))))
	11.3%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	5.6%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
✓	72.7%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
▶	73.8%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
	19.1%	#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
	3.5%	#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (.f64 (.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))

Compiler

Compiled 931 to 591 computations (36.5% saved)

simplify321.0ms (1.8%)

Memory

-31.6MiB live, 389.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
✓	cost-diff	896	(+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
✓	cost-diff	0	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
✓	cost-diff	0	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
✓	cost-diff	128	(*.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))

Rules

13 316×	`lower-fma.f64`
13 316×	`lower-fma.f32`
3 042×	`lower-*.f32`
3 026×	`lower-*.f64`
2 046×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	605
0	85	605
1	144	605
2	239	605
3	359	605
4	607	605
5	1312	605
6	2851	605
7	5024	585
8	7758	585
0	8331	568

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))
(*.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) x)
x
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)))
(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))
(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (*.f64 l l)))
(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(-.f64 x #s(literal 1 binary64))
#s(approx (+ (* l l) (* 2 (* t t))) (*.f64 l l))
(*.f64 l l)
l
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
l
(sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))
(+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 x (+.f64 x #s(literal -1 binary64)))
x
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))
#s(literal 1 binary64)

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))
(.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))
(*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
(*.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
#s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) x)
x
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (neg.f64 (.f64 l l)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)))
(sqrt.f64 (fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (neg.f64 (.f64 l l))))
(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (neg.f64 (.f64 l l)))
(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (*.f64 l l)))
(/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ ( l l) (* 2 (* t t))) (*.f64 l l))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(-.f64 x #s(literal 1 binary64))
(+.f64 x #s(literal -1 binary64))
#s(approx (+ (* l l) (* 2 (* t t))) (*.f64 l l))
(*.f64 l l)
l
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))
l
(sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))
(+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 x (+.f64 x #s(literal -1 binary64)))
x
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))
#s(literal 1 binary64)

localize287.0ms (1.6%)

Memory

13.5MiB live, 361.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
✓	accuracy	99.6%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	accuracy	69.0%	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))))
✓	accuracy	47.6%	(+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
✓	accuracy	99.6%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	accuracy	77.5%	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)))
✓	accuracy	74.9%	(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))
✓	accuracy	74.5%	#s(approx (+ (* l l) (* 2 (* t t))) (*.f64 l l))
✓	accuracy	99.6%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	accuracy	99.6%	(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	98.5%	#s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	75.1%	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
✓	accuracy	74.4%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
✓	accuracy	99.9%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
✓	accuracy	99.6%	(.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))
✓	accuracy	99.6%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	accuracy	75.1%	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))

Samples

97.0ms	85×	1	valid
40.0ms	55×	2	valid
34.0ms	60×	1	invalid
28.0ms	39×	2	invalid
3.0ms	10×	0	valid
2.0ms	7×	0	invalid

Compiler

Compiled 473 to 39 computations (91.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-div: 25.0ms (23.6% of total)

ival-mult: 22.0ms (20.8% of total)

adjust: 19.0ms (18% of total)

ival-add: 18.0ms (17% of total)

ival-sqrt: 16.0ms (15.1% of total)

ival-sub: 5.0ms (4.7% of total)

exact: 1.0ms (0.9% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series70.0ms (0.4%)

Memory

-5.1MiB live, 110.7MiB allocated

Counts

19 → 492

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64)) (patch #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))) (patch #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))) (patch (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))) #<representation binary64>) () ())
#s(alt (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))) (patch (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))) (patch #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))) #<representation binary64>) () ())
#s(alt (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))) (patch (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 t (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 t (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (patch #s(approx (+ ( l l) (* 2 (* t t))) (*.f64 l l)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)) (patch (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))) (patch #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))) (patch (.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))) #<representation binary64>) () ())

Outputs
#s(alt -2 (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* -4 x) 2) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (- (* -4 x) 4)) 2) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (- (* x (- (* -4 x) 4)) 4)) 2) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* 4 (/ 1 x))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2)))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (+ (* 4 (/ 1 x)) (+ (* 4 (/ 1 (pow x 3))) (/ 4 (pow x 2))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* 4 (/ 1 x))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2)))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* -1 (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 x))) x)) 4) x))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (patch (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (taylor 0 t) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))) (taylor 0 t) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) #<representation binary64>) () ())) ())
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#s(alt (+ (* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x))) (+ (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 3)))) (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 5)))))) (taylor -inf x) (#s(alt (.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))) (patch (.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1 (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt x))) (* -1/2 (* (/ (* l (* (sqrt -1) (- 2 (* -1 (/ x (pow (sqrt -2) 2)))))) (sqrt -2)) (sqrt (/ 1 x))))) (pow x 3))) (+ (* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x))) (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 3)))))) (taylor -inf x) (#s(alt (.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))) (patch (.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())

Calls

123 calls:

Time	Variable		Point	Expression
8.0ms	l	@	inf	(* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1))))
3.0ms	t	@	0	(* t (sqrt (* 2 (/ (+ x 1) (+ x -1)))))
1.0ms	l	@	0	(* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1))))
1.0ms	x	@	-inf	(* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1))))
1.0ms	x	@	inf	(* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1))))

simplify665.0ms (3.6%)

Memory

19.6MiB live, 922.6MiB allocated

Algorithm

1×	egg-herbie

Rules

9 702×	`lower-fma.f64`
9 702×	`lower-fma.f32`
8 866×	`lower-*.f64`
8 866×	`lower-*.f32`
5 214×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	936	44150
1	3121	39080
0	9573	37446

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

Inputs
-2
(- (* -4 x) 2)
(- (* x (- (* -4 x) 4)) 2)
(- (* x (- (* x (- (* -4 x) 4)) 4)) 2)
2
(+ 2 (* 4 (/ 1 x)))
(+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2))))
(+ 2 (+ (* 4 (/ 1 x)) (+ (* 4 (/ 1 (pow x 3))) (/ 4 (pow x 2)))))
2
(+ 2 (* 4 (/ 1 x)))
(+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2))))
(+ 2 (* -1 (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 x))) x)) 4) x)))
(* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))
(* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (pow t 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* 8 (/ (pow (+ 1 x) 3) (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 4)))) (/ (* (+ 1 x) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))))
(* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))
(+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))
(+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))))
(+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/2 (* (/ (* (sqrt 2) (+ (* 1/16 (/ (* (pow (- x 1) 4) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)) (pow (+ 1 x) 4))) (* 1/8 (/ (* (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))) (* (pow (sqrt 1/2) 2) (+ 1 x)))))) (* (pow t 6) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))))
(* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (+ (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* 1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1)))))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (+ (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (* 1/2 (* (/ (* (sqrt 2) (+ (* 1/16 (/ (* (pow (- x 1) 4) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)) (pow (+ 1 x) 4))) (* 1/8 (/ (* (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))) (* (pow (sqrt 1/2) 2) (+ 1 x)))))) (* (pow t 6) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))))))
(* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))
(+ (* 1/2 (* (* t (* x (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))
(+ (* x (+ (* 1/2 (* (* t (* x (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* 1/4 (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) (pow (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))) 2))) (/ (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))) (* 1/2 (* (* t (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))
(+ (* x (+ (* 1/2 (* (* t (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))) (* x (+ (* 1/2 (* (* t (* x (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* 1/2 (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) (* (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* 1/4 (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) (pow (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))) 2))) (/ (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))))) (+ (/ (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))) (/ (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))) (* 1/2 (* (* t (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* 1/4 (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) (pow (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))) 2))) (/ (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1/8 (/ (* (sqrt 2) (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* (pow t 2) (* x (sqrt 1/2))))) (* (sqrt 1/2) (sqrt 2)))
(+ (* -1/2 (/ (* (pow t 2) (* (sqrt 2) (+ (* -1/8 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (pow t 6))) (+ (* 1/64 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 6) (pow (sqrt 1/2) 2)))) (* 1/4 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (pow t 4))))))) (* (pow x 2) (sqrt 1/2)))) (+ (* -1/8 (/ (* (sqrt 2) (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* (pow t 2) (* x (sqrt 1/2))))) (* (sqrt 1/2) (sqrt 2))))
(+ (* -1/2 (/ (* (pow t 2) (* (sqrt 2) (+ (* -1/2 (/ (* (+ (* -1/8 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (pow t 6))) (* 1/4 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (pow t 4)))) (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (pow t 2))) (+ (* -1/8 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (pow t 6))) (+ (* 1/8 (/ (* (+ (* -1/8 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (pow t 6))) (+ (* 1/64 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 6) (pow (sqrt 1/2) 2)))) (* 1/4 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (pow t 4))))) (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* (pow t 2) (pow (sqrt 1/2) 2)))) (* 1/4 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (pow t 4)))))))) (* (pow x 3) (sqrt 1/2)))) (+ (* -1/2 (/ (* (pow t 2) (* (sqrt 2) (+ (* -1/8 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (pow t 6))) (+ (* 1/64 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 6) (pow (sqrt 1/2) 2)))) (* 1/4 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (pow t 4))))))) (* (pow x 2) (sqrt 1/2)))) (+ (* -1/8 (/ (* (sqrt 2) (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* (pow t 2) (* x (sqrt 1/2))))) (* (sqrt 1/2) (sqrt 2)))))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1/8 (/ (* (sqrt 2) (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* (pow t 2) (* x (sqrt 1/2))))) (* (sqrt 1/2) (sqrt 2)))
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1
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(* t (sqrt 2))
(+ (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (* t (* x (sqrt 2))))) (* t (sqrt 2)))
(+ (* -1/2 (/ (+ (* -1 (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* 1/4 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (* t (* x (sqrt 2))))) (* t (sqrt 2))))
(+ (* -1/2 (/ (+ (* -1 (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* -1/2 (/ (* (+ (* -1 (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* 1/4 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* (pow x 3) (sqrt 2))))) (+ (* -1/2 (/ (+ (* -1 (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* 1/4 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* (pow x 2) (sqrt 2))))) (+ (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (* t (* x (sqrt 2))))) (* t (sqrt 2)))))
(* t (sqrt 2))
(+ (* 1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (* t (* x (sqrt 2))))) (* t (sqrt 2)))
(+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2)))) (* 1/4 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* x (sqrt 2))))) (* -1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (* t (sqrt 2))))) x)) (* t (sqrt 2)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1 (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* -1/2 (/ (* (- (* -1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2)))) (* 1/4 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2))))) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (* x (sqrt 2))))) (* 1/2 (/ (- (* -1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2)))) (* 1/4 (/ (pow (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) 2) (* (pow t 2) (pow (sqrt 2) 2))))) (* t (sqrt 2))))) x)) (* -1/2 (/ (- (+ (* 2 (pow t 2)) (pow l 2)) (* -1 (+ (* 2 (pow t 2)) (pow l 2)))) (* t (sqrt 2))))) x)) (* t (sqrt 2)))
(* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1))))
(+ (* 1/2 (* (/ (* (pow l 2) (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* t (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1)))))
(+ (* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1)))) (* (pow l 2) (+ (* -1/8 (* (/ (* (pow l 2) (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 2)) (* (pow t 3) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* 1/2 (* (/ (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) (* t (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))))))
(+ (* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1)))) (* (pow l 2) (+ (* 1/2 (* (/ (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) (* t (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (pow l 2) (+ (* -1/8 (* (/ (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 2) (* (pow t 3) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* 1/16 (* (/ (* (pow l 2) (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3)) (* (pow t 5) (pow (sqrt 2) 5))) (sqrt (/ (pow (- x 1) 5) (pow (+ 1 x) 5))))))))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))
(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
(* -1 (* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))
(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))))
(sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))
(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (/ (* (pow t 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))
(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (+ (* -1/2 (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (pow (- x 1) 2)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (/ (+ 1 x) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))))
(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (+ (* (/ (+ 1 x) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1/2 (* (/ (pow (+ 1 x) 2) (pow (- x 1) 2)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* 1/2 (* (/ (* (pow t 2) (pow (+ 1 x) 3)) (pow (- x 1) 3)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 5))))))))))
(* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1))))
(* t (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1))))))
(* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2) (* (pow t 4) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1)))))))
(* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2) (* (pow t 4) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/16 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3) (* (pow t 6) (pow (sqrt 2) 5))) (sqrt (/ (pow (- x 1) 5) (pow (+ 1 x) 5))))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1))))))))
(* -1 (* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1)))))
(* -1 (* t (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1)))))))
(* -1 (* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2) (* (pow t 4) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1))))))))
(* -1 (* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2) (* (pow t 4) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/16 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3) (* (pow t 6) (pow (sqrt 2) 5))) (sqrt (/ (pow (- x 1) 5) (pow (+ 1 x) 5))))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1)))))))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(* l (sqrt -2))
(+ (* -1 (/ (* l x) (sqrt -2))) (* l (sqrt -2)))
(+ (* l (sqrt -2)) (* x (+ (* -1 (/ l (sqrt -2))) (* -1/2 (/ (* l (* x (+ 2 (/ 1 (pow (sqrt -2) 2))))) (sqrt -2))))))
(+ (* l (sqrt -2)) (* x (+ (* -1 (/ l (sqrt -2))) (* x (+ (* -1/2 (/ (* l (* x (+ 2 (+ (* 2 (/ 1 (pow (sqrt -2) 2))) (/ 1 (pow (sqrt -2) 4)))))) (sqrt -2))) (* -1/2 (/ (* l (+ 2 (/ 1 (pow (sqrt -2) 2)))) (sqrt -2))))))))
(* (* l (sqrt 2)) (sqrt (/ 1 x)))
(+ (* (* l (sqrt 2)) (sqrt (/ 1 x))) (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 3)))))
(+ (* (* l (sqrt 2)) (sqrt (/ 1 x))) (+ (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 3)))) (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 5))))))
(+ (* 1/2 (* (/ (* l (- 2 (/ x (pow (sqrt 2) 2)))) (sqrt 2)) (sqrt (/ 1 (pow x 7))))) (+ (* (* l (sqrt 2)) (sqrt (/ 1 x))) (+ (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 3)))) (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 5)))))))
(* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x)))
(+ (* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x))) (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 3)))))
(+ (* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x))) (+ (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 3)))) (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 5))))))
(+ (* -1 (/ (+ (* -1 (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt x))) (* -1/2 (* (/ (* l (* (sqrt -1) (- 2 (* -1 (/ x (pow (sqrt -2) 2)))))) (sqrt -2)) (sqrt (/ 1 x))))) (pow x 3))) (+ (* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x))) (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 3))))))

Outputs
-2
#s(literal -2 binary64)
(- (* -4 x) 2)
(fma.f64 #s(literal -4 binary64) x #s(literal -2 binary64))
(- (* x (- (* -4 x) 4)) 2)
(fma.f64 x (fma.f64 #s(literal -4 binary64) x #s(literal -4 binary64)) #s(literal -2 binary64))
(- (* x (- (* x (- (* -4 x) 4)) 4)) 2)
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -4 binary64) x #s(literal -4 binary64)) #s(literal -4 binary64)) #s(literal -2 binary64))
2
#s(literal 2 binary64)
(+ 2 (* 4 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x))
(+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2))))
(+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 #s(literal 4 binary64) (*.f64 x x))))
(+ 2 (+ (* 4 (/ 1 x)) (+ (* 4 (/ 1 (pow x 3))) (/ 4 (pow x 2)))))
(+.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 #s(literal 4 binary64) (.f64 x x)))) (/.f64 #s(literal 4 binary64) (.f64 x (*.f64 x x))))
2
#s(literal 2 binary64)
(+ 2 (* 4 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x))
(+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2))))
(+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 #s(literal 4 binary64) (*.f64 x x))))
(+ 2 (* -1 (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 x))) x)) 4) x)))
(-.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 4 binary64) (/.f64 #s(literal 4 binary64) x)) (neg.f64 x)) #s(literal -4 binary64)) x))
(* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (*.f64 l l)))))
(* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))
(.f64 t (fma.f64 (.f64 (.f64 t t) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (*.f64 l l)))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))
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(* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))))
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(* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))))
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(* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1))))
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(* t (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1))))))
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(* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2) (* (pow t 4) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1)))))))
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(* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2) (* (pow t 4) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/16 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3) (* (pow t 6) (pow (sqrt 2) 5))) (sqrt (/ (pow (- x 1) 5) (pow (+ 1 x) 5))))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1))))))))
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(* -1 (* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1)))))
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(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) (/.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 t t)))))) (neg.f64 t))
(* -1 (* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2) (* (pow t 4) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1))))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 t t))) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l))) (.f64 (pow.f64 t #s(literal 4 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))))) (neg.f64 t))
(* -1 (* t (+ (* -1/8 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2) (* (pow t 4) (pow (sqrt 2) 3))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/16 (* (/ (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3) (* (pow t 6) (pow (sqrt 2) 5))) (sqrt (/ (pow (- x 1) 5) (pow (+ 1 x) 5))))) (+ (* 1/2 (* (/ (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) (* (pow t 2) (sqrt 2))) (sqrt (/ (- x 1) (+ 1 x))))) (* (sqrt 2) (sqrt (/ (+ 1 x) (- x 1)))))))))
(.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 5 binary64)))) (/.f64 (.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)))) (.f64 (pow.f64 t #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 t t))) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (/.f64 (.f64 (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l)) (-.f64 (.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l l))) (.f64 (pow.f64 t #s(literal 4 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))))))) (neg.f64 t))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(* l (sqrt -2))
(*.f64 l (sqrt.f64 #s(literal -2 binary64)))
(+ (* -1 (/ (* l x) (sqrt -2))) (* l (sqrt -2)))
(-.f64 (.f64 l (sqrt.f64 #s(literal -2 binary64))) (/.f64 (.f64 x l) (sqrt.f64 #s(literal -2 binary64))))
(+ (* l (sqrt -2)) (* x (+ (* -1 (/ l (sqrt -2))) (* -1/2 (/ (* l (* x (+ 2 (/ 1 (pow (sqrt -2) 2))))) (sqrt -2))))))
(fma.f64 x (-.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 x l) #s(literal 3/2 binary64))) (sqrt.f64 #s(literal -2 binary64))) (/.f64 l (sqrt.f64 #s(literal -2 binary64)))) (.f64 l (sqrt.f64 #s(literal -2 binary64))))
(+ (* l (sqrt -2)) (* x (+ (* -1 (/ l (sqrt -2))) (* x (+ (* -1/2 (/ (* l (* x (+ 2 (+ (* 2 (/ 1 (pow (sqrt -2) 2))) (/ 1 (pow (sqrt -2) 4)))))) (sqrt -2))) (* -1/2 (/ (* l (+ 2 (/ 1 (pow (sqrt -2) 2)))) (sqrt -2))))))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 l (+.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -2 binary64)) #s(literal 4 binary64))))) (sqrt.f64 #s(literal -2 binary64))) (/.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal -2 binary64)))))) (neg.f64 (/.f64 l (sqrt.f64 #s(literal -2 binary64))))) (.f64 l (sqrt.f64 #s(literal -2 binary64))))
(* (* l (sqrt 2)) (sqrt (/ 1 x)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* (* l (sqrt 2)) (sqrt (/ 1 x))) (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 3)))))
(fma.f64 (/.f64 l (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* (* l (sqrt 2)) (sqrt (/ 1 x))) (+ (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 3)))) (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 5))))))
(fma.f64 (/.f64 l (sqrt.f64 #s(literal 2 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* 1/2 (* (/ (* l (- 2 (/ x (pow (sqrt 2) 2)))) (sqrt 2)) (sqrt (/ 1 (pow x 7))))) (+ (* (* l (sqrt 2)) (sqrt (/ 1 x))) (+ (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 3)))) (* (/ l (sqrt 2)) (sqrt (/ 1 (pow x 5)))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 l (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 l (sqrt.f64 #s(literal 2 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (*.f64 l (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x))) (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 3)))))
(fma.f64 l (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 l (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64)))))
(+ (* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x))) (+ (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 3)))) (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 5))))))
(fma.f64 (/.f64 (.f64 l (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 l (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
(+ (* -1 (/ (+ (* -1 (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt x))) (* -1/2 (* (/ (* l (* (sqrt -1) (- 2 (* -1 (/ x (pow (sqrt -2) 2)))))) (sqrt -2)) (sqrt (/ 1 x))))) (pow x 3))) (+ (* (* l (* (sqrt -2) (sqrt -1))) (sqrt (/ 1 x))) (* (/ (* l (sqrt -1)) (sqrt -2)) (sqrt (/ 1 (pow x 3))))))
(-.f64 (fma.f64 l (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 l (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 (.f64 l (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)))) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 l (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)) (sqrt.f64 #s(literal -2 binary64))))) (.f64 x (*.f64 x x))))

rewrite388.0ms (2.1%)

Memory

8.6MiB live, 519.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 196×	`lower-*.f32`
6 180×	`lower-*.f64`
4 910×	`lower-/.f32`
4 894×	`lower-/.f64`
3 156×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	445
0	85	445
1	322	429
2	2491	427
0	10291	412

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

19 → 316

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l)))
(+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))
#s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* l l) (* 2 (* t t))) (*.f64 l l))
(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))))
(*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))

Outputs
(/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 2 binary64)))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 2 binary64))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) t))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (neg.f64 #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(neg.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) t)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) t)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) t))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
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(/.f64 (neg.f64 (-.f64 (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l (.f64 l (.f64 l l))))) (neg.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))))) (fma.f64 (.f64 l l) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))))) (.f64 (fma.f64 (.f64 l l) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (.f64 (.f64 l l) (.f64 l (.f64 l (.f64 l l)))))) (.f64 (fma.f64 (.f64 l l) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (fma.f64 (.f64 l l) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l))) (.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (.f64 l (.f64 l (.f64 l l))))) (.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l))))
(pow.f64 (/.f64 (fma.f64 (.f64 l l) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (-.f64 (.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))))) (.f64 (.f64 l l) (.f64 l (.f64 l (.f64 l l)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (-.f64 (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l (.f64 l (*.f64 l l))))) #s(literal -1 binary64))
(.f64 (-.f64 (.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (.f64 #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))))) (.f64 (.f64 l l) (.f64 l (.f64 l (.f64 l l))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 l l) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l)) (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(.f64 (-.f64 (/.f64 (.f64 (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l)))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 l (.f64 l (.f64 l l)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(approx (+ ( l l) (* 2 (* t t))) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (.f64 l l))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))) l)

eval162.0ms (0.9%)

Memory: 29.6MiB live, 252.4MiB allocated
Compiler: Compiled 67 411 to 2 358 computations (96.5% saved)

prune111.0ms (0.6%)

Memory

-2.6MiB live, 236.9MiB allocated

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	868	10	878
Fresh	10	4	14
Picked	3	2	5
Done	1	1	2
Total	882	17	899

Accuracy

99.9%

Counts

899 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.0%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t))))))
▶	75.0%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
	74.5%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 #s(approx ( 2 (/ (+ x 1) (+ x -1))) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x)))))))
	7.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
	4.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (+.f64 x #s(literal -1 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) x)) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64))))))))
✓	5.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	26.6%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))
	26.6%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
	74.4%	(.f64 (/.f64 t #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))) (sqrt.f64 #s(literal 2 binary64)))
▶	74.8%	(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
	5.1%	(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
▶	33.6%	(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
	5.0%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
▶	73.9%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
▶	5.6%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
✓	72.7%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
✓	73.8%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))

Compiler

Compiled 679 to 426 computations (37.3% saved)

simplify352.0ms (1.9%)

Memory

-38.3MiB live, 428.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))))
✓	cost-diff	0	(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l))))
✓	cost-diff	0	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
✓	cost-diff	0	(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
✓	cost-diff	0	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))))
✓	cost-diff	0	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
✓	cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
✓	cost-diff	512	(/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))

Rules

11 050×	`lower-fma.f32`
11 044×	`lower-fma.f64`
3 794×	`lower-*.f32`
3 774×	`lower-*.f64`
1 822×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	646
0	101	644
1	171	640
2	293	622
3	506	614
4	1014	606
5	2761	606
6	5623	606
0	8332	599

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
(*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
t
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))
#s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))
(/.f64 #s(literal -1/2 binary64) (*.f64 l l))
#s(literal -1/2 binary64)
(*.f64 l l)
l
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
t
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))
(*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))
(fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))
x
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
t
(sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))))
(/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l))))
#s(literal 2 binary64)
(fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))
(fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))
(*.f64 t t)
(*.f64 l l)
l
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(neg.f64 (*.f64 l l))

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
t
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))
(*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
(*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
t
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))
#s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))
(/.f64 #s(literal -1/2 binary64) (*.f64 l l))
#s(literal -1/2 binary64)
(*.f64 l l)
l
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
t
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))
(*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))
(fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))
x
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(.f64 t (sqrt.f64 (/.f64 #s(literal -2 binary64) (fma.f64 l l (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))))))
t
(sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))))
(sqrt.f64 (/.f64 #s(literal -2 binary64) (fma.f64 l l (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l))))
(/.f64 #s(literal -2 binary64) (fma.f64 l l (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))))
#s(literal 2 binary64)
(fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))
(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l))
(fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))
(*.f64 t t)
(*.f64 l l)
l
(/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
(neg.f64 (*.f64 l l))

localize261.0ms (1.4%)

Memory

27.3MiB live, 376.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 t t)
✓	accuracy	100.0%	(*.f64 l l)
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))))
✓	accuracy	100.0%	(neg.f64 (*.f64 l l))
✓	accuracy	100.0%	(*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
✓	accuracy	100.0%	#s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))
✓	accuracy	100.0%	(*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))

Samples

157.0ms

256×

invalid

Compiler

Compiled 537 to 58 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 128.0ms

ival-mult: 58.0ms (45.4% of total)

ival-div: 42.0ms (32.9% of total)

ival-sqrt: 13.0ms (10.2% of total)

ival-add: 8.0ms (6.3% of total)

ival-sub: 3.0ms (2.3% of total)

ival-neg: 2.0ms (1.6% of total)

exact: 1.0ms (0.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series106.0ms (0.6%)

Memory

-1.3MiB live, 196.1MiB allocated

Counts

29 → 636

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (.f64 l l)))))) (patch #s(approx (/ ( (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (.f64 l l))))) (patch (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ ( l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))) #<representation binary64>) () ())
#s(alt (.f64 t (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 t (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (patch #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (patch (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
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#s(alt #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))) (patch #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l)))) (patch (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l)))) #<representation binary64>) () ())
#s(alt (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l)))))) (patch (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l)))))) #<representation binary64>) () ())
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#s(alt (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))) (patch (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))) #<representation binary64>) () ())
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#s(alt (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (patch (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (patch (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (.f64 l l))) (patch #s(approx (/ 1 (- (+ ( l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))) #<representation binary64>) () ())
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#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ())
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#s(alt (.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))) (patch (.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))) #<representation binary64>) () ())
#s(alt (neg.f64 (.f64 l l)) (patch (neg.f64 (.f64 l l)) #<representation binary64>) () ())
#s(alt (.f64 l l) (patch (.f64 l l) #<representation binary64>) () ())
#s(alt (.f64 t t) (patch (.f64 t t) #<representation binary64>) () ())

Outputs
#s(alt -2 (taylor 0 x) (#s(alt (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))) (taylor 0 t) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))))) (taylor 0 t) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (pow t 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* 8 (/ (pow (+ 1 x) 3) (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 4)))) (/ (* (+ 1 x) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))))))) (taylor 0 t) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))) (taylor inf t) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (taylor inf t) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))) (taylor inf t) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (pow l 2)) (taylor 0 l) (#s(alt (neg.f64 (.f64 l l)) (patch (neg.f64 (.f64 l l)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow l 2)) (taylor inf l) (#s(alt (neg.f64 (.f64 l l)) (patch (neg.f64 (.f64 l l)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow l 2)) (taylor inf l) (#s(alt (neg.f64 (.f64 l l)) (patch (neg.f64 (.f64 l l)) #<representation binary64>) () ())) ())
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#s(alt (pow t 2) (taylor -inf t) (#s(alt (.f64 t t) (patch (.f64 t t) #<representation binary64>) () ())) ())

Calls

159 calls:

Time	Variable		Point	Expression
6.0ms	l	@	0	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
4.0ms	x	@	0	(sqrt (/ (+ (* 2 x) 2) (+ x -1)))
1.0ms	x	@	0	(/ (sqrt 2) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
1.0ms	x	@	inf	(/ (sqrt 2) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
1.0ms	l	@	0	(/ (sqrt 2) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

simplify711.0ms (3.9%)

Memory

17.5MiB live, 968.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 224×	`lower-*.f64`
7 224×	`lower-*.f32`
5 950×	`lower-fma.f64`
5 950×	`lower-fma.f32`
4 378×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1663	56587
1	5565	54953
0	8984	51866

Stop Event

1×	iter limit
1×	node limit

Counts

636 → 636

Calls

Call 1

Inputs
-2
(- (* -4 x) 2)
(- (* x (- (* -4 x) 4)) 2)
(- (* x (- (* x (- (* -4 x) 4)) 4)) 2)
2
(+ 2 (* 4 (/ 1 x)))
(+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2))))
(+ 2 (+ (* 4 (/ 1 x)) (+ (* 4 (/ 1 (pow x 3))) (/ 4 (pow x 2)))))
2
(+ 2 (* 4 (/ 1 x)))
(+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2))))
(+ 2 (* -1 (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 x))) x)) 4) x)))
(* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))
(* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (pow t 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* 8 (/ (pow (+ 1 x) 3) (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 4)))) (/ (* (+ 1 x) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))))
(* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))
(+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))
(+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))))
(+ (* -1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/2 (* (/ (* (sqrt 2) (+ (* 1/16 (/ (* (pow (- x 1) 4) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)) (pow (+ 1 x) 4))) (* 1/8 (/ (* (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))) (* (pow (sqrt 1/2) 2) (+ 1 x)))))) (* (pow t 6) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (+ (* -1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))))
(* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x)))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (+ (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (* 1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1)))))))
(+ (* -1 (* (* (sqrt 1/2) (sqrt 2)) (sqrt (/ (- x 1) (+ 1 x))))) (+ (* 1/8 (* (/ (* (sqrt 2) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (sqrt 1/2))) (sqrt (/ (pow (- x 1) 3) (pow (+ 1 x) 3))))) (+ (* 1/2 (* (/ (* (sqrt 2) (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3)))))) (* (pow t 4) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))) (* 1/2 (* (/ (* (sqrt 2) (+ (* 1/16 (/ (* (pow (- x 1) 4) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)) (pow (+ 1 x) 4))) (* 1/8 (/ (* (+ (* -1/8 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (pow (+ 1 x) 3))) (* 1/64 (/ (* (pow (- x 1) 3) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 2)) (* (pow (sqrt 1/2) 2) (pow (+ 1 x) 3))))) (* (- x 1) (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))) (* (pow (sqrt 1/2) 2) (+ 1 x)))))) (* (pow t 6) (sqrt 1/2))) (sqrt (/ (+ 1 x) (- x 1))))))))
(* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)))))
(+ (* 1/2 (* (* t (* x (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))
(+ (* x (+ (* 1/2 (* (* t (* x (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (+ (* 1/4 (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) (pow (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))) 2))) (/ (* (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (+ (* 2 (pow t 2)) (pow l 2))) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))))) (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))) (* 1/2 (* (* t (* (sqrt 2) (- (+ (* 2 (/ (pow t 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (/ (pow l 2) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2))) (* -1 (/ (+ (* 2 (pow t 2)) (pow l 2)) (pow (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2)) 2)))))) (sqrt (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))) (* (* t (sqrt 2)) (sqrt (/ 1 (- (* -1 (+ (* 2 (pow t 2)) (pow l 2))) (pow l 2))))))
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(* (pow (sqrt -1) 2) (* (sqrt 1/2) (sqrt 2)))
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(sqrt 2)
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(* t (* (sqrt -1) (sqrt 2)))
(+ (* -1 (/ (* t (* x (sqrt 2))) (sqrt -1))) (* t (* (sqrt -1) (sqrt 2))))
(+ (* t (* (sqrt -1) (sqrt 2))) (* x (+ (* -1 (/ (* t (sqrt 2)) (sqrt -1))) (* -1/2 (/ (* t (* x (* (sqrt 2) (+ 2 (/ 1 (pow (sqrt -1) 2)))))) (sqrt -1))))))
(+ (* t (* (sqrt -1) (sqrt 2))) (* x (+ (* -1 (/ (* t (sqrt 2)) (sqrt -1))) (* x (+ (* -1/2 (/ (* t (* x (* (sqrt 2) (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4))))))) (sqrt -1))) (* -1/2 (/ (* t (* (sqrt 2) (+ 2 (/ 1 (pow (sqrt -1) 2))))) (sqrt -1))))))))
(* t (sqrt 2))
(+ (* t (sqrt 2)) (/ (* t (sqrt 2)) x))
(+ (* 1/2 (/ (* t (sqrt 2)) (pow x 2))) (+ (* t (sqrt 2)) (/ (* t (sqrt 2)) x)))
(+ (* 1/2 (/ (* t (sqrt 2)) (pow x 2))) (+ (* 1/2 (/ (* t (sqrt 2)) (pow x 3))) (+ (* t (sqrt 2)) (/ (* t (sqrt 2)) x))))
(* t (* (sqrt -2) (sqrt -1)))
(+ (* -1 (/ (* t (sqrt -2)) (* x (sqrt -1)))) (* t (* (sqrt -2) (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (/ (* t (* (sqrt -2) (+ 2 (/ 1 (pow (sqrt -1) 2))))) (* x (sqrt -1)))) (/ (* t (sqrt -2)) (sqrt -1))) x)) (* t (* (sqrt -2) (sqrt -1))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* t (* (sqrt -2) (+ 2 (/ 1 (pow (sqrt -1) 2))))) (sqrt -1))) (* -1/2 (/ (* t (* (sqrt -2) (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))))) (* x (sqrt -1))))) x)) (/ (* t (sqrt -2)) (sqrt -1))) x)) (* t (* (sqrt -2) (sqrt -1))))
(/ -1/2 (pow t 2))
(- (* 1/2 (/ (pow l 2) (pow t 4))) (* 1/2 (/ 1 (pow t 2))))
(- (* (pow l 2) (+ (* -1/2 (/ (pow l 2) (pow t 6))) (* 1/2 (/ 1 (pow t 4))))) (* 1/2 (/ 1 (pow t 2))))
(- (* (pow l 2) (+ (* (pow l 2) (- (* 1/2 (/ (pow l 2) (pow t 8))) (* 1/2 (/ 1 (pow t 6))))) (* 1/2 (/ 1 (pow t 4))))) (* 1/2 (/ 1 (pow t 2))))
(/ -1/2 (pow l 2))
(/ (- (* 1/2 (/ (pow t 2) (pow l 2))) 1/2) (pow l 2))
(/ (- (* -1/2 (/ (pow t 4) (pow l 4))) (+ 1/2 (* -1/2 (/ (pow t 2) (pow l 2))))) (pow l 2))
(/ (- (* 1/2 (/ (pow t 6) (pow l 6))) (+ 1/2 (+ (* -1/2 (/ (pow t 2) (pow l 2))) (* 1/2 (/ (pow t 4) (pow l 4)))))) (pow l 2))
(/ -1/2 (pow l 2))
(/ (- (* 1/2 (/ (pow t 2) (pow l 2))) 1/2) (pow l 2))
(/ (- (* -1/2 (/ (pow t 4) (pow l 4))) (+ 1/2 (* -1/2 (/ (pow t 2) (pow l 2))))) (pow l 2))
(/ (- (* 1/2 (/ (pow t 6) (pow l 6))) (+ 1/2 (+ (* -1/2 (/ (pow t 2) (pow l 2))) (* 1/2 (/ (pow t 4) (pow l 4)))))) (pow l 2))
(/ 1 (- (* -1 (pow l 2)) (pow l 2)))
(+ (* 2 (/ (pow t 2) (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (/ 1 (- (* -1 (pow l 2)) (pow l 2))))
(+ (* (pow t 2) (+ (* 4 (/ (pow t 2) (pow (- (* -1 (pow l 2)) (pow l 2)) 3))) (* 2 (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))))) (/ 1 (- (* -1 (pow l 2)) (pow l 2))))
(+ (* (pow t 2) (+ (* (pow t 2) (+ (* 8 (/ (pow t 2) (pow (- (* -1 (pow l 2)) (pow l 2)) 4))) (* 4 (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 3))))) (* 2 (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))))) (/ 1 (- (* -1 (pow l 2)) (pow l 2))))
(/ -1/2 (pow t 2))
(/ (- (* -1/4 (/ (- (* -1 (pow l 2)) (pow l 2)) (pow t 2))) 1/2) (pow t 2))
(/ (- (* -1/8 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow t 4))) (+ 1/2 (* 1/4 (/ (- (* -1 (pow l 2)) (pow l 2)) (pow t 2))))) (pow t 2))
(/ (- (* -1/16 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 3) (pow t 6))) (+ 1/2 (+ (* 1/8 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow t 4))) (* 1/4 (/ (- (* -1 (pow l 2)) (pow l 2)) (pow t 2)))))) (pow t 2))
(/ -1/2 (pow t 2))
(/ (- (* -1/4 (/ (- (* -1 (pow l 2)) (pow l 2)) (pow t 2))) 1/2) (pow t 2))
(/ (- (* -1/8 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow t 4))) (+ 1/2 (* 1/4 (/ (- (* -1 (pow l 2)) (pow l 2)) (pow t 2))))) (pow t 2))
(/ (- (* -1/16 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 3) (pow t 6))) (+ 1/2 (+ (* 1/8 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow t 4))) (* 1/4 (/ (- (* -1 (pow l 2)) (pow l 2)) (pow t 2)))))) (pow t 2))
(/ (sqrt -1/2) t)
(+ (* 1/4 (/ (pow l 2) (* (pow t 3) (sqrt -1/2)))) (/ (sqrt -1/2) t))
(+ (* (pow l 2) (+ (* -1/2 (/ (* (pow l 2) (* t (+ (* 1/16 (/ 1 (* (pow t 6) (pow (sqrt -1/2) 2)))) (* 1/2 (/ 1 (pow t 6)))))) (sqrt -1/2))) (* 1/4 (/ 1 (* (pow t 3) (sqrt -1/2)))))) (/ (sqrt -1/2) t))
(+ (* (pow l 2) (+ (* (pow l 2) (+ (* -1/2 (/ (* t (+ (* 1/16 (/ 1 (* (pow t 6) (pow (sqrt -1/2) 2)))) (* 1/2 (/ 1 (pow t 6))))) (sqrt -1/2))) (* 1/2 (/ (* (pow l 2) (* t (- (* 1/2 (/ 1 (pow t 8))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow t 6) (pow (sqrt -1/2) 2)))) (* 1/2 (/ 1 (pow t 6)))) (* (pow t 2) (pow (sqrt -1/2) 2))))))) (sqrt -1/2))))) (* 1/4 (/ 1 (* (pow t 3) (sqrt -1/2)))))) (/ (sqrt -1/2) t))
(/ (sqrt -1/2) l)
(/ (+ (sqrt -1/2) (* 1/4 (/ (pow t 2) (* (pow l 2) (sqrt -1/2))))) l)
(/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* 1/16 (/ (pow t 4) (pow (sqrt -1/2) 2))) (* 1/2 (pow t 4))) (* (pow l 4) (sqrt -1/2)))) (* 1/4 (/ (pow t 2) (* (pow l 2) (sqrt -1/2)))))) l)
(/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* -1/2 (pow t 6)) (* -1/4 (/ (* (pow t 2) (+ (* 1/16 (/ (pow t 4) (pow (sqrt -1/2) 2))) (* 1/2 (pow t 4)))) (pow (sqrt -1/2) 2)))) (* (pow l 6) (sqrt -1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (/ (pow t 4) (pow (sqrt -1/2) 2))) (* 1/2 (pow t 4))) (* (pow l 4) (sqrt -1/2)))) (* 1/4 (/ (pow t 2) (* (pow l 2) (sqrt -1/2))))))) l)
(* -1 (/ (sqrt -1/2) l))
(* -1 (/ (+ (sqrt -1/2) (* 1/4 (/ (pow t 2) (* (pow l 2) (sqrt -1/2))))) l))
(* -1 (/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* 1/16 (/ (pow t 4) (pow (sqrt -1/2) 2))) (* 1/2 (pow t 4))) (* (pow l 4) (sqrt -1/2)))) (* 1/4 (/ (pow t 2) (* (pow l 2) (sqrt -1/2)))))) l))
(* -1 (/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* -1/2 (pow t 6)) (* -1/4 (/ (* (pow t 2) (+ (* 1/16 (/ (pow t 4) (pow (sqrt -1/2) 2))) (* 1/2 (pow t 4)))) (pow (sqrt -1/2) 2)))) (* (pow l 6) (sqrt -1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (/ (pow t 4) (pow (sqrt -1/2) 2))) (* 1/2 (pow t 4))) (* (pow l 4) (sqrt -1/2)))) (* 1/4 (/ (pow t 2) (* (pow l 2) (sqrt -1/2))))))) l))
(sqrt (/ 1 (- (* -1 (pow l 2)) (pow l 2))))
(+ (sqrt (/ 1 (- (* -1 (pow l 2)) (pow l 2)))) (* (pow t 2) (sqrt (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 3)))))
(+ (sqrt (/ 1 (- (* -1 (pow l 2)) (pow l 2)))) (* (pow t 2) (+ (sqrt (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 3))) (* 3/2 (* (pow t 2) (sqrt (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 5))))))))
(+ (sqrt (/ 1 (- (* -1 (pow l 2)) (pow l 2)))) (* (pow t 2) (+ (sqrt (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 3))) (* (pow t 2) (+ (* 3/2 (sqrt (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 5)))) (* 5/2 (* (pow t 2) (sqrt (/ 1 (pow (- (* -1 (pow l 2)) (pow l 2)) 7))))))))))
(/ (sqrt -1/2) t)
(/ (+ (sqrt -1/2) (* -1/8 (/ (- (* -1 (pow l 2)) (pow l 2)) (* (pow t 2) (sqrt -1/2))))) t)
(/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* 1/64 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow (sqrt -1/2) 2))) (* 1/8 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (* (pow t 4) (sqrt -1/2)))) (* -1/8 (/ (- (* -1 (pow l 2)) (pow l 2)) (* (pow t 2) (sqrt -1/2)))))) t)
(/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* 1/64 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow (sqrt -1/2) 2))) (* 1/8 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (* (pow t 4) (sqrt -1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (pow (- (* -1 (pow l 2)) (pow l 2)) 3)) (* 1/8 (/ (* (+ (* 1/64 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow (sqrt -1/2) 2))) (* 1/8 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (- (* -1 (pow l 2)) (pow l 2))) (pow (sqrt -1/2) 2)))) (* (pow t 6) (sqrt -1/2)))) (* -1/8 (/ (- (* -1 (pow l 2)) (pow l 2)) (* (pow t 2) (sqrt -1/2))))))) t)
(* -1 (/ (sqrt -1/2) t))
(* -1 (/ (+ (sqrt -1/2) (* -1/8 (/ (- (* -1 (pow l 2)) (pow l 2)) (* (pow t 2) (sqrt -1/2))))) t))
(* -1 (/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* 1/64 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow (sqrt -1/2) 2))) (* 1/8 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (* (pow t 4) (sqrt -1/2)))) (* -1/8 (/ (- (* -1 (pow l 2)) (pow l 2)) (* (pow t 2) (sqrt -1/2)))))) t))
(* -1 (/ (+ (sqrt -1/2) (+ (* -1/2 (/ (+ (* 1/64 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow (sqrt -1/2) 2))) (* 1/8 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (* (pow t 4) (sqrt -1/2)))) (+ (* -1/2 (/ (+ (* 1/16 (pow (- (* -1 (pow l 2)) (pow l 2)) 3)) (* 1/8 (/ (* (+ (* 1/64 (/ (pow (- (* -1 (pow l 2)) (pow l 2)) 2) (pow (sqrt -1/2) 2))) (* 1/8 (pow (- (* -1 (pow l 2)) (pow l 2)) 2))) (- (* -1 (pow l 2)) (pow l 2))) (pow (sqrt -1/2) 2)))) (* (pow t 6) (sqrt -1/2)))) (* -1/8 (/ (- (* -1 (pow l 2)) (pow l 2)) (* (pow t 2) (sqrt -1/2))))))) t))
(sqrt -1)
(+ (sqrt -1) (/ x (sqrt -1)))
(+ (sqrt -1) (* x (+ (* -1/2 (/ (* x (+ 2 (/ 1 (pow (sqrt -1) 2)))) (sqrt -1))) (/ 1 (sqrt -1)))))
(+ (sqrt -1) (* x (+ (* x (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (* x (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2))))) (sqrt -1))))) (/ 1 (sqrt -1)))))
1
(- 1 (/ 1 x))
(- (+ 1 (/ 1/2 (pow x 2))) (/ 1 x))
(- (+ 1 (/ 1/2 (pow x 2))) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 3)))))
(pow (sqrt -1) 2)
(+ (/ 1 x) (pow (sqrt -1) 2))
(+ (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) x)) 1) x)) (pow (sqrt -1) 2))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1/2 (+ 2 (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) x))) x)) 1) x)) (pow (sqrt -1) 2))
(sqrt -2)
(+ (sqrt -2) (* -2 (/ x (sqrt -2))))
(+ (sqrt -2) (* x (- (* -1/2 (/ (* x (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2))))) (sqrt -2))) (* 2 (/ 1 (sqrt -2))))))
(+ (sqrt -2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 4 (* 2 (/ (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))) (pow (sqrt -2) 2))))) (sqrt -2))) (* -1/2 (/ (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))) (sqrt -2))))) (* 2 (/ 1 (sqrt -2))))))
(sqrt 2)
(+ (sqrt 2) (* 2 (/ 1 (* x (sqrt 2)))))
(+ (sqrt 2) (+ (* 1/2 (/ (- 4 (* 4 (/ 1 (pow (sqrt 2) 2)))) (* (pow x 2) (sqrt 2)))) (/ 2 (* x (sqrt 2)))))
(+ (sqrt 2) (+ (* 1/2 (/ (- 4 (* 2 (/ (- 4 (* 4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))) (* (pow x 3) (sqrt 2)))) (+ (* 1/2 (/ (- 4 (* 4 (/ 1 (pow (sqrt 2) 2)))) (* (pow x 2) (sqrt 2)))) (/ 2 (* x (sqrt 2))))))
(* (sqrt -2) (sqrt -1))
(+ (* -2 (/ (sqrt -1) (* x (sqrt -2)))) (* (sqrt -2) (sqrt -1)))
(+ (* -1 (/ (+ (* 1/2 (/ (* (sqrt -1) (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2))))) (* x (sqrt -2)))) (* 2 (/ (sqrt -1) (sqrt -2)))) x)) (* (sqrt -2) (sqrt -1)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (sqrt -1) (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2))))) (sqrt -2))) (* -1/2 (/ (* (sqrt -1) (- 4 (* -2 (/ (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))) (pow (sqrt -2) 2))))) (* x (sqrt -2))))) x)) (* 2 (/ (sqrt -1) (sqrt -2)))) x)) (* (sqrt -2) (sqrt -1)))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt (/ (+ 2 (* 2 x)) (- x 1))))
(* t (sqrt -2))
(+ (* -2 (/ (* t x) (sqrt -2))) (* t (sqrt -2)))
(+ (* t (sqrt -2)) (* x (+ (* -2 (/ t (sqrt -2))) (* -1/2 (/ (* t (* x (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))))) (sqrt -2))))))
(+ (* t (sqrt -2)) (* x (+ (* -2 (/ t (sqrt -2))) (* x (+ (* -1/2 (/ (* t (* x (+ 4 (* 2 (/ (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))) (pow (sqrt -2) 2)))))) (sqrt -2))) (* -1/2 (/ (* t (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2))))) (sqrt -2))))))))
(* t (sqrt 2))
(+ (* 2 (/ t (* x (sqrt 2)))) (* t (sqrt 2)))
(+ (* 1/2 (/ (* t (- 4 (* 4 (/ 1 (pow (sqrt 2) 2))))) (* (pow x 2) (sqrt 2)))) (+ (* 2 (/ t (* x (sqrt 2)))) (* t (sqrt 2))))
(+ (* 1/2 (/ (* t (- 4 (* 2 (/ (- 4 (* 4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (pow x 3) (sqrt 2)))) (+ (* 1/2 (/ (* t (- 4 (* 4 (/ 1 (pow (sqrt 2) 2))))) (* (pow x 2) (sqrt 2)))) (+ (* 2 (/ t (* x (sqrt 2)))) (* t (sqrt 2)))))
(* t (* (sqrt -2) (sqrt -1)))
(+ (* -2 (/ (* t (sqrt -1)) (* x (sqrt -2)))) (* t (* (sqrt -2) (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (/ (* t (* (sqrt -1) (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))))) (* x (sqrt -2)))) (* 2 (/ (* t (sqrt -1)) (sqrt -2)))) x)) (* t (* (sqrt -2) (sqrt -1))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* t (* (sqrt -1) (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))))) (sqrt -2))) (* -1/2 (/ (* t (* (sqrt -1) (- 4 (* -2 (/ (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))) (pow (sqrt -2) 2)))))) (* x (sqrt -2))))) x)) (* 2 (/ (* t (sqrt -1)) (sqrt -2)))) x)) (* t (* (sqrt -2) (sqrt -1))))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(* -1 (pow l 2))
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow l 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)
(pow t 2)

Outputs
-2
#s(literal -2 binary64)
(- (* -4 x) 2)
(fma.f64 #s(literal -4 binary64) x #s(literal -2 binary64))
(- (* x (- (* -4 x) 4)) 2)
(fma.f64 x (fma.f64 #s(literal -4 binary64) x #s(literal -4 binary64)) #s(literal -2 binary64))
(- (* x (- (* x (- (* -4 x) 4)) 4)) 2)
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -4 binary64) x #s(literal -4 binary64)) #s(literal -4 binary64)) #s(literal -2 binary64))
2
#s(literal 2 binary64)
(+ 2 (* 4 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x))
(+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2))))
(+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 #s(literal 4 binary64) (*.f64 x x))))
(+ 2 (+ (* 4 (/ 1 x)) (+ (* 4 (/ 1 (pow x 3))) (/ 4 (pow x 2)))))
(+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x)) (+.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 4 binary64) (.f64 x (*.f64 x x)))))
2
#s(literal 2 binary64)
(+ 2 (* 4 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x))
(+ 2 (+ (* 4 (/ 1 x)) (/ 4 (pow x 2))))
(+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 4 binary64) x) (/.f64 #s(literal 4 binary64) (*.f64 x x))))
(+ 2 (* -1 (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 x))) x)) 4) x)))
(-.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 4 binary64) (/.f64 #s(literal 4 binary64) x)) (neg.f64 x)) #s(literal -4 binary64)) x))
(* (* t (sqrt 2)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 l (neg.f64 l))))))
(* t (+ (* -1 (* (/ (* (pow t 2) (* (sqrt 2) (+ 1 x))) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))
(.f64 t (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 l (neg.f64 l)))))) (.f64 (.f64 (.f64 t t) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 l (neg.f64 l))) (.f64 (fma.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 l (neg.f64 l))) (fma.f64 (.f64 l l) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (.f64 l (neg.f64 l))))))))))
(* t (+ (* (sqrt 2) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1 (* (/ (* (sqrt 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* -1/2 (* (* (pow t 2) (* (sqrt 2) (+ (* -4 (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))) (/ (pow (+ 1 x) 2) (* (pow (- x 1) 2) (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3)))))) (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))
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(* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1))))))))
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(* -1 (* l (+ (sqrt (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)) (+ (* -1/2 (* (/ (* (pow t 4) (pow (+ 1 x) 2)) (* (pow l 4) (pow (- x 1) 2))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 3))))) (+ (* 1/2 (* (/ (* (pow t 6) (pow (+ 1 x) 3)) (* (pow l 6) (pow (- x 1) 3))) (sqrt (/ 1 (pow (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1) 5))))) (* (/ (* (pow t 2) (+ 1 x)) (* (pow l 2) (- x 1))) (sqrt (/ 1 (- (+ (/ 1 (- x 1)) (/ x (- x 1))) 1)))))))))
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(sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)))
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(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (/ (* (pow t 2) (+ 1 x)) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))
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(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (+ (* -1/2 (* (/ (* (pow t 2) (pow (+ 1 x) 2)) (pow (- x 1) 2)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* (/ (+ 1 x) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))))))
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(+ (sqrt (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))) (* (pow t 2) (+ (* (/ (+ 1 x) (- x 1)) (sqrt (/ 1 (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2))))) (* (pow t 2) (+ (* -1/2 (* (/ (pow (+ 1 x) 2) (pow (- x 1) 2)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 3))))) (* 1/2 (* (/ (* (pow t 2) (pow (+ 1 x) 3)) (pow (- x 1) 3)) (sqrt (/ 1 (pow (- (/ (* (pow l 2) (+ 1 x)) (- x 1)) (pow l 2)) 5))))))))))
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(* (* t (sqrt 2)) (sqrt (/ (+ 1 x) (- x 1))))
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(.f64 (.f64 t (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -2 (/ (* t (sqrt -1)) (* x (sqrt -2)))) (* t (* (sqrt -2) (sqrt -1))))
(fma.f64 (.f64 t (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 t (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (sqrt.f64 #s(literal -2 binary64)))))
(+ (* -1 (/ (+ (* 1/2 (/ (* t (* (sqrt -1) (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))))) (* x (sqrt -2)))) (* 2 (/ (* t (sqrt -1)) (sqrt -2)))) x)) (* t (* (sqrt -2) (sqrt -1))))
(-.f64 (.f64 (.f64 t (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 t (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (sqrt.f64 #s(literal -2 binary64)))) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 t (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -2 binary64)))) x))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* t (* (sqrt -1) (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))))) (sqrt -2))) (* -1/2 (/ (* t (* (sqrt -1) (- 4 (* -2 (/ (+ 4 (* 4 (/ 1 (pow (sqrt -2) 2)))) (pow (sqrt -2) 2)))))) (* x (sqrt -2))))) x)) (* 2 (/ (* t (sqrt -1)) (sqrt -2)))) x)) (* t (* (sqrt -2) (sqrt -1))))
(-.f64 (.f64 (.f64 t (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 t (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 t (/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) (/.f64 (.f64 t (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (sqrt.f64 #s(literal -2 binary64)))))) x)) x))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(* -1 (pow l 2))
(*.f64 l (neg.f64 l))
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow l 2)
(*.f64 l l)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)
(pow t 2)
(*.f64 t t)

rewrite390.0ms (2.1%)

Memory

9.6MiB live, 596.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 548×	`lower-/.f32`
4 532×	`lower-/.f64`
4 314×	`lower-*.f32`
4 294×	`lower-*.f64`
3 488×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	65	546
0	101	530
1	375	515
2	2587	515
0	8751	515

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

29 → 663

Calls

Call 1

Inputs
(/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
(.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))))
(*.f64 t (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))
(/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l))))
(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))))
(fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l)))
#s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
#s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l)))
(sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))
(*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))
(neg.f64 (*.f64 l l))
(*.f64 l l)
(*.f64 t t)

Outputs
(+.f64 (.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) x) (.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) x))
(+.f64 (.f64 x (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64)))))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64)))) (.f64 x (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))) #s(literal -1 binary64)))
(fma.f64 x (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 x (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) x (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(fma.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) x))
(neg.f64 (/.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64)))))))
(/.f64 #s(literal -2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 2 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (*.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (.f64 #s(literal 2 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 x)))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (neg.f64 (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 2 binary64))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (neg.f64 x)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (neg.f64 #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))))))
(neg.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t)) (neg.f64 #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t))) (neg.f64 (neg.f64 #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))))))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(literal 1 binary64)) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t)))) (neg.f64 (neg.f64 (neg.f64 #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))))))
(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(literal 1 binary64))) (neg.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))))
(pow.f64 (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t)) #s(literal 1 binary64)) #s(literal -1 binary64))
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(/.f64 (-.f64 #s(literal 0 binary64) (.f64 l (.f64 l (.f64 l l)))) (+.f64 #s(literal 0 binary64) (.f64 l l)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 l l) (.f64 l (.f64 l (.f64 l l)))))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 l (.f64 l (.f64 l l)) (.f64 #s(literal 0 binary64) (*.f64 l l))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 l (.f64 l (.f64 l l))))) (neg.f64 (+.f64 #s(literal 0 binary64) (.f64 l l))))
(.f64 #s(literal -1 binary64) (.f64 l l))
(*.f64 l (neg.f64 l))
(*.f64 (neg.f64 l) l)
(.f64 (.f64 l l) #s(literal -1 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 l)))
(pow.f64 l #s(literal 2 binary64))
(pow.f64 (neg.f64 l) #s(literal 2 binary64))
(pow.f64 (*.f64 l l) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 l)) #s(literal 2 binary64))
(*.f64 l l)
(*.f64 (neg.f64 l) (neg.f64 l))
(*.f64 (exp.f64 (log.f64 l)) (exp.f64 (log.f64 l)))
(exp.f64 (*.f64 (log.f64 t) #s(literal 2 binary64)))
(pow.f64 t #s(literal 2 binary64))
(pow.f64 (*.f64 t t) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 t)) #s(literal 2 binary64))
(*.f64 t t)
(*.f64 (exp.f64 (log.f64 t)) (exp.f64 (log.f64 t)))

eval361.0ms (2%)

Memory: -27.1MiB live, 413.9MiB allocated
Compiler: Compiled 104 604 to 4 584 computations (95.6% saved)

prune258.0ms (1.4%)

Memory

7.0MiB live, 501.8MiB allocated

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	1 349	11	1 360
Fresh	2	7	9
Picked	5	0	5
Done	0	3	3
Total	1 356	21	1 377

Accuracy

99.9%

Counts

1 377 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.0%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t))))))
	7.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
	4.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (+.f64 x #s(literal -1 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) x)) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64))))))))
✓	5.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	26.6%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))
	26.6%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
	25.2%	(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (/.f64 (*.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))) t) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))))
	73.5%	(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64))))))
	5.1%	(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
	49.4%	(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) #s(approx (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l))) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 t t) x) (fma.f64 #s(literal 2 binary64) (.f64 t t) (/.f64 (.f64 l l) x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) x))))))
	1.8%	(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (fma.f64 x (fma.f64 x (neg.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))))) (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))) (.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)) (.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l))))) (/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))) (.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)))))) (.f64 #s(literal -2 binary64) (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))))) (.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)))))) (/.f64 #s(literal 2 binary64) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))))
	26.1%	(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 t t))))))
	36.5%	(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 #s(literal 1 binary64) (*.f64 t t)))))
	5.0%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
	73.4%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(approx (sqrt (/ (+ x -1) (+ x 1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))))
	20.8%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
	33.5%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
	5.6%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))) t))
✓	72.7%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
	75.1%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
✓	73.8%	#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))

Compiler

Compiled 1 960 to 545 computations (72.2% saved)

regimes146.0ms (0.8%)

Memory

23.0MiB live, 176.4MiB allocated

Counts

56 → 4

Calls

Call 1

Inputs
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 #s(literal 1 binary64) (*.f64 t t)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))) t))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 t t))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(approx (sqrt (/ (+ x -1) (+ x 1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 #s(approx ( 2 (/ (+ x 1) (+ x -1))) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 t #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (/.f64 (*.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))) t) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l)))) (.f64 l (sqrt.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) (neg.f64 (.f64 l l)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (.f64 (.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) l) l (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l))))))
(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) #s(approx (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l))) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 t t) x) (fma.f64 #s(literal 2 binary64) (.f64 t t) (/.f64 (.f64 l l) x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 l (.f64 l (+.f64 x #s(literal 1 binary64)))) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (+.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 t t) x) (.f64 t t)) (/.f64 (.f64 l l) x)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) x)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 l (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (/.f64 l (+.f64 x #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (-.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (-.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) #s(literal -2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))) x)) x)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) (+.f64 x #s(literal -1 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) x)) (.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (fma.f64 #s(literal 2 binary64) (.f64 t t) (/.f64 (-.f64 (-.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) #s(literal -2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x)) (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 t t) x) (/.f64 (.f64 l l) x))) (neg.f64 x))))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (fma.f64 x (fma.f64 x (neg.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))))) (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))) (.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)) (.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l))))) (/.f64 (.f64 #s(literal 2 binary64) (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)))))) (.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)))))) (.f64 #s(literal -2 binary64) (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (fma.f64 l l (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))))) (.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 l l)))))) (/.f64 #s(literal 2 binary64) (-.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (*.f64 l l)))))))

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) #s(approx (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l))) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 t t) x) (fma.f64 #s(literal 2 binary64) (.f64 t t) (/.f64 (.f64 l l) x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (*.f64 l l)) x))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))

Calls

6 calls:

49.0ms	(*.f64 l l)
29.0ms	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
19.0ms	l
17.0ms	t
15.0ms	x

Results

Accuracy	Segments	Branch
75.1%	1	`x`
82.2%	2	`l`
85.7%	4	`t`
81.8%	2	`(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))`
76.9%	2	`(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))`
82.2%	2	`(*.f64 l l)`

Compiler

Compiled 58 to 38 computations (34.5% saved)

regimes18.0ms (0.1%)

Memory

-2.4MiB live, 35.4MiB allocated

Counts

48 → 4

Calls

Call 1

Inputs
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 #s(literal 1 binary64) (*.f64 t t)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))) t))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 t t))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(approx (sqrt (/ (+ x -1) (+ x 1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 #s(approx ( 2 (/ (+ x 1) (+ x -1))) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 t #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (/.f64 (*.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))) t) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l)))) (.f64 l (sqrt.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) (neg.f64 (.f64 l l)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (.f64 (.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) l) l (fma.f64 (.f64 #s(literal 2 binary64) (.f64 t t)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (*.f64 l l))))))

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))

Calls

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
85.6%	4	`t`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes33.0ms (0.2%)

Memory

-1.8MiB live, 72.2MiB allocated

Counts

46 → 2

Calls

Call 1

Inputs
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 #s(literal 1 binary64) (*.f64 t t)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))) t))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 t t))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(approx (sqrt (/ (+ x -1) (+ x 1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 #s(approx ( 2 (/ (+ x 1) (+ x -1))) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 t #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(.f64 t (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) t))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (/.f64 (*.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))) t) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(approx (+ (* l l) (* 2 (* t t))) (.f64 l l))) (.f64 l l))))
(.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 l l))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l)))) (.f64 l (sqrt.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (neg.f64 l) l (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) (neg.f64 (.f64 l l)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (.f64 (.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) l)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 l l)))))

Outputs

#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))

Calls

2 calls:

15.0ms	t
15.0ms	l

Results

Accuracy	Segments	Branch
82.2%	2	`l`
84.3%	4	`t`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes15.0ms (0.1%)

Memory

-17.5MiB live, 23.9MiB allocated

Counts

26 → 2

Calls

Call 1

Inputs
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 #s(literal 1 binary64) (*.f64 t t)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))) t))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 t t))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(approx (sqrt (/ (+ x -1) (+ x 1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 #s(approx ( 2 (/ (+ x 1) (+ x -1))) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) x)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (+ (* (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 t #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (/ (+ 1 x) (+ x -1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 t (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)) (.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) (+.f64 x #s(literal -1 binary64)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 l (neg.f64 l) (.f64 #s(literal -2 binary64) (.f64 t t))) (*.f64 l l))))))

Outputs

#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x))))))

Calls

1 calls:

14.0ms

Results

Accuracy	Segments	Branch
82.2%	2	`l`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes21.0ms (0.1%)

Memory

11.3MiB live, 48.2MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 #s(literal 1 binary64) (*.f64 t t)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))) t))
(.f64 t (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 t (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(.f64 t (sqrt.f64 #s(approx (/ 2 (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 t t))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(approx (sqrt (/ (+ x -1) (+ x 1))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ 1 (- (+ (* l (neg l)) (* -2 (* t t))) (* l l))) (/.f64 #s(literal -1/2 binary64) (*.f64 l l))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))

Outputs
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))

Calls

5 calls:

6.0ms	t
4.0ms	l
4.0ms	(*.f64 l l)
4.0ms	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
3.0ms	(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
75.1%	1	`(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))`
75.1%	1	`t`
75.1%	1	`(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))`
75.1%	1	`(*.f64 l l)`
75.1%	1	`l`

Compiler

Compiled 54 to 35 computations (35.2% saved)

regimes12.0ms (0.1%)

Memory

-9.2MiB live, 27.8MiB allocated

Accuracy

Total -0.7b remaining (-4.2%)

Threshold costs -0.7b (-4.2%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))

#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))

Outputs
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))

Calls

6 calls:

4.0ms	l
2.0ms	x
1.0ms	t
1.0ms	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
1.0ms	(*.f64 l l)

Results

Accuracy	Segments	Branch
73.8%	1	`l`
73.8%	1	`x`
73.8%	1	`(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))`
73.8%	1	`(*.f64 l l)`
73.8%	1	`t`
73.8%	1	`(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))`

Compiler

Compiled 58 to 38 computations (34.5% saved)

bsearch102.0ms (0.6%)

Memory

29.7MiB live, 194.2MiB allocated

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	9.182490601333325e-10	1.0463697092788113e-8
44.0ms	9.033363430310456e-160	4.748970704696029e-154
30.0ms	4.837590714817483e-236	2.9976424023159728e-235

Samples

34.0ms	182×	1	valid
24.0ms	57×	1	invalid
13.0ms	136×	0	valid
5.0ms	18×	2	valid
2.0ms	6×	2	invalid
0.0ms	2×	0	invalid

Compiler

Compiled 1 278 to 660 computations (48.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-div: 17.0ms (27.4% of total)

ival-mult: 13.0ms (20.9% of total)

ival-sqrt: 10.0ms (16.1% of total)

adjust: 8.0ms (12.9% of total)

ival-add: 7.0ms (11.3% of total)

ival-sub: 6.0ms (9.7% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

bsearch66.0ms (0.4%)

Memory

-32.9MiB live, 121.5MiB allocated

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
22.0ms	4.9655736467148416e-18	5.788471857830709e-16
31.0ms	9.033363430310456e-160	4.748970704696029e-154
1.0ms	4.837590714817483e-236	2.9976424023159728e-235

Samples

23.0ms	113×	1	valid
14.0ms	125×	0	valid
3.0ms	18×	1	invalid
1.0ms	5×	2	invalid
1.0ms	2×	2	valid
0.0ms	3×	0	invalid

Compiler

Compiled 1 153 to 655 computations (43.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 10.0ms (29.8% of total)

ival-div: 7.0ms (20.8% of total)

ival-sub: 4.0ms (11.9% of total)

adjust: 4.0ms (11.9% of total)

ival-sqrt: 4.0ms (11.9% of total)

ival-add: 4.0ms (11.9% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

bsearch13.0ms (0.1%)

Memory

18.4MiB live, 18.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	2.2931486868361526e+163	3.057466846714075e+163

Samples

5.0ms	30×	1	valid
2.0ms	18×	0	valid
2.0ms	9×	1	invalid
0.0ms	2×	0	invalid

Compiler

Compiled 132 to 93 computations (29.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 2.0ms (29.7% of total)

ival-div: 1.0ms (14.8% of total)

adjust: 1.0ms (14.8% of total)

ival-add: 1.0ms (14.8% of total)

ival-sub: 1.0ms (14.8% of total)

ival-sqrt: 1.0ms (14.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	2.2931486868361526e+163	3.057466846714075e+163

Compiler

Compiled 123 to 87 computations (29.3% saved)

simplify10.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
8×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	648
1	120	648

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 t #s(literal 6300558862064491/114555615673899844817675135734699353962886956688682610117765798809244256021411616637381137063298513501717438036875998880297587443028293506801780104166258318482051497231916848409067205045915915104980160032926980989903722214426950334461435148425897181184 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))) (if (<=.f64 t #s(literal 2264377454892925/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64)))))) (if (<=.f64 t #s(literal 4835703278458517/604462909807314587353088 binary64)) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) #s(approx (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l))) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 t t) x) (fma.f64 #s(literal 2 binary64) (.f64 t t) (/.f64 (.f64 l l) x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x)))))) #s(approx (/ ( (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(if (<=.f64 t #s(literal 6300558862064491/114555615673899844817675135734699353962886956688682610117765798809244256021411616637381137063298513501717438036875998880297587443028293506801780104166258318482051497231916848409067205045915915104980160032926980989903722214426950334461435148425897181184 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))) (if (<=.f64 t #s(literal 5255771031303471/15458150092069033378781407563727949377195709318825739994628941005806076569158241698144775066327690311849854464126008708709460314644171950622971634693868322994787923259293696 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64)))))) (if (<=.f64 t #s(literal 8924260225606735/324518553658426726783156020576256 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t)))))) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(if (<=.f64 l #s(literal 27500000000000000688376226690882964028456114365723342412755819754571704979097582560839021580091180428104836592363924708334602596322774240437527544512695778764914688 binary64)) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 l #s(literal 27500000000000000688376226690882964028456114365723342412755819754571704979097582560839021580091180428104836592363924708334602596322774240437527544512695778764914688 binary64)) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))

Outputs
(if (<=.f64 t #s(literal 6300558862064491/114555615673899844817675135734699353962886956688682610117765798809244256021411616637381137063298513501717438036875998880297587443028293506801780104166258318482051497231916848409067205045915915104980160032926980989903722214426950334461435148425897181184 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))) (if (<=.f64 t #s(literal 2264377454892925/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64)))))) (if (<=.f64 t #s(literal 4835703278458517/604462909807314587353088 binary64)) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) #s(approx (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l))) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 t t) x) (fma.f64 #s(literal 2 binary64) (.f64 t t) (/.f64 (.f64 l l) x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x)))))) #s(approx (/ ( (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(if (<=.f64 t #s(literal 6300558862064491/114555615673899844817675135734699353962886956688682610117765798809244256021411616637381137063298513501717438036875998880297587443028293506801780104166258318482051497231916848409067205045915915104980160032926980989903722214426950334461435148425897181184 binary64)) (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))) (if (<=.f64 t #s(literal 2264377454892925/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64)))))) (if (<=.f64 t #s(literal 4835703278458517/604462909807314587353088 binary64)) (.f64 t (sqrt.f64 (/.f64 #s(literal 2 binary64) #s(approx (+ ( (+ (* 2 (* t t)) (* l l)) (/ (+ x 1) (+ x -1))) (neg (* l l))) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (.f64 t t) x) (fma.f64 #s(literal 2 binary64) (.f64 t t) (/.f64 (.f64 l l) x))) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x)))))) #s(approx (/ ( (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(if (<=.f64 t #s(literal 6300558862064491/114555615673899844817675135734699353962886956688682610117765798809244256021411616637381137063298513501717438036875998880297587443028293506801780104166258318482051497231916848409067205045915915104980160032926980989903722214426950334461435148425897181184 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))) (if (<=.f64 t #s(literal 5255771031303471/15458150092069033378781407563727949377195709318825739994628941005806076569158241698144775066327690311849854464126008708709460314644171950622971634693868322994787923259293696 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64)))))) (if (<=.f64 t #s(literal 8924260225606735/324518553658426726783156020576256 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x) (.f64 t t)))))) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(if (<=.f64 t #s(literal 6300558862064491/114555615673899844817675135734699353962886956688682610117765798809244256021411616637381137063298513501717438036875998880297587443028293506801780104166258318482051497231916848409067205045915915104980160032926980989903722214426950334461435148425897181184 binary64)) (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))) (if (<=.f64 t #s(literal 5255771031303471/15458150092069033378781407563727949377195709318825739994628941005806076569158241698144775066327690311849854464126008708709460314644171950622971634693868322994787923259293696 binary64)) (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l))) (.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 t (sqrt.f64 #s(literal 2 binary64)))))) (if (<=.f64 t #s(literal 8924260225606735/324518553658426726783156020576256 binary64)) (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(approx (+ ( (/ (+ (* 2 (* t t)) (* l l)) (+ (* x x) -1)) (* (+ x 1) (+ x 1))) (neg (* l l))) (.f64 #s(literal 2 binary64) (+.f64 (.f64 t t) (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 t t) (.f64 l l)) x)))))) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))))))
(if (<=.f64 l #s(literal 27500000000000000688376226690882964028456114365723342412755819754571704979097582560839021580091180428104836592363924708334602596322774240437527544512695778764914688 binary64)) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 l #s(literal 27500000000000000688376226690882964028456114365723342412755819754571704979097582560839021580091180428104836592363924708334602596322774240437527544512695778764914688 binary64)) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) #s(approx (* l (sqrt (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 l #s(literal 27500000000000000688376226690882964028456114365723342412755819754571704979097582560839021580091180428104836592363924708334602596322774240437527544512695778764914688 binary64)) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))))
(if (<=.f64 l #s(literal 27500000000000000688376226690882964028456114365723342412755819754571704979097582560839021580091180428104836592363924708334602596322774240437527544512695778764914688 binary64)) #s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (- ( (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (*.f64 l (sqrt.f64 #s(approx (+ (/ x (+ x -1)) (+ (/ 1 (+ x -1)) -1)) (/.f64 #s(literal 2 binary64) x)))))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) #s(literal 1 binary64))

soundness1.5s (8.4%)

Memory

7.0MiB live, 1 401.3MiB allocated

Rules

13 380×	`lower-fma.f64`
13 380×	`lower-fma.f32`
10 416×	`lower-fma.f64`
10 416×	`lower-fma.f32`
9 702×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	387
0	97	363
1	399	353
2	3370	347
0	10002	347
0	18	85
0	31	85
1	116	85
2	928	84
0	8797	80
0	1904	43885
1	6784	42850
0	8185	39928
0	65	546
0	101	530
1	375	515
2	2587	515
0	8751	515
0	1663	56587
1	5565	54953
0	8984	51866
0	936	44150
1	3121	39080
0	9573	37446
0	676	10349
1	2332	9162
0	8701	8754

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 857 to 499 computations (41.8% saved)

preprocess427.0ms (2.3%)

Memory: -146.8MiB live, 265.6MiB allocated
Compiler: Compiled 964 to 334 computations (65.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze320.0ms (1.8%)

sample2.9s (15.6%)

preprocess689.0ms (3.8%)

explain443.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify689.0ms (3.8%)

localize128.0ms (0.7%)

series78.0ms (0.4%)

simplify3.4s (18.4%)

rewrite726.0ms (4%)

eval139.0ms (0.8%)

prune122.0ms (0.7%)

simplify350.0ms (1.9%)

localize204.0ms (1.1%)

series142.0ms (0.8%)

simplify456.0ms (2.5%)

rewrite334.0ms (1.8%)

eval165.0ms (0.9%)

prune211.0ms (1.2%)

simplify321.0ms (1.8%)

localize287.0ms (1.6%)

series70.0ms (0.4%)

simplify665.0ms (3.6%)

rewrite388.0ms (2.1%)

eval162.0ms (0.9%)

prune111.0ms (0.6%)

simplify352.0ms (1.9%)

localize261.0ms (1.4%)

series106.0ms (0.6%)

simplify711.0ms (3.9%)

rewrite390.0ms (2.1%)

eval361.0ms (2%)

prune258.0ms (1.4%)

regimes146.0ms (0.8%)

regimes18.0ms (0.1%)

regimes33.0ms (0.2%)

regimes15.0ms (0.1%)

regimes21.0ms (0.1%)

regimes12.0ms (0.1%)

bsearch102.0ms (0.6%)

bsearch66.0ms (0.4%)

bsearch13.0ms (0.1%)

bsearch1.0ms (0%)

simplify10.0ms (0.1%)

soundness1.5s (8.4%)

preprocess427.0ms (2.3%)

end0.0ms (0%)

Profiling