Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

2.0MiB live, 2.0MiB 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)

sample951.0ms (15.9%)

Memory

47.8MiB live, 965.5MiB allocated

Samples

462.0ms	8 256×	0	valid
149.0ms	2 716×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 395.0ms

ival-expm1: 145.0ms (36.7% of total)

ival-mult: 85.0ms (21.5% of total)

ival-div: 75.0ms (19% of total)

ival-sqrt: 71.0ms (18% of total)

ival-true: 8.0ms (2% of total)

exact: 6.0ms (1.5% of total)

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

Bogosity

explain160.0ms (2.7%)

Memory

-37.7MiB live, 135.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
164	0	-	1	(0.006085329751297451)	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
164	0	-	0	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
3	0	-	0	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	1	(186.97499701162613)	0	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	0	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(exp.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	164	1
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	163	1
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	2	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	3
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	3
↳	`(exp.f64 x)`	overflow	2
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	2
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/n	1	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	3
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	3
`exp.f64`	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	165	0
-	3	88

Precision

0.9821428571428571

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	165	0	0
-	3	1	87

Precision?

0.9763313609467456

Recall?

1.0

Freqs

test

number	freq
0	88
1	5
2	163

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms

512×

valid

Compiler

Compiled 106 to 34 computations (67.9% saved)

Precisions

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

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

ival-expm1: 6.0ms (24% of total)

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

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

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

exact: 1.0ms (4% of total)

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

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

preprocess210.0ms (3.5%)

Memory

31.3MiB live, 144.9MiB allocated

Algorithm

1×	egg-herbie

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	37.2%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify152.0ms (2.6%)

Memory

-2.2MiB live, 109.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	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))))
cost-diff	192	(-.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	6336	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
cost-diff	7232	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

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 (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 x) #s(literal -1 binary64))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
(exp.f64 x)

localize48.0ms (0.8%)

Memory

4.1MiB live, 48.1MiB 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	0.6579952771666512	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	37.32962730858605	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	37.394657075115894	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

41.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-exp: 21.0ms (71.9% of total)

ival-expm1: 3.0ms (10.3% of total)

ival-div: 2.0ms (6.8% of total)

ival-mult: 2.0ms (6.8% of total)

ival-sqrt: 2.0ms (6.8% 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

5.2MiB live, 5.2MiB allocated

Counts

4 → 48

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 (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 (* 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 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 (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 (/ (- (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) (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 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 (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 (/ (- (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) (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 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 (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

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

1.0ms

((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

1.0ms

-inf

((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

simplify160.0ms (2.7%)

Memory

18.3MiB live, 125.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	444
1	252	410
2	661	410
3	1434	404
4	2557	324
5	5968	289
0	8342	234

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

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

rewrite212.0ms (3.5%)

Memory

-39.2MiB live, 212.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	17	33
1	63	19
2	429	19
3	4997	19
0	8103	15

Stop Event

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

Counts

4 → 687

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))
(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
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eval166.0ms (2.8%)

Memory: 6.9MiB live, 127.0MiB allocated
Compiler: Compiled 16 704 to 2 386 computations (85.7% saved)

prune19.0ms (0.3%)

Memory

9.1MiB live, 47.3MiB allocated

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	724	10	734
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	725	10	735

Accuracy

100.0%

Counts

735 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
▶	100.0%	(sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	65.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
	63.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
▶	69.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	65.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
▶	64.6%	#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 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	64.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 174 to 148 computations (14.9% saved)

simplify116.0ms (1.9%)

Memory

-6.6MiB live, 70.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	214
0	56	212
1	98	206
2	188	206
3	332	206
4	609	164
5	857	164
6	1470	164
7	3766	164
0	8463	164

Stop Event

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

Calls

Call 1

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

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

localize111.0ms (1.9%)

Memory

-7.6MiB live, 76.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.17578125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.40625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.962586403447396	#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 #s(literal 7/192 binary64) x #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	0.171875	(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.98828125	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.347997071232474	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy	21.481246161847068	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	19.08766026415818	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0.00390625	(sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
accuracy	0.0078125	(-.f64 (exp.f64 x) #s(literal -1 binary64))
accuracy	0.015625	(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
accuracy	0.015625	(/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Samples

84.0ms	245×	0	valid
3.0ms	3×	5	exit
2.0ms	4×	2	valid
2.0ms	4×	1	valid

Compiler

Compiled 182 to 34 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-add: 18.0ms (29.9% of total)

ival-mult: 11.0ms (18.3% of total)

ival-sqrt: 10.0ms (16.6% of total)

ival-div: 8.0ms (13.3% of total)

const: 4.0ms (6.6% of total)

ival-expm1: 3.0ms (5% of total)

ival-exp: 2.0ms (3.3% of total)

adjust: 1.0ms (1.7% of total)

ival-sub: 1.0ms (1.7% of total)

exact: 1.0ms (1.7% of total)

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

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

series16.0ms (0.3%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

18 → 192

Calls

Call 1

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

Outputs
#s(alt 2 (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (/.f64 #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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (/.f64 #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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 #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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 #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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 #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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))) (patch (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 x) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/4 (* -1/48 (pow x 2)))) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/4 (* (pow x 2) (- (* 1/480 (pow x 2)) 1/48)))) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (/.f64 #s(literal -1 binary64) (-.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 (sqrt 2) (taylor 0 x) (#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 (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#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 (+ (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(literal 2 binary64))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #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)) #s(literal 2 binary64))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#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 (+ 2 x) (taylor 0 x) (#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 (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#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 (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#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 2) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ x (sqrt 2))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (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 (* 7/192 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((/ -1 (/ -1 (- (exp x) -1))) (sqrt (/ -1 (/ -1 (- (exp x) -1)))) (/ -1 (- (exp x) -1)) (- (exp x) -1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (+ (* 7/192 x) 3/16))
3.0ms	x	@	inf	((/ -1 (/ -1 (- (exp x) -1))) (sqrt (/ -1 (/ -1 (- (exp x) -1)))) (/ -1 (- (exp x) -1)) (- (exp x) -1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (+ (* 7/192 x) 3/16))
2.0ms	x	@	0	((/ -1 (/ -1 (- (exp x) -1))) (sqrt (/ -1 (/ -1 (- (exp x) -1)))) (/ -1 (- (exp x) -1)) (- (exp x) -1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (+ (* 7/192 x) 3/16))

Time

Variable

Point

Expression

4.0ms

-inf

((/ -1 (/ -1 (- (exp x) -1))) (sqrt (/ -1 (/ -1 (- (exp x) -1)))) (/ -1 (- (exp x) -1)) (- (exp x) -1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (+ (* 7/192 x) 3/16))

3.0ms

inf

((/ -1 (/ -1 (- (exp x) -1))) (sqrt (/ -1 (/ -1 (- (exp x) -1)))) (/ -1 (- (exp x) -1)) (- (exp x) -1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (+ (* 7/192 x) 3/16))

2.0ms

((/ -1 (/ -1 (- (exp x) -1))) (sqrt (/ -1 (/ -1 (- (exp x) -1)))) (/ -1 (- (exp x) -1)) (- (exp x) -1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (+ (* 7/192 x) 3/16))

simplify198.0ms (3.3%)

Memory

10.9MiB live, 160.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	146	1867
1	452	1658
2	1269	1590
3	4600	1575
0	8106	1274

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 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))))))
-1/2
(- (* 1/4 x) 1/2)
(- (* x (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* x (+ 1/4 (* (pow x 2) (- (* 1/480 (pow x 2)) 1/48)))) 1/2)
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 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 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* 1/2 (/ x (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 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))))))
(/ 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))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(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)))
(/ (- (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 (/ (- (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)))
(/ (- (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))
(* 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 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(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)))
(* 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)))
(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)))
(* 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))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(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)))
(/ (- (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 (/ (- (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)))
(/ (- (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))
(* 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 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(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)))
(* 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 (/ (- (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)))
(* 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))
(* 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
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 x) 1/2)
(fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))
(- (* x (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64))
(- (* x (+ 1/4 (* (pow x 2) (- (* 1/480 (pow x 2)) 1/48)))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/480 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
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))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #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)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/ -1 (+ 1 (exp x)))
(/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/ -1 (+ 1 (exp x)))
(/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/ -1 (+ 1 (exp x)))
(/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/ -1 (+ 1 (exp x)))
(/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(* 1/2 (/ x (sqrt 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #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 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #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 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) (.f64 x x) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #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)))
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/ -1 (+ 1 (exp x)))
(/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/ -1 (+ 1 (exp x)))
(/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/ -1 (+ 1 (exp x)))
(/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/ -1 (+ 1 (exp x)))
(/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) 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 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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(* 1/2 (/ x (sqrt 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #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 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.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)))) (pow.f64 x #s(literal 3 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 (-.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 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)))
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))

rewrite210.0ms (3.5%)

Memory

15.8MiB live, 216.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	188
0	56	186
1	244	138
2	1850	135
0	8756	135

Stop Event

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

Counts

18 → 630

Calls

Call 1

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

Outputs
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eval197.0ms (3.3%)

Memory: -0.6MiB live, 237.3MiB allocated
Compiler: Compiled 18 580 to 2 493 computations (86.6% saved)

prune30.0ms (0.5%)

Memory

-10.9MiB live, 64.4MiB allocated

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	833	10	843
Fresh	1	4	5
Picked	3	2	5
Done	0	0	0
Total	837	16	853

Accuracy

100.0%

Counts

853 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
	65.8%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/480 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
	65.0%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
▶	66.2%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	65.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	63.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
	65.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
	5.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	69.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	64.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
▶	64.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 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 (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
▶	3.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))

Compiler

Compiled 330 to 274 computations (17% saved)

simplify164.0ms (2.8%)

Memory

-7.9MiB live, 148.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #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 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
cost-diff	0	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
cost-diff	0	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
cost-diff	0	(fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))
cost-diff	0	(/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))))
cost-diff	0	(+.f64 x #s(literal 2 binary64))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #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)))

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	47	264
0	68	260
1	122	260
2	230	260
3	352	260
4	467	240
5	556	232
6	644	232
7	1059	232
8	3494	232
9	7727	232
0	8370	232

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

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

localize162.0ms (2.7%)

Memory

-17.7MiB live, 114.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.05859375	(fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.17578125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.7109375	(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.962586403447396	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.17578125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.40625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.962586403447396	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
accuracy	40.22189868345107	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
accuracy	0	(fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))
accuracy	0.00390625	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))))
accuracy	0.015625	(/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))))
accuracy	21.23662349980976	#s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))
accuracy	0	(+.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
accuracy	22.39028801023075	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))
accuracy	0	(exp.f64 x)
accuracy	0.00390625	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
accuracy	0.0078125	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

63.0ms	245×	0	valid
3.0ms	3×	5	exit
3.0ms	4×	2	valid
2.0ms	4×	1	valid

Compiler

Compiled 199 to 39 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 14.0ms (26.2% of total)

ival-div: 11.0ms (20.6% of total)

ival-add: 8.0ms (15% of total)

ival-sqrt: 7.0ms (13.1% of total)

const: 4.0ms (7.5% of total)

ival-expm1: 3.0ms (5.6% of total)

adjust: 2.0ms (3.7% of total)

ival-exp: 2.0ms (3.7% of total)

ival-sub: 1.0ms (1.9% of total)

exact: 1.0ms (1.9% of total)

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

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

series16.0ms (0.3%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

20 → 240

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

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

3.0ms

-inf

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

2.0ms

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

simplify204.0ms (3.4%)

Memory

22.0MiB live, 174.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	163	2292
1	511	2052
2	1423	1926
3	3748	1859
4	7963	1859
0	8006	1592

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 238

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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
-1/2
(- (* 1/4 x) 1/2)
(- (* x (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* x (+ 1/4 (* (pow x 2) (- (* 1/480 (pow x 2)) 1/48)))) 1/2)
-1/2
(- (* 1/4 x) 1/2)
(- (* 1/4 x) 1/2)
(- (* 1/4 x) 1/2)
(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 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))))))
(* 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)))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt 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))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(/ 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))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(exp x)
(exp x)
(exp x)
(exp x)
(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)))
(/ (- (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))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(* 1/4 x)
(* x (- 1/4 (* 1/2 (/ 1 x))))
(* x (- 1/4 (* 1/2 (/ 1 x))))
(* x (- 1/4 (* 1/2 (/ 1 x))))
(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)))
(* 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))))))
(* (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 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (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)))
(* 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 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(exp x)
(exp x)
(exp x)
(exp x)
(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)))
(/ (- (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))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(/ -1 (+ 1 (exp x)))
(* 1/4 x)
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/4)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/4)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/4)))
(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)))
(* 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)))
(* (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))))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (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)))
(* 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 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(* 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 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 x) 1/2)
(fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))
(- (* x (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64))
(- (* x (+ 1/4 (* (pow x 2) (- (* 1/480 (pow x 2)) 1/48)))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/480 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 x) 1/2)
(fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))
(- (* 1/4 x) 1/2)
(fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))
(- (* 1/4 x) 1/2)
(fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
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(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #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 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 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 (+.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 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 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))
(* 7/192 (pow x 2))
(.f64 (.f64 #s(literal 7/192 binary64) x) x)
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #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)))
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))

rewrite169.0ms (2.8%)

Memory

-27.3MiB live, 253.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	239
0	68	235
1	284	207
2	1829	207
0	8340	207

Stop Event

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

Counts

20 → 590

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

Outputs
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eval170.0ms (2.8%)

Memory: 14.9MiB live, 220.6MiB allocated
Compiler: Compiled 16 404 to 2 687 computations (83.6% saved)

prune115.0ms (1.9%)

Memory

7.3MiB live, 80.3MiB allocated

Pruning

19 alts after pruning (13 fresh and 6 done)

	Pruned	Kept	Total
New	862	4	866
Fresh	0	9	9
Picked	1	4	5
Done	0	2	2
Total	863	19	882

Accuracy

100.0%

Counts

882 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
	65.8%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/480 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
	65.0%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
✓	66.2%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	65.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	63.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
	65.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x))))
	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
▶	5.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	69.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	64.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	64.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 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 (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))))
▶	2.8%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
▶	3.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
	2.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) (*.f64 #s(literal 7/192 binary64) x)))))
▶	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)))))

Compiler

Compiled 373 to 311 computations (16.6% saved)

simplify248.0ms (4.1%)

Memory

9.6MiB live, 197.2MiB 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 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
cost-diff	320	(fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
cost-diff	0	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
cost-diff	0	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)))
cost-diff	0	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64))))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)))))
cost-diff	0	(.f64 (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
cost-diff	0	(exp.f64 x)
cost-diff	0	(-.f64 (exp.f64 x) #s(literal -1 binary64))
cost-diff	0	(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	430
0	76	426
1	134	426
2	250	426
3	407	426
4	640	401
5	844	391
6	1114	391
7	1521	391
8	3758	391
9	7475	391
0	8385	369

Stop Event

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

Calls

Call 1

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

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

localize171.0ms (2.9%)

Memory

-46.1MiB live, 310.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.35546875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.390625	(*.f64 #s(literal 7/192 binary64) x)
accuracy	19.70178131092696	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
accuracy	34.66017768670929	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
accuracy	0.1796875	(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.35546875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	19.70178131092696	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
accuracy	34.74272001557026	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x))
accuracy	0.35546875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	19.70178131092696	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)))))
accuracy	20.13159287842865	#s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64))
accuracy	34.74272001557026	#s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64))))
accuracy	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	19.16869058120812	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	35.19578747326907	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0	(exp.f64 x)
accuracy	0.00390625	(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
accuracy	0.0078125	(-.f64 (exp.f64 x) #s(literal -1 binary64))
accuracy	0.54296875	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))

Samples

68.0ms	34×	5	exit
65.0ms	213×	0	valid
4.0ms	6×	1	valid
1.0ms	2×	2	valid
0.0ms	1×	1	exit

Compiler

Compiled 270 to 42 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 107.0ms

ival-mult: 32.0ms (29.9% of total)

adjust: 30.0ms (28.1% of total)

ival-add: 10.0ms (9.4% of total)

ival-pow: 9.0ms (8.4% of total)

const: 8.0ms (7.5% of total)

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

ival-sqrt: 4.0ms (3.7% of total)

ival-exp: 3.0ms (2.8% of total)

ival-expm1: 3.0ms (2.8% of total)

ival-sub: 2.0ms (1.9% of total)

exact: 1.0ms (0.9% of total)

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

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

series26.0ms (0.4%)

Memory

-4.5MiB live, 32.7MiB allocated

Counts

23 → 276

Calls

Call 1

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

Outputs
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 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 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 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 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt 1/2) (taylor 0 x) (#s(alt (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2)))) (taylor 0 x) (#s(alt (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2)))))) (taylor 0 x) (#s(alt (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2)))))) (taylor 0 x) (#s(alt (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 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 (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>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 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 (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 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)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 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)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 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)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 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)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 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)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 7/192 (/ (pow x 3) (sqrt 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 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 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 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 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor -inf x) (#s(alt #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) (patch #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) (patch #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) (patch #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) (patch #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 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 (* 7/192 x) (taylor -inf x) (#s(alt (.f64 #s(literal 7/192 binary64) x) (patch (.f64 #s(literal 7/192 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor -inf x) (#s(alt (.f64 #s(literal 7/192 binary64) x) (patch (.f64 #s(literal 7/192 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor -inf x) (#s(alt (.f64 #s(literal 7/192 binary64) x) (patch (.f64 #s(literal 7/192 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor -inf x) (#s(alt (.f64 #s(literal 7/192 binary64) x) (patch (.f64 #s(literal 7/192 binary64) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

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

4.0ms

inf

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

3.0ms

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

simplify213.0ms (3.6%)

Memory

34.6MiB live, 151.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	177	3025
1	540	2746
2	1505	2521
3	4059	2439
4	7641	2439
0	8206	2111

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 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 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))))))
(* 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)))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt 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))))))
(* 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)))))
(* 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)))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(+ 1/2 (* x (+ 3/16 (* 7/192 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 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))))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(* 7/192 x)
(* 7/192 x)
(* 7/192 x)
(* 7/192 x)
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(exp x)
(exp x)
(exp x)
(exp x)
(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)))
(/ (- (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))
(* 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))
(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)))
(* 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))))))
(* (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 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (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)))
(* 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))))))
(* (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 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))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(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)))
(* 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))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(* 7/192 x)
(* 7/192 x)
(* 7/192 x)
(* 7/192 x)
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(exp x)
(exp x)
(exp x)
(exp x)
(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)))
(/ (- (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))
(* 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))
(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)))
(* 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)))
(* (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))))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (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)))
(* 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)))
(* (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 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))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(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)))
(* 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)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(* 7/192 x)
(* 7/192 x)
(* 7/192 x)
(* 7/192 x)

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 x #s(literal -1/64 binary64) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) #s(literal 1/96 binary64)) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (sqrt.f64 #s(literal 1/2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* 3/16 (/ x (sqrt 2)))
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 1/2 (/ x (sqrt 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 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)))
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
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(*.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #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 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* 7/192 (pow x 2))
(.f64 (.f64 #s(literal 7/192 binary64) x) x)
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 (fma.f64 #s(literal 7/192 binary64) x (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64))) x)
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(*.f64 (fma.f64 #s(literal 7/192 binary64) x (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64))) x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #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 (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)))) (pow.f64 x #s(literal 3 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 (-.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #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 (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)))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (fma.f64 (/.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)))) (pow.f64 x #s(literal 3 binary64)))
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 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)))
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)

rewrite238.0ms (4%)

Memory

-28.5MiB live, 128.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	387
0	76	381
1	285	345
2	2196	345
0	8251	323

Stop Event

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

Counts

23 → 996

Calls

Call 1

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

Outputs
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eval436.0ms (7.3%)

Memory: 31.1MiB live, 216.0MiB allocated
Compiler: Compiled 33 888 to 4 923 computations (85.5% saved)

prune161.0ms (2.7%)

Memory

-2.7MiB live, 130.8MiB allocated

Pruning

24 alts after pruning (13 fresh and 11 done)

	Pruned	Kept	Total
New	1 332	8	1 340
Fresh	3	5	8
Picked	0	5	5
Done	0	6	6
Total	1 335	24	1 359

Accuracy

100.0%

Counts

1 359 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
	68.9%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(literal 1/2 binary64))))
	65.8%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/480 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
	65.0%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
✓	66.2%	(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	65.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	63.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
	65.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x))))
	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
✓	5.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	69.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	64.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	64.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 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 (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))))
	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 x (.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) 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 (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
	4.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (* 7/192 x) x) (+ (* 3/16 x) 1/2)) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
	2.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (* 7/192 x) x) (+ (* 3/16 x) 1/2)) (.f64 (.f64 #s(literal 7/192 binary64) x) x)))))
✓	3.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
	2.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) (*.f64 #s(literal 7/192 binary64) x)))))
✓	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)))))
	2.8%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (*.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))

Compiler

Compiled 633 to 372 computations (41.2% saved)

regimes31.0ms (0.5%)

Memory

-12.6MiB live, 63.4MiB allocated

Counts

33 → 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 x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 x (.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (* 7/192 x) x) (+ (* 3/16 x) 1/2)) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 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 (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) (*.f64 #s(literal 7/192 binary64) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (* 7/192 x) x) (+ (* 3/16 x) 1/2)) (.f64 (.f64 #s(literal 7/192 binary64) x) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (*.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (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 (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #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 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/480 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))

Calls

3 calls:

11.0ms

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

11.0ms

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 24 to 20 computations (16.7% saved)

regimes26.0ms (0.4%)

Memory

18.9MiB live, 57.1MiB allocated

Counts

30 → 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 x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 x (.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (* 7/192 x) x) (+ (* 3/16 x) 1/2)) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 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 (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) (*.f64 #s(literal 7/192 binary64) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (* 7/192 x) x) (+ (* 3/16 x) 1/2)) (.f64 (.f64 #s(literal 7/192 binary64) x) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (*.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (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 (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #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 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/480 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

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

Calls

3 calls:

9.0ms

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

8.0ms

7.0ms

(/.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
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 24 to 20 computations (16.7% saved)

regimes31.0ms (0.5%)

Memory

-26.9MiB live, 49.9MiB allocated

Accuracy

Total -44.0b remaining (-228%)

Threshold costs -44b (-228%)

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 x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 #s(literal 1/4 binary64) x #s(literal -1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/.f64 (.f64 x (.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (* 7/192 x) x) (+ (* 3/16 x) 1/2)) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 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 (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x)) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(approx (+ (* 7/192 x) 3/16) (*.f64 #s(literal 7/192 binary64) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(approx (+ ( (* 7/192 x) x) (+ (* 3/16 x) 1/2)) (.f64 (.f64 #s(literal 7/192 binary64) x) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (*.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x #s(literal -1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (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 (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #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 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) #s(approx (/ -1 (- (exp x) -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/480 binary64) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #s(literal 1/4 binary64)) x #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 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (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:

13.0ms

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

10.0ms

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
69.9%	1	`x`
69.9%	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))))`
69.9%	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 24 to 20 computations (16.7% saved)

simplify24.0ms (0.4%)

Memory

20.7MiB live, 58.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
2	26	28
3	27	28
4	28	28

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

(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)))

soundness347.0ms (5.8%)

Memory

-8.1MiB live, 304.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	444
1	252	410
2	661	410
3	1434	404
4	2557	324
5	5968	289
0	8342	234
0	10	33
0	17	33
1	63	19
2	429	19
3	4997	19
0	8103	15

Stop Event

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

Compiler

Compiled 48 to 37 computations (22.9% saved)

preprocess52.0ms (0.9%)

Memory: 23.8MiB live, 62.6MiB allocated
Compiler: Compiled 58 to 42 computations (27.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample951.0ms (15.9%)

explain160.0ms (2.7%)

preprocess210.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify152.0ms (2.6%)

localize48.0ms (0.8%)

series5.0ms (0.1%)

simplify160.0ms (2.7%)

rewrite212.0ms (3.5%)

eval166.0ms (2.8%)

prune19.0ms (0.3%)

simplify116.0ms (1.9%)

localize111.0ms (1.9%)

series16.0ms (0.3%)

simplify198.0ms (3.3%)

rewrite210.0ms (3.5%)

eval197.0ms (3.3%)

prune30.0ms (0.5%)

simplify164.0ms (2.8%)

localize162.0ms (2.7%)

series16.0ms (0.3%)

simplify204.0ms (3.4%)

rewrite169.0ms (2.8%)

eval170.0ms (2.8%)

prune115.0ms (1.9%)

simplify248.0ms (4.1%)

localize171.0ms (2.9%)

series26.0ms (0.4%)

simplify213.0ms (3.6%)

rewrite238.0ms (4%)

eval436.0ms (7.3%)

prune161.0ms (2.7%)

regimes31.0ms (0.5%)

regimes26.0ms (0.4%)

regimes31.0ms (0.5%)

simplify24.0ms (0.4%)

soundness347.0ms (5.8%)

preprocess52.0ms (0.9%)

end0.0ms (0%)

Profiling