Metrics for sqrtexp (problem 3.4.4)

analyze2.0ms (0%)

Memory

2.0MiB live, 2.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample910.0ms (11.1%)

Memory

37.9MiB live, 917.9MiB allocated

Samples

444.0ms	8 256×	0	valid
161.0ms	2 687×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 412.0ms

ival-expm1: 151.0ms (36.7% of total)

ival-mult: 101.0ms (24.5% of total)

ival-sqrt: 72.0ms (17.5% of total)

ival-div: 70.0ms (17% of total)

ival-true: 7.0ms (1.7% of total)

exact: 6.0ms (1.5% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

preprocess402.0ms (4.9%)

Memory

-2.7MiB live, 349.7MiB allocated

Algorithm

1×	egg-herbie

Rules

15 394×	`lower-fma.f64`
15 394×	`lower-fma.f32`
2 850×	`lower--.f32`
2 846×	`lower--.f64`
2 458×	`lower-*.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	32	27
2	55	27
3	89	27
4	143	13
5	250	13
6	513	13
7	2039	13
8	7136	13
0	10	12
0	17	12
1	29	12
2	35	12
3	47	12
4	73	7
5	126	5
6	203	5
7	606	5
8	2926	5
9	6783	5
0	8197	5

Stop Event

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

Calls

Call 1

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

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

explain197.0ms (2.4%)

Memory

-4.8MiB live, 160.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
171	1	(-0.0011382403801612098)	1	(-0.010979846515637208)	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
170	1	(-0.0011382403801612098)	0	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
3	0	-	0	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	0	-	0	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	0	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(exp.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	171	1
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	171	1
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	3	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	3
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	3
↳	`(exp.f64 x)`	overflow	3
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	3

Confusion

	Predicted +	Predicted -
+	173	0
-	1	82

Precision

0.9942528735632183

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	173	0	0
-	1	1	81

Precision?

0.9885714285714285

Recall?

1.0

Freqs

test

number	freq
0	82
1	3
2	171

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms

512×

valid

Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-exp: 7.0ms (28.8% of total)

ival-expm1: 6.0ms (24.7% of total)

ival-mult: 4.0ms (16.5% of total)

ival-div: 3.0ms (12.4% of total)

ival-sqrt: 3.0ms (12.4% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	34.2%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify408.0ms (5%)

Memory

-2.0MiB live, 393.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	192	(-.f64 (exp.f64 x) #s(literal 1 binary64))
✓	cost-diff	192	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	cost-diff	7104	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Rules

15 394×	`lower-fma.f64`
15 394×	`lower-fma.f32`
2 850×	`lower--.f32`
2 846×	`lower--.f64`
2 458×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
0	17	45
1	29	45
2	35	45
3	47	45
4	73	35
5	126	31
6	203	31
7	606	31
8	2926	31
9	6783	31
0	8197	27

Stop Event

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

Calls

Call 1

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

Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(expm1.f64 (+.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 x x)
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
(exp.f64 x)

localize90.0ms (1.1%)

Memory

7.0MiB live, 44.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
✓	accuracy	99.0%	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	accuracy	38.6%	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	accuracy	38.5%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

78.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-exp: 3.0ms (25.3% of total)

ival-expm1: 3.0ms (25.3% of total)

ival-div: 2.0ms (16.8% of total)

ival-mult: 2.0ms (16.8% of total)

ival-sqrt: 2.0ms (16.8% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#s(alt 2 (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* 2 x))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* x (+ 2 (* 4/3 x))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
1.0ms	x	@	inf	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms	x	@	0	(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
0.0ms	x	@	0	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms	x	@	0	(- (exp (* 2 x)) 1)

simplify434.0ms (5.3%)

Memory

-6.3MiB live, 400.1MiB allocated

Algorithm

1×	egg-herbie

Rules

15 504×	`lower-fma.f64`
15 504×	`lower-fma.f32`
4 704×	`lower-*.f64`
4 704×	`lower-*.f32`
2 492×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	480
1	252	446
2	663	446
3	1429	440
4	2558	360
5	5941	325
0	8294	270

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

Outputs
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(* 2 x)
(+.f64 x x)
(* x (+ 2 (* 2 x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

rewrite336.0ms (4.1%)

Memory

15.2MiB live, 412.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 562×	`lower-fma.f64`
4 562×	`lower-fma.f32`
3 484×	`lower-*.f32`
3 482×	`lower-*.f64`
2 734×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
0	17	36
1	63	22
2	429	22
3	4997	22
0	8103	18

Stop Event

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

Counts

5 → 711

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)))
(+.f64 (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (+.f64 x x))) (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(+.f64 (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (+.f64 x x))))
(+.f64 (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 x)))
(+.f64 (.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))))
(+.f64 (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (.f64 (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
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(.f64 (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (expm1.f64 (+.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 6 binary64)))) (.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (.f64 x #s(literal 4 binary64)))))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 4 binary64)))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (neg.f64 (expm1.f64 (+.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 (+.f64 x x))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) #s(literal 1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (.f64 x #s(literal 4 binary64)))))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 (+.f64 x x))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 4 binary64))) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (/.f64 (expm1.f64 x) (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (/.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))
(.f64 (.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 x) (expm1.f64 (.f64 x #s(literal 6 binary64))))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (.f64 x #s(literal 4 binary64))))))
(.f64 (.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 4 binary64))))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (expm1.f64 x)))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (fma.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal -3 binary64))))) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64))))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))) (exp.f64 (.f64 x #s(literal 4 binary64)))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (-.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (+.f64 x x)) (exp.f64 x)))
(log.f64 (exp.f64 (+.f64 x x)))
(+.f64 x x)
(+.f64 (+.f64 x x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 x x))
(+.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (log.f64 (.f64 (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(+.f64 (log.f64 (exp.f64 (.f64 x #s(literal 1 binary64)))) (log.f64 (exp.f64 (.f64 x #s(literal 1 binary64)))))
(+.f64 (log.f64 (.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))))) (.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64) (.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64) (log.f64 (.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 4 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 x x) x)) (fma.f64 x x (-.f64 (.f64 x x) (*.f64 x x))))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 4 binary64))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(.f64 (fma.f64 x #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(neg.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (expm1.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 6 binary64)))) (sqrt.f64 (.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64))))))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 4 binary64)))) (sqrt.f64 (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal -3 binary64))))) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (.f64 (exp.f64 (.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) #s(literal 1 binary64)) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
(*.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))

eval114.0ms (1.4%)

Memory: -14.0MiB live, 172.6MiB allocated
Compiler: Compiled 17 442 to 2 477 computations (85.8% saved)

prune118.0ms (1.4%)

Memory

16.9MiB live, 256.9MiB allocated

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	760	10	770
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	761	10	771

Accuracy

100.0%

Counts

771 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
	66.2%	(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
▶	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
	66.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	72.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	67.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	68.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	67.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 202 to 138 computations (31.7% saved)

simplify364.0ms (4.5%)

Memory

-25.4MiB live, 465.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	cost-diff	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	cost-diff	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
✓	cost-diff	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	cost-diff	(exp.f64 x)
✓	cost-diff	(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓	cost-diff	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Rules

12 460×	`lower-fma.f32`
12 448×	`lower-fma.f64`
2 252×	`lower--.f32`
2 250×	`lower--.f64`
2 190×	`lower-*.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	32	196
0	52	196
1	98	196
2	185	196
3	382	196
4	694	166
5	968	154
6	1048	154
7	1452	154
8	3697	154
9	7369	154
0	8297	154

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
x
#s(literal -1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)

Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
x
#s(literal -1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)

localize94.0ms (1.2%)

Memory

10.2MiB live, 127.2MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.8%	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.8%	(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	98.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	accuracy	68.3%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	accuracy	71.8%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Samples

54.0ms	249×	0	valid
2.0ms	4×	1	valid
2.0ms	3×	2	valid

Compiler

Compiled 164 to 32 computations (80.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 11.0ms (26.1% of total)

ival-sqrt: 7.0ms (16.6% of total)

ival-add: 7.0ms (16.6% of total)

const: 5.0ms (11.9% of total)

ival-div: 5.0ms (11.9% of total)

ival-expm1: 3.0ms (7.1% of total)

ival-exp: 2.0ms (4.7% of total)

adjust: 1.0ms (2.4% of total)

ival-sub: 1.0ms (2.4% of total)

exact: 1.0ms (2.4% of total)

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

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

series13.0ms (0.2%)

Memory

16.3MiB live, 16.3MiB allocated

Counts

17 → 180

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1 (exp x))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1 (exp x))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1 (exp x))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1 (exp x))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1 (exp x))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1 (exp x))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1 (exp x))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1 (exp x))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 7/192 (/ (pow x 3) (sqrt 2))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3)))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 7/192 (/ (pow x 3) (sqrt 2))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 3/16 (taylor 0 x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3/16 (* 7/192 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3/16 (* 7/192 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3/16 (* 7/192 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())

Calls

45 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))
1.0ms	x	@	inf	(sqrt (- (exp x) -1))
0.0ms	x	@	inf	(+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))
0.0ms	x	@	inf	(+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))
0.0ms	x	@	0	(+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))

simplify486.0ms (5.9%)

Memory

-11.0MiB live, 520.3MiB allocated

Algorithm

1×	egg-herbie

Rules

21 334×	`lower-fma.f64`
21 334×	`lower-fma.f32`
5 222×	`lower-*.f64`
5 222×	`lower-*.f32`
2 740×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	132	1803
1	419	1545
2	1201	1476
3	4309	1462
0	8038	1163

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* 1/2 (/ x (sqrt 2)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 1/2 (/ x (sqrt 2)))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 1/2 (/ x (sqrt 2)))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (*.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))

rewrite369.0ms (4.5%)

Memory

-9.5MiB live, 466.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 334×	`lower-fma.f32`
4 322×	`lower-fma.f64`
4 294×	`lower-/.f32`
4 290×	`lower-/.f64`
3 990×	`lower-*.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	172
0	52	172
1	229	130
2	1778	127
0	8465	127

Stop Event

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

Counts

17 → 489

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))

Outputs
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))) (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64)))) (sqrt.f64 (.f64 (expm1.f64 x) (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64)))) (sqrt.f64 (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64)))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x))))) (sqrt.f64 (neg.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))
(.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 x)))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
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(pow.f64 (/.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal -2 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (-.f64 #s(literal 2 binary64) (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (+.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))
(+.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(-.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (-.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (.f64 (.f64 x x) #s(literal 49/36864 binary64))) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
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(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (.f64 (.f64 x x) #s(literal 49/36864 binary64)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (fma.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))

eval91.0ms (1.1%)

Memory: 33.9MiB live, 183.6MiB allocated
Compiler: Compiled 15 830 to 1 651 computations (89.6% saved)

prune94.0ms (1.2%)

Memory

-1.6MiB live, 232.1MiB allocated

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	681	9	690
Fresh	2	3	5
Picked	1	4	5
Done	0	0	0
Total	684	16	700

Accuracy

100.0%

Counts

700 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.2%	(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	66.7%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
▶	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
▶	66.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	68.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))))
▶	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	72.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	67.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
	67.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
✓	67.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	2.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))))
	2.9%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))))
▶	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))

Compiler

Compiled 378 to 235 computations (37.8% saved)

simplify580.0ms (7.1%)

Memory

-18.8MiB live, 422.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
✓	cost-diff	0	(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
✓	cost-diff	0	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
✓	cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
✓	cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	cost-diff	0	#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
✓	cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	cost-diff	0	#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))
✓	cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
✓	cost-diff	704	(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)

Rules

10 750×	`lower-fma.f32`
10 738×	`lower-fma.f64`
2 394×	`lower-+.f32`
2 392×	`lower-+.f64`
2 318×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	393
0	76	393
1	159	393
2	319	393
3	686	393
4	1049	348
5	1406	330
6	1637	330
7	2125	330
8	4299	330
0	8310	306

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
x
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
#s(literal 1/2 binary64)
(*.f64 x x)
x
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
x
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)

Outputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 x #s(literal 1/2 binary64))))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 x x)
x
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 (.f64 x x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 (.f64 x x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 (.f64 (.f64 x x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)

localize137.0ms (1.7%)

Memory

3.4MiB live, 200.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
✓	accuracy	35.2%	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	99.9%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	99.8%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	67.3%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	accuracy	68.3%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
✓	accuracy	34.6%	#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	accuracy	67.1%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
✓	accuracy	99.8%	(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
✓	accuracy	68.3%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))

Samples

72.0ms	249×	0	valid
2.0ms	4×	1	valid
2.0ms	3×	2	valid

Compiler

Compiled 249 to 42 computations (83.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 23.0ms (39.3% of total)

ival-add: 16.0ms (27.4% of total)

const: 7.0ms (12% of total)

ival-div: 5.0ms (8.6% of total)

ival-sqrt: 3.0ms (5.1% of total)

ival-expm1: 3.0ms (5.1% of total)

adjust: 1.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.3%)

Memory

-19.8MiB live, 34.7MiB allocated

Counts

22 → 264

Calls

Call 1

Inputs
#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)) (patch #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 2 binary64) x) (patch (+.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (patch #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/2 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) (patch #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (patch (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt 2 (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) (patch (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))) #<representation binary64>) () ())) ())
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#s(alt (* 7/192 (/ (pow x 2) (sqrt 2))) (taylor inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 7/192 (/ (pow x 2) (sqrt 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* 1/2 (pow x 2))) x) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* 1/2 (pow x 2))) x) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* 1/2 (pow x 2))) x) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/6 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/6 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/6 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor -inf x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())

Calls

66 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)))
0.0ms	x	@	-inf	(* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))
0.0ms	x	@	0	(* 1/2 (* x x))
0.0ms	x	@	inf	(* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)))
0.0ms	x	@	-inf	(+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)

simplify546.0ms (6.7%)

Memory

26.0MiB live, 672.3MiB allocated

Algorithm

1×	egg-herbie

Rules

23 306×	`lower-fma.f64`
23 306×	`lower-fma.f32`
5 042×	`lower-*.f64`
5 042×	`lower-*.f32`
2 916×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	159	2638
1	527	2433
2	1565	2294
3	4589	2255
0	8362	1795

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 262

Calls

Call 1

Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/ 2 x)
(/ (+ 2 (* 1/2 (pow x 2))) x)
(/ (+ 2 (* 1/2 (pow x 2))) x)
(/ (+ 2 (* 1/2 (pow x 2))) x)
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* x (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* x (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* x (+ 1/2 (* 2 (/ 1 (pow x 2)))))
(* x (+ 1/2 (* 2 (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))

Outputs
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
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(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))

rewrite265.0ms (3.2%)

Memory

-1.3MiB live, 382.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 210×	`lower-/.f32`
4 206×	`lower-/.f64`
3 352×	`lower-*.f32`
3 344×	`lower-*.f64`
2 900×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	365
0	76	365
1	341	302
2	2736	302
0	8164	278

Stop Event

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

Counts

22 → 487

Calls

Call 1

Inputs
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))

Outputs
(+.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(+.f64 #s(literal 2 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
(+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) #s(literal 2 binary64))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal 2 binary64)))
(+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)
(-.f64 (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)))
(-.f64 (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))))
(-.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x))) (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (-.f64 #s(literal 2 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 x (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(fma.f64 x #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (+.f64 x #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (+.f64 x #s(literal 2 binary64)))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x x)
(fma.f64 #s(literal 1 binary64) x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x (+.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fma.f64 x (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x))) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal 8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #s(literal -4 binary64))))
(/.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #s(literal 8 binary64)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x))))
(/.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #s(literal 8 binary64)) (+.f64 #s(literal 4 binary64) (-.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x)))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))))) (fma.f64 x (-.f64 x (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))))) (fma.f64 x x (-.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x))) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal 8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #s(literal -4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fma.f64 x (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)))))
(/.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #s(literal -4 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64)))
(/.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)) (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))))) (neg.f64 (fma.f64 x (-.f64 x (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))))) (neg.f64 (fma.f64 x x (-.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x))) (neg.f64 (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #s(literal 8 binary64))) (neg.f64 (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x)))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) #s(literal 8 binary64))) (neg.f64 (+.f64 #s(literal 4 binary64) (-.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x))))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) #s(literal -4 binary64))) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))))
(/.f64 (-.f64 #s(literal 4 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x))) (-.f64 #s(literal 2 binary64) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (-.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x))) x)) (.f64 (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x))) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) x (.f64 (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x))) (+.f64 x x))) (.f64 (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) x))) x))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (neg.f64 x) (.f64 (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x))) (.f64 #s(literal -2 binary64) x))) (.f64 (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x))) (neg.f64 x)))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (neg.f64 x) (.f64 (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x))) (.f64 x #s(literal -2 binary64)))) (.f64 (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x))) (neg.f64 x)))
(/.f64 (fma.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (.f64 x #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x) x)) (.f64 (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x) (.f64 x #s(literal 1/2 binary64))))
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(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x)))
(/.f64 (+.f64 #s(literal -2 binary64) (.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (neg.f64 x))) (.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)))
(/.f64 (+.f64 #s(literal -4 binary64) (.f64 (neg.f64 x) x)) (.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 x) #s(literal 1 binary64))) (.f64 (neg.f64 x) (/.f64 #s(literal 2 binary64) x)))
(/.f64 (+.f64 #s(literal -2 binary64) (.f64 (neg.f64 (.f64 x #s(literal 1/2 binary64))) x)) (.f64 (neg.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))) (.f64 (neg.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 2 binary64) x)))
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (neg.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 x))) (.f64 (neg.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(/.f64 (fma.f64 x x #s(literal 4 binary64)) (+.f64 x x))
(/.f64 (fma.f64 x x #s(literal 4 binary64)) (*.f64 #s(literal -2 binary64) (neg.f64 x)))
(/.f64 (fma.f64 x (neg.f64 (neg.f64 x)) #s(literal 4 binary64)) (*.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 x))))
(/.f64 (fma.f64 x (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (fma.f64 x (neg.f64 x) #s(literal -4 binary64)) (*.f64 #s(literal 2 binary64) (neg.f64 x)))
(/.f64 (fma.f64 x (neg.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (neg.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (+.f64 x (*.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)) (.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 2 binary64) x) (neg.f64 (neg.f64 x))))
(/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x)) (.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 x) (.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -2 binary64))) (.f64 (/.f64 #s(literal 2 binary64) x) (neg.f64 x)))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 2 binary64) x) (neg.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (neg.f64 x) x #s(literal -4 binary64)) (*.f64 #s(literal -2 binary64) x))
(/.f64 (fma.f64 (neg.f64 x) (neg.f64 (neg.f64 x)) #s(literal -4 binary64)) (*.f64 #s(literal -2 binary64) (neg.f64 (neg.f64 x))))
(/.f64 (fma.f64 (neg.f64 x) (.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) (.f64 #s(literal -2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (neg.f64 x) (/.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)) (.f64 #s(literal -2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (fma.f64 (neg.f64 x) (neg.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 #s(literal -2 binary64) (neg.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 4 binary64) (.f64 x x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x)) (-.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 4 binary64) (.f64 x x))))) (neg.f64 (neg.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal -1 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x)) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 4 binary64) (.f64 x x)))) #s(literal -1 binary64))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal -1 binary64)))))
(.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 2 binary64) x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/12 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))

eval136.0ms (1.7%)

Memory: 2.1MiB live, 148.9MiB allocated
Compiler: Compiled 15 012 to 1 810 computations (87.9% saved)

prune141.0ms (1.7%)

Memory

17.3MiB live, 268.5MiB allocated

Pruning

22 alts after pruning (14 fresh and 8 done)

	Pruned	Kept	Total
New	739	10	749
Fresh	3	4	7
Picked	1	4	5
Done	0	4	4
Total	743	22	765

Accuracy

100.0%

Counts

765 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.2%	(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	66.7%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	66.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	2.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
▶	3.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
	2.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))
	66.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x #s(approx (+ (* 1/2 x) (/ 2 x)) (/.f64 #s(literal 2 binary64) x)) x))))
✓	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	72.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	67.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
▶	67.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
✓	67.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	2.9%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
✓	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x #s(approx ( (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))))))
	2.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
▶	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))

Compiler

Compiled 480 to 292 computations (39.2% saved)

simplify280.0ms (3.4%)

Memory

-24.5MiB live, 287.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
✓	cost-diff	0	(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
✓	cost-diff	0	(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	cost-diff	0	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	cost-diff	0	(/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))

Rules

9 502×	`lower-fma.f32`
9 494×	`lower-fma.f64`
2 308×	`lower-*.f32`
2 298×	`lower-*.f64`
1 572×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	450
0	83	438
1	168	434
2	417	434
3	897	434
4	1496	409
5	1927	399
6	2056	399
7	2449	399
8	4482	399
9	7992	399
0	8004	393

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) x)
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
#s(literal -1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(*.f64 x x)
x
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
x
(*.f64 x #s(literal 3/16 binary64))
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)

Outputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
x
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) x)
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) #s(approx (exp x) (+.f64 x #s(literal 1 binary64)))))
(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(+.f64 #s(literal 1 binary64) #s(approx (exp x) (+.f64 x #s(literal 1 binary64))))
#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
#s(literal -1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(*.f64 x x)
x
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
x
(*.f64 x #s(literal 3/16 binary64))
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)

localize170.0ms (2.1%)

Memory

11.6MiB live, 262.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
✓	accuracy	35.0%	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	99.6%	(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
✓	accuracy	66.1%	#s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	35.2%	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.9%	(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	67.3%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓	accuracy	35.2%	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	accuracy	67.4%	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
✓	accuracy	99.8%	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	98.9%	(/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))

Samples

84.0ms	249×	0	valid
2.0ms	3×	2	valid
2.0ms	4×	1	valid

Compiler

Compiled 280 to 45 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 22.0ms (32.4% of total)

ival-div: 14.0ms (20.6% of total)

ival-add: 11.0ms (16.2% of total)

const: 7.0ms (10.3% of total)

ival-sqrt: 5.0ms (7.4% of total)

ival-expm1: 3.0ms (4.4% of total)

ival-exp: 2.0ms (2.9% of total)

adjust: 1.0ms (1.5% of total)

ival-sub: 1.0ms (1.5% of total)

exact: 1.0ms (1.5% of total)

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

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

series19.0ms (0.2%)

Memory

-9.3MiB live, 28.0MiB allocated

Counts

22 → 264

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
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#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
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#s(alt #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
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Outputs
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#s(alt (+ 3/16 (* 7/192 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3/16 (* 7/192 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3/16 (* 7/192 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (patch (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/6 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/6 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/6 x)) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

66 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/ (* x (* x 3/16)) (sqrt 2))
0.0ms	x	@	inf	(/ (* x (* x 3/16)) (sqrt 2))
0.0ms	x	@	-inf	(/ 1 (/ 1 x))
0.0ms	x	@	inf	(/ (+ (* x (+ (* x 7/192) 3/16)) 1/2) (sqrt 2))
0.0ms	x	@	-inf	(/ (+ (* x (+ (* x 7/192) 3/16)) 1/2) (sqrt 2))

simplify363.0ms (4.4%)

Memory

28.1MiB live, 489.3MiB allocated

Algorithm

1×	egg-herbie

Rules

15 290×	`lower-fma.f64`
15 290×	`lower-fma.f32`
4 684×	`lower-*.f64`
4 684×	`lower-*.f32`
2 420×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	2811
1	516	2536
2	1512	2381
3	4352	2255
0	8639	1932

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 250

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))

Outputs
x
x
x
x
x
x
x
x
x
x
x
x
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (fma.f64 x (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))) (neg.f64 (*.f64 x x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) x))))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (fma.f64 x (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))) (neg.f64 (*.f64 x x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) x))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (fma.f64 x (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))) (neg.f64 (*.f64 x x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) x))))
(* 1/2 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (fma.f64 x (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))) (neg.f64 (*.f64 x x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (fma.f64 x (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))) (neg.f64 (*.f64 x x)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))

rewrite364.0ms (4.5%)

Memory

-12.6MiB live, 402.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 556×	`lower-*.f32`
4 546×	`lower-*.f64`
3 632×	`lower-/.f32`
3 622×	`lower-/.f64`
3 242×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	392
0	83	380
1	341	341
2	2975	341
0	8368	335

Stop Event

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

Counts

22 → 482

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))

Outputs
x
(log.f64 (exp.f64 x))
(exp.f64 (log.f64 x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(+.f64 x #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) x)
(fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 x (log.f64 (E.f64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 0 binary64))
(neg.f64 (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 x #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 x) #s(literal -1 binary64))
(pow.f64 x #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(*.f64 x (log.f64 (E.f64)))
(*.f64 #s(literal -1 binary64) (neg.f64 x))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (-.f64 (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (/.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) x (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))) (fma.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (+.f64 #s(literal 2 binary64) (-.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 (+.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal -2 binary64)) (-.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (+.f64 (/.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))))
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(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/12 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/12 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/12 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/12 binary64)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))

eval99.0ms (1.2%)

Memory: -2.7MiB live, 182.1MiB allocated
Compiler: Compiled 15 726 to 1 451 computations (90.8% saved)

prune143.0ms (1.7%)

Memory

15.4MiB live, 233.6MiB allocated

Pruning

23 alts after pruning (11 fresh and 12 done)

	Pruned	Kept	Total
New	757	6	763
Fresh	4	5	9
Picked	1	4	5
Done	0	8	8
Total	762	23	785

Accuracy

100.0%

Counts

785 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.2%	(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	66.7%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	66.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	2.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
✓	3.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
	2.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) #s(approx (+ (* x 1/6) 1/2) (*.f64 x #s(literal 1/6 binary64)))))))
	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))
	66.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x #s(approx (+ (* 1/2 x) (/ 2 x)) (/.f64 #s(literal 2 binary64) x)) x))))
✓	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	72.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	67.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	67.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
	2.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* x (+ (* x 7/192) 3/16)) 1/2) (sqrt 2)) (/ 1 (/ 1 x))) (sqrt 2)) (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
	2.9%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x)))))
✓	2.9%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
	4.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(approx (+ ( x 7/192) 3/16) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
✓	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
✓	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))))

Compiler

Compiled 715 to 295 computations (58.7% saved)

regimes33.0ms (0.4%)

Memory

-32.4MiB live, 45.9MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) #s(approx (+ (* x 1/6) 1/2) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x #s(approx (+ (* 1/2 x) (/ 2 x)) (/.f64 #s(literal 2 binary64) x)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x #s(approx ( (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(approx (+ ( x 7/192) 3/16) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* x (+ (* x 7/192) 3/16)) 1/2) (sqrt 2)) (/ 1 (/ 1 x))) (sqrt 2)) (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))

Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Calls

3 calls:

11.0ms

8.0ms

(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

8.0ms

(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
100.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes28.0ms (0.3%)

Memory

15.3MiB live, 52.8MiB allocated

Accuracy

Total -45.5b remaining (-258.4%)

Threshold costs -45.5b (-258.4%)

Counts

32 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) #s(approx (+ (* x 1/6) 1/2) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x #s(approx (+ (* 1/2 x) (/ 2 x)) (/.f64 #s(literal 2 binary64) x)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) #s(approx (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x #s(approx ( (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(approx (+ ( x 7/192) 3/16) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* x (+ (* x 7/192) 3/16)) 1/2) (sqrt 2)) (/ 1 (/ 1 x))) (sqrt 2)) (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (.f64 x #s(literal 7/192 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))

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

Calls

3 calls:

11.0ms

8.0ms

(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

8.0ms

(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
72.5%	1	`x`
72.5%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
72.5%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify5.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	20	19
2	23	19
3	24	19
4	25	19

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness299.0ms (3.7%)

Memory

-0.0MiB live, 234.1MiB allocated

Rules

15 504×	`lower-fma.f64`
15 504×	`lower-fma.f32`
4 704×	`lower-*.f64`
4 704×	`lower-*.f32`
4 562×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
0	17	36
1	63	22
2	429	22
3	4997	22
0	8103	18
0	77	480
1	252	446
2	663	446
3	1429	440
4	2558	360
5	5941	325
0	8294	270

Stop Event

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

Compiler

Compiled 30 to 23 computations (23.3% saved)

preprocess22.0ms (0.3%)

Memory: 16.8MiB live, 55.5MiB allocated
Compiler: Compiled 44 to 34 computations (22.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

sample910.0ms (11.1%)

preprocess402.0ms (4.9%)

explain197.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify408.0ms (5%)

localize90.0ms (1.1%)

series5.0ms (0.1%)

simplify434.0ms (5.3%)

rewrite336.0ms (4.1%)

eval114.0ms (1.4%)

prune118.0ms (1.4%)

simplify364.0ms (4.5%)

localize94.0ms (1.2%)

series13.0ms (0.2%)

simplify486.0ms (5.9%)

rewrite369.0ms (4.5%)

eval91.0ms (1.1%)

prune94.0ms (1.2%)

simplify580.0ms (7.1%)

localize137.0ms (1.7%)

series24.0ms (0.3%)

simplify546.0ms (6.7%)

rewrite265.0ms (3.2%)

eval136.0ms (1.7%)

prune141.0ms (1.7%)

simplify280.0ms (3.4%)

localize170.0ms (2.1%)

series19.0ms (0.2%)

simplify363.0ms (4.4%)

rewrite364.0ms (4.5%)

eval99.0ms (1.2%)

prune143.0ms (1.7%)

regimes33.0ms (0.4%)

regimes28.0ms (0.3%)

simplify5.0ms (0.1%)

soundness299.0ms (3.7%)

preprocess22.0ms (0.3%)

end0.0ms (0%)

Profiling