Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

1.9MiB live, 1.9MiB 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)

sample915.0ms (16.7%)

Memory

52.4MiB live, 894.1MiB allocated

Samples

467.0ms	8 256×	0	valid
138.0ms	2 542×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 397.0ms

ival-expm1: 129.0ms (32.5% of total)

ival-div: 97.0ms (24.4% of total)

ival-mult: 80.0ms (20.2% of total)

ival-sqrt: 73.0ms (18.4% of total)

ival-true: 7.0ms (1.8% of total)

exact: 7.0ms (1.8% of total)

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

Bogosity

explain236.0ms (4.3%)

Memory

-24.3MiB live, 226.8MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	158	1
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	158	1

Confusion

	Predicted +	Predicted -
+	158	0
-	0	98

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	158	0	0
-	0	1	97

Precision?

0.9937106918238994

Recall?

1.0

Freqs

test

number	freq
0	98
2	158

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms

512×

valid

Compiler

Compiled 196 to 77 computations (60.7% saved)

Precisions

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

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

ival-expm1: 6.0ms (24.3% of total)

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

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

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

exact: 1.0ms (4.1% of total)

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

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

preprocess204.0ms (3.7%)

Memory

23.7MiB live, 135.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB 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
▶	39.2%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify182.0ms (3.3%)

Memory

-1.6MiB live, 148.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
cost-diff	192	(-.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	6336	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
cost-diff	7232	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize32.0ms (0.6%)

Memory

-4.9MiB live, 32.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 x)
accuracy	0.01171875	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	36.904774547064996	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	36.917094631683945	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

19.0ms

256×

valid

Compiler

Compiled 92 to 22 computations (76.1% saved)

Precisions

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

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

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

ival-div: 2.0ms (16.9% of total)

ival-mult: 2.0ms (16.9% of total)

ival-sqrt: 2.0ms (16.9% 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

3.9MiB live, 3.9MiB 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))

simplify166.0ms (3%)

Memory

15.3MiB live, 137.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	241
1	258	207
2	680	207
3	1464	201
4	2608	191
5	6086	187
0	8257	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)

rewrite183.0ms (3.3%)

Memory

-16.7MiB live, 190.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
0	17	35
1	63	21
2	429	21
3	4997	21
0	8103	17

Stop Event

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

Counts

5 → 690

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)))))
(.f64 (/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)))
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(-.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 (exp.f64 (log1p.f64 (exp.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)

eval137.0ms (2.5%)

Memory: 22.4MiB live, 139.6MiB allocated
Compiler: Compiled 16 758 to 2 427 computations (85.5% saved)

prune59.0ms (1.1%)

Memory

-2.1MiB live, 35.7MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	708	6	714
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	709	6	715

Accuracy

100.0%

Counts

715 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	62.3%	(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))))
▶	64.2%	(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))))
▶	62.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	62.7%	#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))))

Compiler

Compiled 216 to 170 computations (21.3% saved)

simplify173.0ms (3.1%)

Memory

-2.0MiB live, 123.1MiB 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	409	146
6	487	146
7	891	146
8	3237	146
9	7151	146
0	8176	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)

localize78.0ms (1.4%)

Memory

6.4MiB live, 44.2MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0625	(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	0.06640625	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.11328125	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.94438690762853	#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	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0	(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	23.1333472013189	#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	(+.f64 #s(literal 2 binary64) x)
accuracy	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	24.01741591903097	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	20.15165851914354	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
accuracy	0	(exp.f64 x)
accuracy	0.0078125	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

62.0ms

256×

valid

Compiler

Compiled 365 to 58 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 9.0ms (29.2% of total)

ival-add: 7.0ms (22.7% of total)

const: 4.0ms (13% of total)

ival-expm1: 3.0ms (9.7% of total)

ival-sqrt: 3.0ms (9.7% of total)

ival-div: 2.0ms (6.5% of total)

ival-exp: 2.0ms (6.5% of total)

ival-sub: 1.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series29.0ms (0.5%)

Memory

-24.7MiB live, 19.1MiB 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
25.0ms	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

25.0ms

-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))

simplify149.0ms (2.7%)

Memory

27.1MiB live, 99.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	326
1	322	288
2	922	280
3	3272	274
4	6534	274
0	8223	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))

rewrite227.0ms (4.1%)

Memory

11.4MiB live, 165.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	188
0	47	188
1	179	132
2	1267	132
0	8450	132

Stop Event

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

Counts

17 → 436

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))))
(.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64))) (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))))
(.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (neg.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))))
(.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x))))
(.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
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(/.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 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 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 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))

eval78.0ms (1.4%)

Memory: -24.1MiB live, 136.6MiB allocated
Compiler: Compiled 13 371 to 1 928 computations (85.6% saved)

prune9.0ms (0.2%)

Memory

23.7MiB live, 23.7MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	468	1	469
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	468	7	475

Accuracy

100.0%

Counts

475 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	62.3%	(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))))
✓	64.2%	(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))))
▶	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
✓	62.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	62.7%	#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))))

Compiler

Compiled 129 to 102 computations (20.9% saved)

simplify385.0ms (7%)

Memory

-1.0MiB live, 160.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	142
0	39	142
1	63	142
2	95	142
3	219	142
4	514	125
5	749	119
6	1030	115
7	1513	115
8	3715	115
9	7315	115
0	8223	109

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

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

localize94.0ms (1.7%)

Memory

-4.8MiB live, 79.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
accuracy	0.00390625	(+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))
accuracy	0.00390625	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	23.1333472013189	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64)))
accuracy	0.1875	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.38671875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.87980719584232	#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))))

Samples

56.0ms	243×	0	valid
8.0ms	7×	2	valid
2.0ms	6×	1	valid

Compiler

Compiled 259 to 53 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-mult: 27.0ms (49.9% of total)

const: 9.0ms (16.6% of total)

ival-add: 6.0ms (11.1% of total)

ival-div: 5.0ms (9.2% of total)

ival-sqrt: 3.0ms (5.5% of total)

ival-expm1: 3.0ms (5.5% of total)

adjust: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

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

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

series14.0ms (0.2%)

Memory

-27.8MiB live, 9.8MiB allocated

Counts

10 → 34

Calls

Call 1

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

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

8.0ms

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

2.0ms

inf

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

2.0ms

-inf

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

simplify279.0ms (5.1%)

Memory

12.6MiB live, 168.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	472
1	411	403
2	1211	369
3	3287	348
4	7897	348
0	8461	305

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 33

Calls

Call 1

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

rewrite190.0ms (3.5%)

Memory

12.6MiB live, 171.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	127
0	39	127
1	173	106
2	1423	102
0	8100	99

Stop Event

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

Counts

10 → 493

Calls

Call 1

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

eval90.0ms (1.6%)

Memory: 10.3MiB live, 165.9MiB allocated
Compiler: Compiled 24 800 to 2 735 computations (89% saved)

prune13.0ms (0.2%)

Memory

0.4MiB live, 36.4MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	522	3	525
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	523	9	532

Accuracy

100.0%

Counts

532 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	62.3%	(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))))
✓	64.2%	(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))))
✓	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
✓	62.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	62.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶	62.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (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))))) x (sqrt.f64 #s(literal 2 binary64))))
▶	62.6%	#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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)) x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)))

Compiler

Compiled 235 to 175 computations (25.5% saved)

simplify145.0ms (2.6%)

Memory

17.5MiB live, 205.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (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)))))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (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))))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (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))))) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	2368	(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))))
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 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)) x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)))
cost-diff	704	(fma.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)) x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
cost-diff	832	(*.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)) x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)
cost-diff	1536	(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	43	436
0	67	448
1	136	413
2	330	358
3	742	357
4	1470	329
5	2198	322
6	4019	322
7	5149	322
8	6313	322
0	8208	322

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

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

localize214.0ms (3.9%)

Memory

-69.5MiB live, 130.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.12890625	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
accuracy	0.1875	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.87980719584232	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.38671875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.4375	(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
accuracy	1.0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.87980719584232	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (/ 1/2 (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))))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.4375	(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.87980719584232	#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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)) x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)))

Samples

176.0ms	243×	0	valid
6.0ms	7×	2	valid
3.0ms	6×	1	valid

Compiler

Compiled 746 to 86 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 166.0ms

ival-mult: 135.0ms (81.5% of total)

ival-div: 10.0ms (6% of total)

ival-add: 9.0ms (5.4% of total)

const: 4.0ms (2.4% of total)

ival-sqrt: 3.0ms (1.8% of total)

ival-expm1: 3.0ms (1.8% of total)

adjust: 1.0ms (0.6% of total)

exact: 1.0ms (0.6% of total)

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

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

series9.0ms (0.2%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

17 → 37

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

3.0ms

inf

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

2.0ms

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

simplify213.0ms (3.9%)

Memory

-6.5MiB live, 145.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	546
1	421	544
2	1289	488
3	3371	462
0	8961	415

Stop Event

1×	iter limit
1×	node limit

Counts

37 → 37

Calls

Call 1

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

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

rewrite258.0ms (4.7%)

Memory

2.2MiB live, 247.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	332
0	67	337
1	307	285
2	2930	237
0	8794	237

Stop Event

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

Counts

17 → 883

Calls

Call 1

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

Outputs
(.f64 (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64))) (pow.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64))))) (neg.f64 (neg.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (neg.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))) (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) x (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64))))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) (neg.f64 (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) x))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) (neg.f64 (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) (neg.f64 (.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64) (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (neg.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(/.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) x (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)))) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)))))
(/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) x)) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64))) (/.f64 (-.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64) (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64)))))
(fma.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x))
(fma.f64 (/.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) #s(literal -1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x))
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(fma.f64 (/.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x)))
(fma.f64 (/.f64 (*.f64 x #s(literal 7/192 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fma.f64 #s(literal 3/16 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) x)))
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(-.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))) (/.f64 (pow.f64 (.f64 x #s(literal 7/192 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(-.f64 (/.f64 (pow.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 2 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(+.f64 (.f64 (.f64 x #s(literal 7/192 binary64)) #s(literal 1 binary64)) #s(literal 3/16 binary64))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal 7/192 binary64))) #s(literal 3/16 binary64))
(+.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64))
(+.f64 #s(literal 3/16 binary64) (.f64 (.f64 x #s(literal 7/192 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 3/16 binary64) (.f64 #s(literal 1 binary64) (.f64 x #s(literal 7/192 binary64))))
(+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))

eval212.0ms (3.9%)

Memory: 26.8MiB live, 219.2MiB allocated
Compiler: Compiled 53 027 to 4 738 computations (91.1% saved)

prune22.0ms (0.4%)

Memory

15.9MiB live, 52.2MiB allocated

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	916	4	920
Fresh	0	0	0
Picked	3	0	3
Done	0	6	6
Total	919	10	929

Accuracy

100.0%

Counts

929 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	62.3%	(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))))
✓	64.2%	(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))))
✓	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
✓	62.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	62.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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))))
	62.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #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))))
	62.6%	#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)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x (*.f64 (fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
	69.3%	#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 #s(approx (+ ( (+ (* (/ 1 (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ (/ 1/2 (sqrt 2)) x)) x) (/ (sqrt 2) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)))

Compiler

Compiled 720 to 294 computations (59.2% saved)

regimes42.0ms (0.8%)

Memory

-30.2MiB live, 18.6MiB allocated

Counts

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

33.0ms

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

4.0ms

(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)

regimes11.0ms (0.2%)

Memory

16.1MiB live, 16.1MiB allocated

Accuracy

Total -4.9b remaining (-25%)

Threshold costs -4.9b (-25%)

Counts

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

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

Calls

3 calls:

4.0ms

3.0ms

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

3.0ms

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

Results

Accuracy	Segments	Branch
69.3%	1	`x`
69.3%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
69.3%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify52.0ms (1%)

Memory

-3.3MiB live, 34.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness372.0ms (6.8%)

Memory

-26.8MiB live, 134.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	241
1	258	207
2	680	207
3	1464	201
4	2608	191
5	6086	187
0	8257	155
0	10	35
0	17	35
1	63	21
2	429	21
3	4997	21
0	8103	17

Stop Event

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

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess17.0ms (0.3%)

Memory: 19.4MiB live, 19.4MiB 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%)

sample915.0ms (16.7%)

explain236.0ms (4.3%)

preprocess204.0ms (3.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify182.0ms (3.3%)

localize32.0ms (0.6%)

series3.0ms (0.1%)

simplify166.0ms (3%)

rewrite183.0ms (3.3%)

eval137.0ms (2.5%)

prune59.0ms (1.1%)

simplify173.0ms (3.1%)

localize78.0ms (1.4%)

series29.0ms (0.5%)

simplify149.0ms (2.7%)

rewrite227.0ms (4.1%)

eval78.0ms (1.4%)

prune9.0ms (0.2%)

simplify385.0ms (7%)

localize94.0ms (1.7%)

series14.0ms (0.2%)

simplify279.0ms (5.1%)

rewrite190.0ms (3.5%)

eval90.0ms (1.6%)

prune13.0ms (0.2%)

simplify145.0ms (2.6%)

localize214.0ms (3.9%)

series9.0ms (0.2%)

simplify213.0ms (3.9%)

rewrite258.0ms (4.7%)

eval212.0ms (3.9%)

prune22.0ms (0.4%)

regimes42.0ms (0.8%)

regimes11.0ms (0.2%)

simplify52.0ms (1%)

soundness372.0ms (6.8%)

preprocess17.0ms (0.3%)

end0.0ms (0%)

Profiling