Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

2.1MiB 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)

sample901.0ms (12.1%)

Memory

50.6MiB live, 931.2MiB allocated

Samples

414.0ms	8 256×	0	valid
154.0ms	2 651×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 380.0ms

ival-expm1: 126.0ms (33.1% of total)

ival-mult: 95.0ms (25% of total)

ival-div: 71.0ms (18.7% of total)

ival-sqrt: 70.0ms (18.4% of total)

ival-true: 8.0ms (2.1% of total)

exact: 6.0ms (1.6% of total)

ival-assert: 4.0ms (1.1% of total)

Bogosity

explain128.0ms (1.7%)

Memory

-21.0MiB live, 139.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
180	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
180	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
2	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	-	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 #s(literal 2 binary64) x)`
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	-	-	`#s(literal 2 binary64)`
0	-	-	`(exp.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	180	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	180	0
`/.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	2	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	2
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	2
↳	`(exp.f64 x)`	overflow	2
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	2

Confusion

	Predicted +	Predicted -
+	181	0
-	1	74

Precision

0.9945054945054945

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	181	0	0
-	1	0	74

Precision?

0.9945054945054945

Recall?

1.0

Freqs

test

number	freq
0	74
1	2
2	180

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 107 to 34 computations (68.2% saved)

Precisions

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

ival-exp: 7.0ms (28.4% of total)

ival-expm1: 6.0ms (24.4% of total)

ival-mult: 4.0ms (16.2% of total)

ival-div: 3.0ms (12.2% of total)

ival-sqrt: 3.0ms (12.2% of total)

exact: 1.0ms (4.1% of total)

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

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

preprocess273.0ms (3.7%)

Memory

36.3MiB live, 225.2MiB 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)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	31.7%	(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)

simplify340.0ms (4.6%)

Memory

-25.7MiB live, 255.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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)

localize30.0ms (0.4%)

Memory

-1.1MiB live, 38.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(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	0.40234375000000006	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	41.33914065670512	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	41.37122866151166	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

19.0ms

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 (25.1% of total)

ival-expm1: 3.0ms (25.1% 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

7.1MiB live, 7.1MiB 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)

simplify359.0ms (4.8%)

Memory

6.5MiB live, 243.0MiB 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)))

rewrite255.0ms (3.4%)

Memory

-8.1MiB live, 239.0MiB allocated

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))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
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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)))))

eval104.0ms (1.4%)

Memory: -7.2MiB live, 145.4MiB allocated
Compiler: Compiled 17 442 to 2 477 computations (85.8% saved)

prune202.0ms (2.7%)

Memory

18.1MiB live, 183.7MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	761	9	770
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	762	9	771

Accuracy

100.0%

Counts

771 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	70.3%	(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))))
▶	71.5%	(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))))
	69.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	75.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	70.5%	#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))))
	71.3%	#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))))
▶	70.2%	#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 176 to 118 computations (33% saved)

simplify242.0ms (3.2%)

Memory

6.3MiB live, 248.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(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	0	#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	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#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	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
cost-diff	0	(fma.f64 x (fma.f64 x #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 #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 #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)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
cost-diff	0	(exp.f64 x)
cost-diff	0	(-.f64 (exp.f64 x) #s(literal -1 binary64))
cost-diff	0	(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)

localize106.0ms (1.4%)

Memory

-26.1MiB live, 166.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0703125	(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	0.14453125	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
accuracy	0.421875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	18.854531272135905	#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	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.125	(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	19.07561228403185	#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	0	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
accuracy	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
accuracy	0.0078125	(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	18.364877507085193	#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	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	16.21379560851937	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0	(-.f64 (exp.f64 x) #s(literal -1 binary64))
accuracy	0	(exp.f64 x)
accuracy	0.0078125	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Samples

63.0ms	246×	0	valid
6.0ms	5×	1	valid
3.0ms	5×	2	valid

Compiler

Compiled 164 to 32 computations (80.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 15.0ms (34.1% of total)

ival-add: 7.0ms (15.9% of total)

ival-div: 5.0ms (11.4% of total)

ival-sqrt: 5.0ms (11.4% of total)

const: 4.0ms (9.1% of total)

ival-expm1: 3.0ms (6.8% of total)

ival-exp: 2.0ms (4.6% of total)

adjust: 1.0ms (2.3% of total)

ival-sub: 1.0ms (2.3% of total)

exact: 1.0ms (2.3% of total)

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

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

series14.0ms (0.2%)

Memory

24.9MiB live, 24.9MiB 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>) () ())) ())
#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 (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<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 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))
1.0ms	x	@	inf	(+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))
0.0ms	x	@	inf	(+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))
0.0ms	x	@	0	(+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))

simplify497.0ms (6.7%)

Memory

-23.7MiB live, 420.3MiB 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 x (.f64 #s(literal 1/2 binary64) 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 x (.f64 #s(literal 1/2 binary64) 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))

rewrite277.0ms (3.7%)

Memory

26.6MiB live, 301.5MiB allocated

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))))
(.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x)))) (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #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 #s(literal 2 binary64) (sqrt.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))) (.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))))) (.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))))))
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(/.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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(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))))

eval97.0ms (1.3%)

Memory: 15.2MiB live, 126.4MiB allocated
Compiler: Compiled 15 830 to 1 651 computations (89.6% saved)

prune385.0ms (5.2%)

Memory

-60.1MiB live, 175.7MiB allocated

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	680	10	690
Fresh	2	2	4
Picked	1	4	5
Done	0	0	0
Total	683	16	699

Accuracy

100.0%

Counts

699 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	69.9%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
▶	71.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))))
▶	70.3%	(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))))
✓	71.5%	(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))))
▶	69.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	71.4%	(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))))
	3.6%	(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))))
▶	4.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) x)))))
✓	75.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	70.4%	#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))))
	70.5%	#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))))
✓	70.2%	#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))))
▶	2.6%	#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)))))
	2.8%	#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 360 to 219 computations (39.2% saved)

simplify232.0ms (3.1%)

Memory

42.1MiB live, 266.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x)))
cost-diff	0	(/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#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))))
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 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 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 x (.f64 #s(literal 1/2 binary64) x))
cost-diff	0	#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) x))))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) 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	(*.f64 x x)
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))))
cost-diff	128	(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))

Rules

12 754×	`lower-fma.f32`
12 746×	`lower-fma.f64`
2 220×	`lower-*.f32`
2 210×	`lower-*.f64`
2 206×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	344
0	72	334
1	146	331
2	265	331
3	533	331
4	884	286
5	1151	268
6	1233	268
7	1631	268
8	3848	268
9	7441	268
0	8335	256

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

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

localize130.0ms (1.8%)

Memory

-18.8MiB live, 216.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.14453125	(.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x)))
accuracy	0.16015625	(/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	18.854531272135905	#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)))))
accuracy	44.00956244776171	#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))))
accuracy	0.015625	(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	0.03515625	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
accuracy	0.09765625	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy	18.876718427030156	#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	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) x)))))
accuracy	18.364877507085193	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) x))))
accuracy	43.575936490259195	#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) x)))
accuracy	0	(+.f64 #s(literal 2 binary64) x)
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	19.094001642255893	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))))
accuracy	18.364877507085193	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))

Samples

84.0ms

256×

valid

Compiler

Compiled 227 to 42 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 24.0ms (42.2% of total)

ival-add: 14.0ms (24.6% of total)

const: 6.0ms (10.5% of total)

ival-div: 5.0ms (8.8% of total)

ival-expm1: 3.0ms (5.3% of total)

ival-sqrt: 3.0ms (5.3% of total)

exact: 1.0ms (1.8% of total)

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

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

series18.0ms (0.2%)

Memory

-1.8MiB live, 36.1MiB allocated

Counts

21 → 252

Calls

Call 1

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

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

Calls

63 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/ (* 7/192 (* x (* x x))) (sqrt 2))
1.0ms	x	@	inf	(/ (* 7/192 (* x (* x x))) (sqrt 2))
0.0ms	x	@	-inf	(/ (* 7/192 (* x (* x x))) (sqrt 2))
0.0ms	x	@	-inf	(* 7/192 (* x (* x x)))
0.0ms	x	@	-inf	(+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)

simplify319.0ms (4.3%)

Memory

21.7MiB live, 408.3MiB allocated

Algorithm

1×	egg-herbie

Rules

21 986×	`lower-fma.f64`
21 986×	`lower-fma.f32`
4 786×	`lower-*.f64`
4 786×	`lower-*.f32`
2 974×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	2344
1	485	2139
2	1477	2073
3	4464	2049
0	8199	1632

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 250

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

rewrite248.0ms (3.3%)

Memory

-6.1MiB live, 309.3MiB allocated

Rules

4 480×	`lower-/.f32`
4 478×	`lower-/.f64`
3 662×	`lower-*.f32`
3 652×	`lower-*.f64`
2 752×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	316
0	72	308
1	317	242
2	2547	242
0	8162	230

Stop Event

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

Counts

21 → 284

Calls

Call 1

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

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

eval130.0ms (1.7%)

Memory: -16.1MiB live, 127.6MiB allocated
Compiler: Compiled 9 314 to 984 computations (89.4% saved)

prune86.0ms (1.2%)

Memory

2.9MiB live, 124.5MiB allocated

Pruning

19 alts after pruning (11 fresh and 8 done)

	Pruned	Kept	Total
New	549	5	554
Fresh	1	6	7
Picked	1	4	5
Done	0	4	4
Total	551	19	570

Accuracy

100.0%

Counts

570 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	69.9%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	71.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))))
✓	70.3%	(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))))
✓	71.5%	(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))))
✓	69.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	3.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (* x x) 1/2) (+ x 2)) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))
▶	2.2%	(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))))
	3.6%	(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 (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)))))))
▶	71.4%	(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))))
✓	4.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) x)))))
✓	75.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	70.4%	#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))))
	70.5%	#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))))
✓	70.2%	#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))))
	2.6%	#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 (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	2.8%	#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 393 to 234 computations (40.5% saved)

simplify205.0ms (2.7%)

Memory

2.3MiB live, 280.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
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 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
cost-diff	0	#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))
cost-diff	0	#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)))
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) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
cost-diff	0	(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
cost-diff	0	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 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 x (.f64 x (*.f64 x #s(literal 1/6 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 x (.f64 x (*.f64 x #s(literal 1/6 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	#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

10 754×	`lower-fma.f32`
10 744×	`lower-fma.f64`
2 402×	`lower-+.f32`
2 400×	`lower-+.f64`
2 322×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	447
0	86	447
1	179	441
2	345	433
3	709	433
4	1055	398
5	1409	384
6	1638	384
7	2128	384
8	4279	384
0	8354	360

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 (-.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 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
#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))))))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
x
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(*.f64 x #s(literal 1/6 binary64))
#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) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
#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)))
#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))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(*.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)) (.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 (-.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 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 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))))
#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))))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
x
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(*.f64 x #s(literal 1/6 binary64))
#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) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
#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)))
#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))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(*.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)) (.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 x x) (/.f64 (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 x x) (/.f64 (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 x x) (/.f64 (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 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)

localize156.0ms (2.1%)

Memory

10.6MiB live, 212.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2578125	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
accuracy	0.421875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	18.854531272135905	#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	43.29868792064267	#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	0.03125	(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.09765625	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
accuracy	18.876718427030156	#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)))
accuracy	43.39474604821657	#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))
accuracy	0.11328125	(.f64 x (.f64 x #s(literal 1/6 binary64)))
accuracy	0.31640625	(*.f64 x #s(literal 1/6 binary64))
accuracy	18.876718427030156	#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))))))
accuracy	43.99587870197843	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
accuracy	0	(-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0.0078125	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
accuracy	18.891860361199296	#s(approx (exp x) (+.f64 x #s(literal 1 binary64)))
accuracy	0.00390625	(fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
accuracy	0.0078125	(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	0.09375	(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x)
accuracy	18.364877507085193	#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

96.0ms	246×	0	valid
4.0ms	5×	1	valid
4.0ms	5×	2	valid

Compiler

Compiled 252 to 49 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-mult: 27.0ms (32.6% of total)

ival-div: 21.0ms (25.3% of total)

ival-add: 15.0ms (18.1% of total)

const: 7.0ms (8.4% of total)

ival-sqrt: 5.0ms (6% of total)

ival-expm1: 3.0ms (3.6% of total)

ival-exp: 2.0ms (2.4% of total)

adjust: 1.0ms (1.2% of total)

ival-sub: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

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

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

series45.0ms (0.6%)

Memory

-24.3MiB live, 13.3MiB allocated

Counts

25 → 300

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

75 calls:

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

simplify403.0ms (5.4%)

Memory

24.9MiB live, 205.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 542×	`lower-fma.f64`
14 542×	`lower-fma.f32`
5 212×	`lower-*.f64`
5 212×	`lower-*.f32`
2 070×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	2736
1	520	2521
2	1541	2367
3	5644	2359
0	8130	1967

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 297

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

rewrite541.0ms (7.3%)

Memory

9.5MiB live, 291.7MiB allocated

Rules

3 714×	`lower-/.f32`
3 710×	`lower-/.f64`
3 624×	`lower-*.f32`
3 612×	`lower-*.f64`
3 292×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	420
0	86	420
1	382	357
2	3014	357
0	8285	333

Stop Event

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

Counts

25 → 513

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 (-.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 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))))
#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))))))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(.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) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
#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)))
#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))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) 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 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))
(*.f64 x #s(literal 1/6 binary64))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(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 #s(literal 1/2 binary64) (*.f64 x x) x))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x) #s(literal 2 binary64))
(+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal 2 binary64)))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 #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 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) 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))))
(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 (*.f64 x #s(literal 1/2 binary64)) (+.f64 x #s(literal 2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (+.f64 #s(literal 2 binary64) x))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (+.f64 x #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (+.f64 #s(literal 2 binary64) x))
(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 (*.f64 x #s(literal 1/2 binary64)) x (+.f64 x #s(literal 2 binary64)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x (+.f64 #s(literal 2 binary64) x))
(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 x) #s(literal 1/2 binary64) (+.f64 #s(literal 2 binary64) x))
(/.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 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) 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 #s(literal 1/2 binary64) (.f64 x x) x) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) 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 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) 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 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) 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 #s(literal 1/2 binary64) (.f64 x x) x) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) 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 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) #s(literal -4 binary64)))))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x)) #s(literal 8 binary64)) (-.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) 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 #s(literal 1/2 binary64) (.f64 x x) x) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x)) #s(literal 8 binary64)) (+.f64 #s(literal 4 binary64) (-.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) 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 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) x) #s(literal -4 binary64)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64)))
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(/.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 #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 (.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 (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)))
(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 #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 x) (neg.f64 (sqrt.f64 #s(literal 2 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)))

eval123.0ms (1.7%)

Memory: 5.0MiB live, 208.6MiB allocated
Compiler: Compiled 15 890 to 1 857 computations (88.3% saved)

prune193.0ms (2.6%)

Memory

6.5MiB live, 390.8MiB allocated

Pruning

21 alts after pruning (10 fresh and 11 done)

	Pruned	Kept	Total
New	806	4	810
Fresh	0	6	6
Picked	1	4	5
Done	1	7	8
Total	808	21	829

Accuracy

100.0%

Counts

829 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	69.9%	(sqrt.f64 (-.f64 #s(approx (exp x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64)))
✓	69.9%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	71.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))))
✓	70.3%	(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))))
✓	71.5%	(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))))
✓	69.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	3.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (* x x) 1/2) (+ x 2)) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))))
✓	2.2%	(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))))
	3.6%	(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 (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)))))))
	69.7%	(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))))
✓	4.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 x (.f64 #s(literal 1/2 binary64) x)))))
✓	75.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	70.4%	#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))))
	70.5%	#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))))
	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 (.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x) (sqrt.f64 #s(literal 2 binary64)))))
	2.6%	#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 (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	2.8%	#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))))))
	4.2%	#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 #s(approx ( (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))

Compiler

Compiled 586 to 258 computations (56% saved)

regimes33.0ms (0.4%)

Memory

-5.3MiB live, 65.0MiB allocated

Counts

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

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

Calls

3 calls:

14.0ms

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

8.0ms

7.0ms

(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)

regimes40.0ms (0.5%)

Memory

-8.6MiB live, 45.2MiB allocated

Accuracy

Total -47.4b remaining (-299.3%)

Threshold costs -47.4b (-299.3%)

Counts

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

26.0ms

6.0ms

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

6.0ms

(/.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
75.3%	1	`x`
75.3%	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))))`
75.3%	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

11.3MiB live, 11.3MiB 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)))

soundness281.0ms (3.8%)

Memory

10.6MiB live, 247.4MiB 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)

preprocess46.0ms (0.6%)

Memory: -1.3MiB live, 79.5MiB allocated
Compiler: Compiled 44 to 34 computations (22.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample901.0ms (12.1%)

explain128.0ms (1.7%)

preprocess273.0ms (3.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify340.0ms (4.6%)

localize30.0ms (0.4%)

series5.0ms (0.1%)

simplify359.0ms (4.8%)

rewrite255.0ms (3.4%)

eval104.0ms (1.4%)

prune202.0ms (2.7%)

simplify242.0ms (3.2%)

localize106.0ms (1.4%)

series14.0ms (0.2%)

simplify497.0ms (6.7%)

rewrite277.0ms (3.7%)

eval97.0ms (1.3%)

prune385.0ms (5.2%)

simplify232.0ms (3.1%)

localize130.0ms (1.8%)

series18.0ms (0.2%)

simplify319.0ms (4.3%)

rewrite248.0ms (3.3%)

eval130.0ms (1.7%)

prune86.0ms (1.2%)

simplify205.0ms (2.7%)

localize156.0ms (2.1%)

series45.0ms (0.6%)

simplify403.0ms (5.4%)

rewrite541.0ms (7.3%)

eval123.0ms (1.7%)

prune193.0ms (2.6%)

regimes33.0ms (0.4%)

regimes40.0ms (0.5%)

simplify5.0ms (0.1%)

soundness281.0ms (3.8%)

preprocess46.0ms (0.6%)

end0.0ms (0%)

Profiling