Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze3.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (19.6%)

Memory

37.4MiB live, 953.7MiB allocated

Samples

524.0ms	8 256×	0	valid
195.0ms	2 665×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 480.0ms

ival-expm1: 162.0ms (33.8% of total)

ival-sqrt: 114.0ms (23.8% of total)

ival-mult: 96.0ms (20% of total)

ival-div: 85.0ms (17.7% of total)

ival-true: 10.0ms (2.1% of total)

exact: 8.0ms (1.7% of total)

ival-assert: 5.0ms (1% of total)

Bogosity

explain241.0ms (4.4%)

Memory

-16.7MiB live, 237.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
167	-	1	(-0.005549053536842374)	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
167	-	0	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
3	-	0	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	-	0	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) x)`
0	-	0	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(exp.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	167	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	166	1
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	3	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	3
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	3
↳	`(exp.f64 x)`	overflow	3
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	3

Confusion

	Predicted +	Predicted -
+	169	0
-	1	86

Precision

0.9941176470588236

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	169	0	0
-	1	1	85

Precision?

0.9883040935672515

Recall?

1.0

Freqs

test

number	freq
0	86
1	4
2	166

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

44.0ms

512×

valid

Compiler

Compiled 196 to 77 computations (60.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-exp: 8.0ms (28.1% of total)

ival-mult: 6.0ms (21.1% of total)

ival-expm1: 6.0ms (21.1% of total)

ival-div: 4.0ms (14.1% of total)

ival-sqrt: 4.0ms (14.1% of total)

ival-true: 1.0ms (3.5% of total)

exact: 1.0ms (3.5% of total)

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

preprocess211.0ms (3.8%)

Memory

15.5MiB live, 128.4MiB 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

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	36.3%	(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)

simplify151.0ms (2.7%)

Memory

5.1MiB live, 115.3MiB 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)

localize53.0ms (1%)

Memory

1.7MiB live, 47.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
accuracy	0.6250000000000001	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	38.22874684265909	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	38.257746784604784	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

45.0ms

256×

valid

Compiler

Compiled 92 to 22 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 20.0ms (52.8% of total)

ival-div: 9.0ms (23.7% of total)

ival-exp: 3.0ms (7.9% of total)

ival-expm1: 3.0ms (7.9% of total)

ival-sqrt: 2.0ms (5.3% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.2%)

Memory

-32.6MiB live, 3.9MiB allocated

Counts

4 → 20

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

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

1.0ms

-inf

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

simplify204.0ms (3.7%)

Memory

-1.2MiB live, 168.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	213
1	252	179
2	661	179
3	1434	173
4	2556	163
5	5965	156
0	8352	129

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

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

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

rewrite159.0ms (2.9%)

Memory

5.7MiB live, 203.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 687

Calls

Call 1

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

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

eval103.0ms (1.9%)

Memory: 3.2MiB live, 122.0MiB allocated
Compiler: Compiled 16 627 to 2 396 computations (85.6% saved)

prune15.0ms (0.3%)

Memory

1.2MiB live, 39.8MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	698	8	706
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	699	8	707

Accuracy

100.0%

Counts

707 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	65.7%	(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))))
▶	67.2%	(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))))
	65.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	71.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	67.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	66.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 274 to 220 computations (19.7% saved)

simplify259.0ms (4.7%)

Memory

10.0MiB live, 90.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(exp.f64 x)
cost-diff	0	(-.f64 (exp.f64 x) #s(literal -1 binary64))
cost-diff	0	(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
cost-diff	0	(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)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
cost-diff	0	(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	30	168
0	47	168
1	70	168
2	95	168
3	168	168
4	263	143
5	357	133
6	492	133
7	896	133
8	3235	133
9	7143	133
0	8168	133

Stop Event

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

Calls

Call 1

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

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

localize82.0ms (1.5%)

Memory

5.7MiB live, 80.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
accuracy	0	(-.f64 (exp.f64 x) #s(literal -1 binary64))
accuracy	0	(exp.f64 x)
accuracy	0.62109375	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.07650375976844201	(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)))
accuracy	0.41015625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.118091846996588	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
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	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy	21.18055203400029	#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	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	18.98013714666995	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0	(-.f64 (exp.f64 x) #s(literal -1 binary64))
accuracy	0	(exp.f64 x)
accuracy	0.0078125	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Samples

52.0ms	248×	0	valid
2.0ms	4×	2	valid
2.0ms	4×	1	valid

Compiler

Compiled 312 to 61 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-sqrt: 9.0ms (22.2% of total)

ival-mult: 8.0ms (19.8% of total)

ival-pow: 6.0ms (14.8% of total)

ival-div: 5.0ms (12.4% of total)

ival-add: 5.0ms (12.4% of total)

ival-exp: 3.0ms (7.4% of total)

ival-expm1: 3.0ms (7.4% of total)

adjust: 1.0ms (2.5% of total)

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

exact: 1.0ms (2.5% of total)

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

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

series11.0ms (0.2%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

16 → 38

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	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)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt 2))
3.0ms	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)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt 2))
2.0ms	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)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt 2))

Time

Variable

Point

Expression

4.0ms

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

3.0ms

inf

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

2.0ms

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

simplify298.0ms (5.4%)

Memory

2.2MiB live, 245.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	135	392
1	393	325
2	1021	308
3	3378	302
0	8142	257

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 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))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
1/2
(+ 1/2 (* 3/16 x))
(/ x (sqrt 2))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(sqrt (/ 1 (+ 1 (exp x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

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

rewrite205.0ms (3.7%)

Memory

-24.0MiB live, 170.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	147
0	47	144
1	185	109
2	1279	109
0	8400	109

Stop Event

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

Counts

16 → 527

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (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))))
(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)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 #s(literal 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 (pow.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (exp.f64 x)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(*.f64 (pow.f64 (-.f64 (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 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
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(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (expm1.f64 x) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (expm1.f64 x))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)) (expm1.f64 x))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))))
(/.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 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (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)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (expm1.f64 x))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (expm1.f64 x))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 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 (neg.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))))
(/.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 #s(literal 2 binary64) x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (expm1.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (expm1.f64 x) (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 #s(literal -1 binary64) (expm1.f64 x) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (expm1.f64 x) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 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)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(neg.f64 (.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))) #s(literal 1 binary64)))
(neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (neg.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))))
(.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 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal -1 binary64) (expm1.f64 x) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) #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)) (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/4 binary64))) (neg.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/4 binary64)) (neg.f64 (neg.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/4 binary64)))))
(*.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 (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))) #s(literal -1 binary64))
(.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))))
(.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 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)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log1p.f64 (exp.f64 x)))
(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 -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (sqrt.f64 (.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 x))) (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) (sqrt.f64 (.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 (exp.f64 x) #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) (/.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(sqrt.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(exp.f64 (neg.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(exp.f64 (neg.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/4 binary64) (*.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/4 binary64))))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #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 -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))

eval126.0ms (2.3%)

Memory: -4.2MiB live, 118.1MiB allocated
Compiler: Compiled 17 220 to 2 171 computations (87.4% saved)

prune54.0ms (1%)

Memory

5.0MiB live, 43.1MiB allocated

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	664	9	673
Fresh	0	3	3
Picked	1	4	5
Done	0	0	0
Total	665	16	681

Accuracy

100.0%

Counts

681 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	65.3%	(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (- (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(literal -1/2 binary64)))
▶	99.0%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
	70.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(literal 1/2 binary64))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	65.7%	(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
▶	67.2%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
	65.7%	(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))))
✓	67.2%	(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))))
▶	65.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	4.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
	5.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	71.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	67.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	66.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
▶	4.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 601 to 463 computations (23% saved)

simplify195.0ms (3.5%)

Memory

12.4MiB live, 171.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	300
0	69	300
1	102	300
2	139	300
3	208	300
4	302	275
5	408	265
6	538	265
7	957	265
8	3379	265
9	7583	265
0	8222	258

Stop Event

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

Calls

Call 1

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

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

localize87.0ms (1.6%)

Memory

15.3MiB live, 90.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.16796875	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
accuracy	0.41015625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.118091846996588	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
accuracy	41.653744310796036	#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64))
accuracy	0.0078125	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
accuracy	21.71246939977363	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy	0.00390625	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
accuracy	21.18055203400029	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
accuracy	41.19467654682125	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
accuracy	0	(+.f64 #s(literal 2 binary64) x)
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	22.172124535251793	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0	#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
accuracy	0.00390625	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
accuracy	0.01171875	(/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	0.62109375	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))

Samples

65.0ms

256×

valid

Compiler

Compiled 492 to 91 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-mult: 15.0ms (30.4% of total)

ival-add: 8.0ms (16.2% of total)

ival-div: 6.0ms (12.2% of total)

ival-sqrt: 6.0ms (12.2% of total)

ival-pow: 6.0ms (12.2% of total)

ival-exp: 3.0ms (6.1% of total)

ival-expm1: 3.0ms (6.1% of total)

ival-sub: 1.0ms (2% of total)

exact: 1.0ms (2% of total)

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

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

series9.0ms (0.2%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

21 → 44

Calls

Call 1

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

Outputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(+ 1 (* 1/2 x))
(/ x (sqrt 2))
(sqrt (+ 1 (exp x)))
(sqrt (/ 1 (+ 1 (exp x))))
(/ 1 (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 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 (exp x))
(exp x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

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

3.0ms

-inf

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

2.0ms

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

simplify239.0ms (4.4%)

Memory

-12.3MiB live, 139.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	151	436
1	434	389
2	1141	368
3	3942	362
0	8045	310

Stop Event

1×	iter limit
1×	node limit

Counts

44 → 43

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(+ 1 (* 1/2 x))
(/ x (sqrt 2))
(sqrt (+ 1 (exp x)))
(sqrt (/ 1 (+ 1 (exp x))))
(/ 1 (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 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 (exp x))
(exp x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 x #s(literal -1/64 binary64) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) #s(literal 1/96 binary64)) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (sqrt.f64 #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(fma.f64 #s(literal -1/4 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal 1/48 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #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)
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))
(+ (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)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (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 (+ 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)))
(*.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 #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp x)
(exp.f64 x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 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))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))

rewrite192.0ms (3.5%)

Memory

1.9MiB live, 248.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	274
0	69	274
1	257	236
2	1748	236
0	8424	228

Stop Event

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

Counts

21 → 426

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))))) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))))) #s(literal -1 binary64))
(pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(*.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (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 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
#s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))))) #s(literal 1 binary64))
(/.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(/.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 #s(approx (pow (- (exp x) -1) -1/2) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
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(.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 x x) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 #s(literal 3/16 binary64) x) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)
(.f64 (.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal 3/16 binary64) x) (pow.f64 x #s(literal -1 binary64))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 3/16 binary64) x))
(.f64 (.f64 #s(literal 3/16 binary64) x) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(literal 3/16 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x))
(.f64 x (.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal 3/16 binary64) x)))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (neg.f64 x) (.f64 #s(literal 3/16 binary64) x))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 3/16 binary64) x))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 x (.f64 #s(literal 3/16 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (neg.f64 x) (.f64 #s(literal 3/16 binary64) x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 3/16 binary64) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 x (.f64 #s(literal 3/16 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x x) #s(literal 3/16 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 x) (.f64 #s(literal 3/16 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (.f64 #s(literal 1 binary64) (.f64 #s(literal 3/16 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 3/16 binary64) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 #s(literal 3/16 binary64) x))))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 x (pow.f64 x #s(literal -1 binary64))))
(.f64 (.f64 x x) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 x (neg.f64 x))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 x x))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 x #s(literal 1 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(/.f64 (*.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 x x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 x) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(/.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))
(.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) x))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(*.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 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 #s(literal 2 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 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(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)))

eval159.0ms (2.9%)

Memory: -28.8MiB live, 109.5MiB allocated
Compiler: Compiled 15 223 to 2 220 computations (85.4% saved)

prune72.0ms (1.3%)

Memory

-0.3MiB live, 38.1MiB allocated

Pruning

19 alts after pruning (10 fresh and 9 done)

	Pruned	Kept	Total
New	490	5	495
Fresh	2	5	7
Picked	0	5	5
Done	0	4	4
Total	492	19	511

Accuracy

100.0%

Counts

511 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.0%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
	66.4%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal 1/48 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
▶	64.9%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
	66.9%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/2 binary64))))))
▶	70.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	65.7%	(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
✓	67.2%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
▶	65.7%	(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))))
✓	67.2%	(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))))
✓	65.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	4.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
▶	5.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	71.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	67.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	66.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	4.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (/.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
✓	4.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 694 to 528 computations (23.9% saved)

simplify203.0ms (3.7%)

Memory

6.7MiB live, 128.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
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 1 binary64))
cost-diff	0	#s(approx (exp 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)))
cost-diff	0	(-.f64 #s(approx (exp 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))) #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
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	(.f64 (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
cost-diff	0	#s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	380
0	68	380
1	103	380
2	142	380
3	249	380
4	444	360
5	567	352
6	661	352
7	1077	352
8	3498	352
9	7637	352
0	8275	346

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))
#s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (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)
(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
(-.f64 #s(approx (exp 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))) #s(literal -1 binary64))
#s(approx (exp 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)))
(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))
(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 -1 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
#s(literal 1 binary64)
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))
#s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(*.f64 x x)
x
#s(literal 1/48 binary64)
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)

Outputs
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))
#s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (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)
(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
(-.f64 #s(approx (exp 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))) #s(literal -1 binary64))
#s(approx (exp 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)))
(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))
(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 -1 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
#s(literal 1 binary64)
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))))
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))
#s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))
#s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(*.f64 x x)
x
#s(literal 1/48 binary64)
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)

localize172.0ms (3.1%)

Memory

13.9MiB live, 87.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.04296875	(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
accuracy	0.05078125	(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
accuracy	0.62109375	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
accuracy	21.5833666372371	#s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))
accuracy	0.04296875	(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))
accuracy	0.0546875	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.12109375	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	21.405574055126127	#s(approx (exp 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)))
accuracy	0.04296875	(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	0.0546875	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.12109375	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	21.607035772475985	#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	(*.f64 x x)
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
accuracy	20.92449342614685	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	41.19613022086534	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0	#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))
accuracy	0.62109375	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))
accuracy	18.601337343139985	#s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))

Samples

143.0ms	254×	0	valid
3.0ms	2×	5	exit

Compiler

Compiled 604 to 92 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 127.0ms

ival-mult: 46.0ms (36.3% of total)

ival-sqrt: 44.0ms (34.7% of total)

ival-add: 10.0ms (7.9% of total)

const: 7.0ms (5.5% of total)

ival-pow: 6.0ms (4.7% of total)

ival-div: 5.0ms (3.9% of total)

ival-exp: 3.0ms (2.4% of total)

ival-expm1: 3.0ms (2.4% of total)

adjust: 1.0ms (0.8% of total)

ival-sub: 1.0ms (0.8% of total)

exact: 1.0ms (0.8% of total)

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

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

series30.0ms (0.5%)

Memory

-26.4MiB live, 11.4MiB allocated

Counts

24 → 56

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))
#s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(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))
(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
(-.f64 #s(approx (exp 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))) #s(literal -1 binary64))
#s(approx (exp 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)))
(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))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))
#s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))
(*.f64 x x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 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))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/2 (pow x 2))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(pow x 2)
(+ 1/2 (* 1/6 x))
-1/4
(- (* 1/48 (pow x 2)) 1/4)
(sqrt (+ 1 (exp x)))
(sqrt (/ 1 (+ 1 (exp x))))
(/ 1 (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 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 (exp x))
(exp x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 3))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

((/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt (/ 1 (+ (exp x) 1))) (/ 1 (+ (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 1) (/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt (/ 1 (+ (exp x) 1))) (/ 1 (+ (exp x) 1)) (* x x) (+ (* 1/6 x) 1/2) (+ (* (* x x) 1/48) -1/4) (+ (* (+ (* (* x x) 1/48) -1/4) x) 1/2))

3.0ms

-inf

((/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt (/ 1 (+ (exp x) 1))) (/ 1 (+ (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 1) (/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt (/ 1 (+ (exp x) 1))) (/ 1 (+ (exp x) 1)) (* x x) (+ (* 1/6 x) 1/2) (+ (* (* x x) 1/48) -1/4) (+ (* (+ (* (* x x) 1/48) -1/4) x) 1/2))

2.0ms

((/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt (/ 1 (+ (exp x) 1))) (/ 1 (+ (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 1) (/ 1 (pow (- (exp x) -1) -1/2)) (pow (- (exp x) -1) -1/2) (sqrt (/ 1 (+ (exp x) 1))) (/ 1 (+ (exp x) 1)) (* x x) (+ (* 1/6 x) 1/2) (+ (* (* x x) 1/48) -1/4) (+ (* (+ (* (* x x) 1/48) -1/4) x) 1/2))

simplify204.0ms (3.7%)

Memory

5.1MiB live, 163.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	173	549
1	495	511
2	1470	492
3	4589	480
0	8620	417

Stop Event

1×	iter limit
1×	node limit

Counts

56 → 56

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/2 (pow x 2))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(pow x 2)
(+ 1/2 (* 1/6 x))
-1/4
(- (* 1/48 (pow x 2)) 1/4)
(sqrt (+ 1 (exp x)))
(sqrt (/ 1 (+ 1 (exp x))))
(/ 1 (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 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 (exp x))
(exp x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 3))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))

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)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 x #s(literal -1/64 binary64) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) #s(literal 1/96 binary64)) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (sqrt.f64 #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(fma.f64 #s(literal -1/4 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal 1/48 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
1
#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 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))
(pow x 2)
(*.f64 x x)
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
-1/4
#s(literal -1/4 binary64)
(- (* 1/48 (pow x 2)) 1/4)
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (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))
(* (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 #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x))
(* (pow x 3) (+ 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)) (*.f64 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 #s(literal 1/6 binary64) x) x)
(* (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 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp x)
(exp.f64 x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 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 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))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(* 1/48 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x)
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/48 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (-.f64 (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) x) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))
(*.f64 (-.f64 (/.f64 (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) x) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x)
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))
(.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/48 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x)

rewrite259.0ms (4.7%)

Memory

-10.9MiB live, 237.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	347
0	68	347
1	274	319
2	1853	319
0	8536	313

Stop Event

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

Counts

24 → 320

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))
#s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(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))
(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
(-.f64 #s(approx (exp 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))) #s(literal -1 binary64))
#s(approx (exp 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)))
(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))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))
#s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64)))
(*.f64 x x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))

Outputs
(*.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))) #s(literal -1 binary64))
(pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 (log.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(*.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
#s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
(/.f64 (neg.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))) #s(literal -1 binary64))
(/.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))))) #s(literal -1 binary64))))
(*.f64 (pow.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)) #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
#s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64))
(.f64 (pow.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)) (pow.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal 1/2 binary64) x))
(.f64 (pow.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(literal 1/4 binary64)) (pow.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(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.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(literal 1/2 binary64))
(pow.f64 (.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)))) #s(literal 1/4 binary64))
(pow.f64 (pow.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(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.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(literal 1/2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(exp.f64 (.f64 (log.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(literal 1/2 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)))
(.f64 (-.f64 (pow.f64 (.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(literal 4 binary64)) (pow.f64 (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(literal -1 binary64)))
(.f64 (+.f64 #s(literal 8 binary64) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x) #s(literal 3 binary64))) (pow.f64 (-.f64 (+.f64 (pow.f64 (.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(literal 4 binary64)) (.f64 (*.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(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 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))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.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))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 4 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))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.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))) (/.f64 (pow.f64 (.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 (/.f64 #s(literal 4 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))) (/.f64 #s(literal 4 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))) (.f64 (/.f64 (pow.f64 (*.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))) (/.f64 #s(literal 4 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)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (pow.f64 (.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)))) (neg.f64 (-.f64 #s(literal 2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (*.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(literal 4 binary64)))) (neg.f64 (neg.f64 (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)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (.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(literal 4 binary64)) (.f64 (.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))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.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))) (.f64 (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(literal 4 binary64))) (.f64 (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))))
(/.f64 (-.f64 #s(literal 4 binary64) (pow.f64 (.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))) (-.f64 #s(literal 2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.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(literal 4 binary64))) (neg.f64 (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))))
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(fma.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))
(fma.f64 x (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal -1/4 binary64)) x))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal -1/4 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal -1/4 binary64)) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal -1/4 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal -1/4 binary64)) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal -1/4 binary64)) x #s(literal -1/2 binary64))))
(+.f64 (.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal -1/4 binary64)) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal 1/48 binary64) (.f64 x x) #s(literal -1/4 binary64)) x))

eval58.0ms (1%)

Memory: 20.8MiB live, 93.7MiB allocated
Compiler: Compiled 15 324 to 1 965 computations (87.2% saved)

prune23.0ms (0.4%)

Memory

-18.5MiB live, 30.2MiB allocated

Pruning

21 alts after pruning (7 fresh and 14 done)

	Pruned	Kept	Total
New	435	3	438
Fresh	1	4	5
Picked	0	5	5
Done	0	9	9
Total	436	21	457

Accuracy

100.0%

Counts

457 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.0%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
	66.4%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal 1/48 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
✓	64.9%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/48 binary64) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
	66.9%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) (fma.f64 #s(approx (+ (* (* x x) 1/48) -1/4) #s(literal -1/4 binary64)) x #s(literal 1/2 binary64))))))
✓	70.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- (exp x) -1) -1/2) (sqrt.f64 #s(approx (/ 1 (+ (exp x) 1)) #s(literal 1/2 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	65.7%	(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
✓	67.2%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	65.7%	(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))))
✓	67.2%	(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))))
✓	65.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	2.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
	3.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x)))))
✓	4.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
✓	5.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	71.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	67.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	66.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	4.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (/.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
✓	4.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 1 095 to 547 computations (50% saved)

regimes21.0ms (0.4%)

Memory

17.3MiB live, 17.3MiB allocated

Counts

26 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms

6.0ms

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

6.0ms

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

Results

Accuracy	Segments	Branch
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)

regimes21.0ms (0.4%)

Memory

-15.8MiB live, 20.9MiB allocated

Accuracy

Total -44.5b remaining (-240.6%)

Threshold costs -44.5b (-240.6%)

Counts

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

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

Calls

3 calls:

10.0ms

5.0ms

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

5.0ms

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

Results

Accuracy	Segments	Branch
71.1%	1	`x`
71.1%	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))))`
71.1%	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)

simplify25.0ms (0.4%)

Memory

9.6MiB live, 47.8MiB 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)))

soundness254.0ms (4.6%)

Memory

-3.1MiB live, 193.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	213
1	252	179
2	661	179
3	1434	173
4	2556	163
5	5965	156
0	8352	129
0	10	33
0	17	33
1	63	19
2	429	19
3	4997	19
0	8103	15

Stop Event

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

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess16.0ms (0.3%)

Memory: 30.1MiB live, 30.1MiB allocated
Compiler: Compiled 62 to 52 computations (16.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze3.0ms (0.1%)

sample1.1s (19.6%)

explain241.0ms (4.4%)

preprocess211.0ms (3.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify151.0ms (2.7%)

localize53.0ms (1%)

series10.0ms (0.2%)

simplify204.0ms (3.7%)

rewrite159.0ms (2.9%)

eval103.0ms (1.9%)

prune15.0ms (0.3%)

simplify259.0ms (4.7%)

localize82.0ms (1.5%)

series11.0ms (0.2%)

simplify298.0ms (5.4%)

rewrite205.0ms (3.7%)

eval126.0ms (2.3%)

prune54.0ms (1%)

simplify195.0ms (3.5%)

localize87.0ms (1.6%)

series9.0ms (0.2%)

simplify239.0ms (4.4%)

rewrite192.0ms (3.5%)

eval159.0ms (2.9%)

prune72.0ms (1.3%)

simplify203.0ms (3.7%)

localize172.0ms (3.1%)

series30.0ms (0.5%)

simplify204.0ms (3.7%)

rewrite259.0ms (4.7%)

eval58.0ms (1%)

prune23.0ms (0.4%)

regimes21.0ms (0.4%)

regimes21.0ms (0.4%)

simplify25.0ms (0.4%)

soundness254.0ms (4.6%)

preprocess16.0ms (0.3%)

end0.0ms (0%)

Profiling