Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

2.3MiB live, 2.3MiB 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)

sample1.2s (21.1%)

Memory

89.4MiB live, 990.4MiB allocated

Samples

471.0ms	8 256×	0	valid
367.0ms	2 684×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 373.0ms

ival-expm1: 121.0ms (32.4% of total)

ival-mult: 83.0ms (22.2% of total)

ival-div: 78.0ms (20.9% of total)

ival-sqrt: 75.0ms (20.1% of total)

ival-true: 7.0ms (1.9% of total)

exact: 6.0ms (1.6% of total)

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

Bogosity

explain125.0ms (2.3%)

Memory

-31.2MiB live, 128.6MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	172	1
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	172	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	1	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	1
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	1
↳	`(exp.f64 x)`	overflow	1
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	1

Confusion

	Predicted +	Predicted -
+	173	0
-	0	83

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	173	0	0
-	0	1	82

Precision?

0.9942528735632183

Recall?

1.0

Freqs

test

number	freq
0	83
1	1
2	172

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 151 to 44 computations (70.9% saved)

Precisions

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

ival-exp: 7.0ms (29.4% of total)

ival-expm1: 6.0ms (25.2% of total)

ival-div: 3.0ms (12.6% of total)

ival-mult: 3.0ms (12.6% of total)

ival-sqrt: 3.0ms (12.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess233.0ms (4.2%)

Memory

13.6MiB live, 138.5MiB 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	252	13
6	528	13
7	2129	13
8	7288	13
0	10	12
0	17	12
1	29	12
2	35	12
3	47	12
4	73	7
5	124	5
6	201	5
7	591	5
8	2986	5
9	6913	5
0	8121	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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	34.5%	(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)

simplify169.0ms (3.1%)

Memory

8.2MiB live, 124.8MiB 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	124	31
6	201	31
7	591	31
8	2986	31
9	6913	31
0	8121	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)

localize27.0ms (0.5%)

Memory

-11.9MiB live, 26.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.21484375000000003	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	39.48674955996317	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	39.5387767508252	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

20.0ms

256×

valid

Compiler

Compiled 92 to 22 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-exp: 4.0ms (31.1% of total)

ival-expm1: 3.0ms (23.3% of total)

ival-div: 2.0ms (15.6% of total)

ival-mult: 2.0ms (15.6% of total)

ival-sqrt: 2.0ms (15.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated

Counts

5 → 25

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))))
(exp.f64 x)

Outputs
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))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(exp x)

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))) (exp x))
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))) (exp x))
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))) (exp x))

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))) (exp x))

1.0ms

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

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))) (exp x))

simplify165.0ms (3%)

Memory

14.2MiB live, 124.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	241
1	258	207
2	692	207
3	1478	201
4	2630	191
5	6089	187
0	8248	155

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 24

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))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(exp x)

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

rewrite164.0ms (3%)

Memory

-8.3MiB live, 157.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
0	17	35
1	63	21
2	429	21
3	5021	21
0	8045	17

Stop Event

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

Counts

5 → 689

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))))
(exp.f64 x)

Outputs
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 #s(literal 4 binary64) x)) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 4 binary64)))) (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 #s(literal 4 binary64) x)) (expm1.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (expm1.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 x) #s(literal 4 binary64))))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 #s(literal 6 binary64) x)) (expm1.f64 x)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 8 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (*.f64 #s(literal 4 binary64) x)) (pow.f64 (exp.f64 #s(literal 2 binary64)) x)))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 #s(literal 6 binary64) x)) (expm1.f64 x)) (+.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal 12 binary64)))) (fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 4 binary64))) (pow.f64 (exp.f64 x) #s(literal 8 binary64))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(.f64 (pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 4 binary64) x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 6 binary64) x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 #s(literal 3 binary64) x))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
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(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (/.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (neg.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64))))
(fma.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (pow.f64 (-.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))))
(expm1.f64 x)
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 x))))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 x)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64))) (neg.f64 (expm1.f64 x)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 x)))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (exp.f64 x) (expm1.f64 (.f64 x #s(literal 2 binary64))))) (pow.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)))
(+.f64 (neg.f64 (neg.f64 (exp.f64 x))) #s(literal -1 binary64))
(+.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (neg.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64))))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 (.f64 (.f64 (log.f64 (expm1.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (expm1.f64 x))) #s(literal -1 binary64)))
(.f64 (/.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (hypot.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (exp.f64 x)))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (hypot.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (exp.f64 x)))
(*.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(.f64 (neg.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))))) (pow.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))))) (pow.f64 (neg.f64 (expm1.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1 binary64))
(.f64 (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(pow.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 4 binary64) x)) (expm1.f64 x))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 6 binary64) x)) (expm1.f64 x))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 (expm1.f64 x)))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (sqrt.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (expm1.f64 x) (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (neg.f64 (expm1.f64 x)))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 4 binary64) x))) (sqrt.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 6 binary64) x))) (sqrt.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (expm1.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (sqrt.f64 (expm1.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (expm1.f64 x))))
(neg.f64 (/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)

eval112.0ms (2%)

Memory: 16.4MiB live, 142.4MiB allocated
Compiler: Compiled 16 753 to 2 426 computations (85.5% saved)

prune16.0ms (0.3%)

Memory

1.9MiB live, 37.8MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	706	7	713
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	707	7	714

Accuracy

100.0%

Counts

714 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	67.4%	(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))))
▶	68.7%	(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))))
▶	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	72.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	67.7%	#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)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
	68.5%	#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))))

Compiler

Compiled 264 to 206 computations (22% saved)

simplify247.0ms (4.5%)

Memory

-5.4MiB live, 114.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	29	202
0	47	202
1	71	202
2	98	202
3	176	202
4	312	162
5	413	146
6	491	146
7	889	146
8	3305	146
9	7294	146
0	8340	146

Stop Event

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

Calls

Call 1

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

localize68.0ms (1.2%)

Memory

3.7MiB live, 79.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(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))
accuracy	0.0234375	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.09765625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	20.689627716951787	#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)))
accuracy	0.0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.0	(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))))
accuracy	20.150379487751994	#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	0.0	(+.f64 #s(literal 2 binary64) x)
accuracy	0.0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	20.91766429454056	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0.0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	17.758897829745493	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0.0	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
accuracy	0.0	(exp.f64 x)
accuracy	0.01171875	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

52.0ms

256×

valid

Compiler

Compiled 365 to 58 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-add: 12.0ms (30.5% of total)

ival-mult: 9.0ms (22.9% of total)

ival-exp: 5.0ms (12.7% of total)

const: 4.0ms (10.2% of total)

ival-expm1: 3.0ms (7.6% of total)

ival-sqrt: 3.0ms (7.6% of total)

ival-div: 2.0ms (5.1% of total)

ival-sub: 1.0ms (2.5% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

17 → 39

Calls

Call 1

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

Outputs
(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))))))
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
1/2
(+ 1/2 (* 1/6 x))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	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)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (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))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))
2.0ms	x	@	-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)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (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))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))
1.0ms	x	@	0	((sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (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)) (+ 2 x) (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))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))

Time

Variable

Point

Expression

2.0ms

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)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (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))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))

2.0ms

-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)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (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))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))

1.0ms

((sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (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))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))

simplify172.0ms (3.1%)

Memory

7.2MiB live, 123.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	326
1	322	288
2	934	280
3	3275	274
4	6472	274
0	8163	227

Stop Event

1×	iter limit
1×	node limit

Counts

39 → 38

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

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

rewrite257.0ms (4.7%)

Memory

-2.6MiB live, 191.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	188
0	47	188
1	179	132
2	1267	132
0	8628	132

Stop Event

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

Counts

17 → 506

Calls

Call 1

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

Outputs
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (hypot.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (exp.f64 x)))
(.f64 (sqrt.f64 (neg.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
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(fma.f64 (.f64 x (fma.f64 #s(literal 1/36 binary64) (.f64 x x) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 x (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(fma.f64 x (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (pow.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))
(.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))))))
(.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (*.f64 (neg.f64 x) #s(literal 1/12 binary64))))))
(.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (pow.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))) (+.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (neg.f64 x) #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (neg.f64 x) #s(literal 1/12 binary64)))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x)) (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (neg.f64 x) #s(literal 1/12 binary64)))) (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))))
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(+.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))))
(+.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))

eval107.0ms (2%)

Memory: -12.1MiB live, 120.6MiB allocated
Compiler: Compiled 15 542 to 2 079 computations (86.6% saved)

prune280.0ms (5.1%)

Memory

-4.5MiB live, 32.9MiB allocated

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	533	6	539
Fresh	0	2	2
Picked	0	5	5
Done	0	0	0
Total	533	13	546

Accuracy

100.0%

Counts

546 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	68.7%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
▶	67.0%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
✓	67.4%	(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))))
✓	68.7%	(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))))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	2.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
	3.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
▶	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
	5.0%	(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)))))
✓	72.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	67.7%	#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)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
	68.5%	#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))))

Compiler

Compiled 486 to 358 computations (26.3% saved)

simplify142.0ms (2.6%)

Memory

12.5MiB live, 133.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.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 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	1344	(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 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 1 binary64))
cost-diff	0	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	352
0	78	349
1	120	349
2	174	349
3	325	349
4	732	322
5	1021	312
6	1298	308
7	1772	308
8	4047	308
9	7636	308
0	8161	299

Stop Event

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

Calls

Call 1

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

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

localize133.0ms (2.4%)

Memory

-27.6MiB live, 167.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.17578125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.4140625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.99609375	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.42613811311926	#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)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0390625	(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
accuracy	0.09765625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	20.443122282138187	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))
accuracy	41.52404417986323	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
accuracy	19.921000837484335	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)))
accuracy	41.5592114256318	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))
accuracy	0.0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.0	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
accuracy	0.01171875	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
accuracy	20.460258241923402	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
accuracy	0.01171875	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64))
accuracy	20.341896162500568	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))

Samples

92.0ms	242×	0	valid
5.0ms	7×	2	valid
3.0ms	6×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 579 to 100 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-add: 30.0ms (37.5% of total)

ival-mult: 20.0ms (25% of total)

ival-sqrt: 9.0ms (11.3% of total)

const: 7.0ms (8.8% of total)

ival-div: 5.0ms (6.3% of total)

ival-expm1: 3.0ms (3.8% of total)

adjust: 2.0ms (2.5% of total)

ival-exp: 2.0ms (2.5% of total)

ival-sub: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

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

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

series11.0ms (0.2%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

26 → 61

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

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

3.0ms

-inf

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

3.0ms

inf

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

simplify163.0ms (3%)

Memory

13.3MiB live, 123.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	165	649
1	537	580
2	1619	533
3	5807	529
0	8333	466

Stop Event

1×	iter limit
1×	node limit

Counts

61 → 60

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

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 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 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))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #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))
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)
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #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 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) 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))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp x)
(exp.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) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(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))
(* 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))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x (*.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 3) (sqrt 2)))
(*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 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))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (*.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.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 (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(*.f64 (-.f64 (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (+.f64 #s(literal 2 binary64) x) x)) x) x) #s(literal -1/6 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 (-.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)))

rewrite238.0ms (4.3%)

Memory

-7.8MiB live, 198.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	333
0	78	330
1	327	295
2	2572	291
0	8807	285

Stop Event

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

Counts

26 → 748

Calls

Call 1

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

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

eval125.0ms (2.3%)

Memory: -2.8MiB live, 230.3MiB allocated
Compiler: Compiled 33 859 to 3 975 computations (88.3% saved)

prune21.0ms (0.4%)

Memory

35.0MiB live, 72.2MiB allocated

Pruning

14 alts after pruning (5 fresh and 9 done)

	Pruned	Kept	Total
New	799	3	802
Fresh	1	2	3
Picked	1	4	5
Done	0	5	5
Total	801	14	815

Accuracy

100.0%

Counts

815 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	68.7%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	67.0%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
✓	67.4%	(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))))
✓	68.7%	(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))))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	2.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
▶	3.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
✓	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
▶	5.0%	(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)))))
✓	72.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	67.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
▶	2.9%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)))
▶	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)))

Compiler

Compiled 543 to 393 computations (27.6% saved)

simplify130.0ms (2.4%)

Memory

-37.7MiB live, 127.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)))
cost-diff	1344	(*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)
cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
cost-diff	0	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)))
cost-diff	0	(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
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	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	384	(/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))
cost-diff	640	(fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	960	(fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	528
0	86	524
1	141	516
2	243	516
3	533	516
4	1119	467
5	1799	453
6	2793	453
7	4757	453
8	6855	453
0	8024	424

Stop Event

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

Calls

Call 1

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

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

localize168.0ms (3.1%)

Memory

3.7MiB live, 147.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.4140625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.99609375	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.42613811311926	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)))
accuracy	41.525918944950234	#s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x))
accuracy	0.25	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
accuracy	0.4140625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.42613811311926	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)))
accuracy	41.39175944055689	#s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x))
accuracy	0.0390625	(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
accuracy	0.09765625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	20.443122282138187	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
accuracy	41.3826481630966	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
accuracy	0.0	(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	0.00390625	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	19.921000837484335	#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	41.50058294117952	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.07650375976844201	(fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy	0.14453125	(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
accuracy	0.17578125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	20.42613811311926	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))

Samples

109.0ms	217×	0	valid
17.0ms	22×	2	valid
11.0ms	16×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 881 to 114 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 32.0ms (43.2% of total)

ival-add: 13.0ms (17.6% of total)

ival-div: 9.0ms (12.2% of total)

const: 7.0ms (9.5% of total)

adjust: 5.0ms (6.8% of total)

ival-sqrt: 4.0ms (5.4% of total)

ival-expm1: 3.0ms (4.1% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.4%)

Memory

-24.4MiB live, 13.1MiB allocated

Counts

26 → 82

Calls

Call 1

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

Outputs
(* 1/2 (sqrt 2))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(* 1/4 (sqrt 2))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (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 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(+ (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)))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 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)))))
(/ 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))))
3/16
(+ 3/16 (* 7/192 x))
(* 3/16 x)
(* x (+ 3/16 (* 7/192 x)))
1/2
(+ 1/2 (* 1/6 x))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(/ x (sqrt 2))
(* 7/192 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(* 7/384 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(* 7/384 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 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))))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1 (* (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))))))

Calls

3 calls:

Time

Variable

Point

Expression

15.0ms

-inf

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

4.0ms

inf

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

3.0ms

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

simplify143.0ms (2.6%)

Memory

19.8MiB live, 138.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	253	1100
1	832	1006
2	2596	913
3	5944	869
0	8317	793

Stop Event

1×	iter limit
1×	node limit

Counts

82 → 82

Calls

Call 1

Inputs
(* 1/2 (sqrt 2))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(* 1/4 (sqrt 2))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (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 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(+ (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)))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 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)))))
(/ 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))))
3/16
(+ 3/16 (* 7/192 x))
(* 3/16 x)
(* x (+ 3/16 (* 7/192 x)))
1/2
(+ 1/2 (* 1/6 x))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(/ x (sqrt 2))
(* 7/192 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(* 7/384 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(* 7/384 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 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))))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1 (* (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))))))

Outputs
(* 1/2 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(*.f64 (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 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64)) #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64)) #s(literal 1/4 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 #s(literal 2 binary64) x)
(+ 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))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(+ (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))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)
(* 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)))
(* 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)))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (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 x)
(*.f64 #s(literal 3/16 binary64) x)
(* x (+ 3/16 (* 7/192 x)))
(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (* (pow x 2) (sqrt 2)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) #s(literal 7/192 binary64))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) #s(literal 7/192 binary64))) x) x)
(* 7/384 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 7/384 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(.f64 (.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/32 binary64)) (.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(*.f64 (fma.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/32 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64))))) (pow.f64 x #s(literal 3 binary64)))
(* 7/384 (* (pow x 2) (sqrt 2)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) #s(literal 7/384 binary64))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64))) x)
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/32 binary64)) (.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(* (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)))))
(.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x (*.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/6 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))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 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))))))
(*.f64 (+.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 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 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x))
(* 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))
(* 7/192 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/192 binary64))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(.f64 x (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64)) x (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal -3/16 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(.f64 (.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(.f64 (.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/32 binary64)) (.f64 #s(literal 7/384 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) x)))) x)
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(*.f64 (fma.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 3/32 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))
(.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/32 binary64)) (.f64 #s(literal 7/384 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x)) (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 (-.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)))

rewrite239.0ms (4.4%)

Memory

-9.8MiB live, 220.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	484
0	86	482
1	330	419
2	2470	407
0	8648	394

Stop Event

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

Counts

26 → 1 217

Calls

Call 1

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

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

eval167.0ms (3.1%)

Memory: 37.0MiB live, 316.1MiB allocated
Compiler: Compiled 50 012 to 4 947 computations (90.1% saved)

prune63.0ms (1.1%)

Memory

-30.2MiB live, 45.1MiB allocated

Pruning

16 alts after pruning (5 fresh and 11 done)

	Pruned	Kept	Total
New	979	5	984
Fresh	0	0	0
Picked	3	2	5
Done	0	9	9
Total	982	16	998

Accuracy

100.0%

Counts

998 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	68.7%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	67.0%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
✓	67.4%	(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))))
✓	68.7%	(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))))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	2.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
✓	3.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
	2.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
✓	4.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
✓	5.0%	(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)))))
✓	72.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	67.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64)) #s(literal 1/4 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
	67.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (.f64 (.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64))))))
	2.9%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 1/2 binary64))))

Compiler

Compiled 1 094 to 478 computations (56.3% saved)

regimes17.0ms (0.3%)

Memory

22.0MiB live, 22.0MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 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 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
(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 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
(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 (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (.f64 (.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 1/2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64)) #s(literal 1/4 binary64)))) x (sqrt.f64 #s(literal 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 (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (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)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (-.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
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Calls

3 calls:

6.0ms

5.0ms

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

5.0ms

(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)

regimes19.0ms (0.4%)

Memory

-21.7MiB live, 23.8MiB allocated

Accuracy

Total -45.7b remaining (-263.6%)

Threshold costs -45.7b (-263.6%)

Counts

20 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 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 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
(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 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
(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 (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (.f64 (.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))) x) #s(literal 1/2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64)) #s(literal 1/4 binary64)))) x (sqrt.f64 #s(literal 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 (+ (* (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (*.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (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)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))

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

Calls

3 calls:

8.0ms

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

5.0ms

4.0ms

(/.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
72.9%	1	`x`
72.9%	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))))`
72.9%	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)

simplify57.0ms (1%)

Memory

1.1MiB live, 39.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	28	19
2	39	19
3	69	19
4	114	14
5	289	12
6	730	12
7	2488	12
8	6362	12

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness290.0ms (5.3%)

Memory

14.1MiB live, 212.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
0	17	35
1	63	21
2	429	21
3	5021	21
0	8045	17
0	80	241
1	258	207
2	692	207
3	1478	201
4	2630	191
5	6089	187
0	8248	155

Stop Event

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

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess30.0ms (0.6%)

Memory: -16.3MiB live, 22.7MiB allocated
Compiler: Compiled 62 to 52 computations (16.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample1.2s (21.1%)

explain125.0ms (2.3%)

preprocess233.0ms (4.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify169.0ms (3.1%)

localize27.0ms (0.5%)

series3.0ms (0.1%)

simplify165.0ms (3%)

rewrite164.0ms (3%)

eval112.0ms (2%)

prune16.0ms (0.3%)

simplify247.0ms (4.5%)

localize68.0ms (1.2%)

series6.0ms (0.1%)

simplify172.0ms (3.1%)

rewrite257.0ms (4.7%)

eval107.0ms (2%)

prune280.0ms (5.1%)

simplify142.0ms (2.6%)

localize133.0ms (2.4%)

series11.0ms (0.2%)

simplify163.0ms (3%)

rewrite238.0ms (4.3%)

eval125.0ms (2.3%)

prune21.0ms (0.4%)

simplify130.0ms (2.4%)

localize168.0ms (3.1%)

series23.0ms (0.4%)

simplify143.0ms (2.6%)

rewrite239.0ms (4.4%)

eval167.0ms (3.1%)

prune63.0ms (1.1%)

regimes17.0ms (0.3%)

regimes19.0ms (0.4%)

simplify57.0ms (1%)

soundness290.0ms (5.3%)

preprocess30.0ms (0.6%)

end0.0ms (0%)

Profiling