Metrics for sqrtexp (problem 3.4.4)

analyze1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample914.0ms (8.6%)

Memory

47.2MiB live, 926.3MiB allocated

Samples

422.0ms	8 256×	0	valid
177.0ms	2 704×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 404.0ms

ival-expm1: 146.0ms (36.1% of total)

ival-sqrt: 93.0ms (23% of total)

ival-mult: 76.0ms (18.8% of total)

ival-div: 72.0ms (17.8% of total)

ival-true: 7.0ms (1.7% of total)

exact: 6.0ms (1.5% of total)

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

Bogosity

preprocess481.0ms (4.5%)

Memory

-29.8MiB live, 370.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 394×	`lower-fma.f64`
15 394×	`lower-fma.f32`
2 850×	`lower--.f32`
2 846×	`lower--.f64`
2 458×	`lower-*.f32`

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

explain133.0ms (1.3%)

Memory

-1.0MiB live, 153.5MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	176	2
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	176	2

Confusion

	Predicted +	Predicted -
+	176	0
-	0	80

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	176	0	0
-	0	2	78

Precision?

0.9887640449438202

Recall?

1.0

Freqs

test

number	freq
0	80
2	176

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions

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

ival-exp: 7.0ms (28.9% of total)

ival-expm1: 6.0ms (24.8% of total)

ival-mult: 4.0ms (16.5% of total)

ival-div: 3.0ms (12.4% of total)

ival-sqrt: 3.0ms (12.4% of total)

exact: 1.0ms (4.1% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	31.8%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify408.0ms (3.9%)

Memory

30.8MiB live, 383.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	192	(-.f64 (exp.f64 x) #s(literal 1 binary64))
✓	cost-diff	192	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	cost-diff	7104	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Rules

15 394×	`lower-fma.f64`
15 394×	`lower-fma.f32`
2 850×	`lower--.f32`
2 846×	`lower--.f64`
2 458×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize33.0ms (0.3%)

Memory

1.8MiB live, 40.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	accuracy	35.6%	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	accuracy	35.6%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

21.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

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

ival-exp: 3.0ms (25.5% of total)

ival-expm1: 3.0ms (25.5% of total)

ival-div: 2.0ms (17% of total)

ival-mult: 2.0ms (17% of total)

ival-sqrt: 2.0ms (17% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2 x)))>
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))>
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
1.0ms	x	@	inf	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms	x	@	0	(- (exp (* 2 x)) 1)
0.0ms	x	@	0	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms	x	@	inf	(* 2 x)

simplify505.0ms (4.8%)

Memory

-3.5MiB live, 405.1MiB allocated

Algorithm

1×	egg-herbie

Rules

18 226×	`lower-fma.f64`
18 226×	`lower-fma.f32`
2 938×	`lower-+.f64`
2 938×	`lower-+.f32`
2 780×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	342
1	155	342
2	335	342
3	752	342
4	1201	302
5	1536	286
6	2025	286
7	2949	286
8	4633	286
0	8302	232

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

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

Outputs
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(* 2 x)
(+.f64 x x)
(* x (+ 2 (* 2 x)))
(*.f64 #s(literal 2 binary64) (fma.f64 x x x))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)

rewrite358.0ms (3.4%)

Memory

-19.8MiB live, 454.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 402×	`lower-fma.f64`
5 402×	`lower-fma.f32`
4 492×	`lower-*.f32`
4 490×	`lower-*.f64`
2 532×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
0	15	26
1	56	19
2	378	19
3	4533	19
0	8161	15

Stop Event

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

Counts

5 → 656

Calls

Call 1

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

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

eval93.0ms (0.9%)

Memory: 7.0MiB live, 157.6MiB allocated
Compiler: Compiled 16 824 to 2 356 computations (86% saved)

prune84.0ms (0.8%)

Memory

32.8MiB live, 191.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	710	5	715
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	711	5	716

Accuracy

100.0%

Counts

716 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	69.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
▶	70.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
▶	69.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	75.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

Compiler

Compiled 70 to 56 computations (20% saved)

simplify822.0ms (7.8%)

Memory

-26.4MiB live, 731.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	cost-diff	0	(+.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	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	cost-diff	384	(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓	cost-diff	6208	(exp.f64 x)

Rules

14 808×	`lower-fma.f32`
14 798×	`lower-fma.f64`
2 514×	`lower--.f32`
2 512×	`lower--.f64`
2 236×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	152
0	45	96
1	84	96
2	136	96
3	239	96
4	311	96
5	369	96
6	446	96
7	849	96
8	3181	96
9	7153	96
0	8177	96

Stop Event

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

Calls

Call 1

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

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

localize141.0ms (1.3%)

Memory

-10.8MiB live, 101.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	99.9%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	99.8%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

76.0ms

256×

valid

Compiler

Compiled 163 to 27 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-mult: 24.0ms (38.4% of total)

ival-expm1: 19.0ms (30.4% of total)

ival-add: 6.0ms (9.6% of total)

const: 4.0ms (6.4% of total)

ival-sqrt: 3.0ms (4.8% of total)

ival-div: 2.0ms (3.2% of total)

ival-exp: 2.0ms (3.2% of total)

ival-sub: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

13 → 156

Calls

Call 1

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

Outputs
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>

Calls

39 calls:

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

simplify398.0ms (3.8%)

Memory

-18.8MiB live, 487.4MiB allocated

Algorithm

1×	egg-herbie

Rules

16 792×	`lower-fma.f64`
16 792×	`lower-fma.f32`
5 038×	`lower-*.f64`
5 038×	`lower-*.f32`
2 370×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	1362
1	322	1184
2	921	1176
3	3242	1146
4	6418	1146
0	8346	914

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 154

Calls

Call 1

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

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

rewrite1.1s (10.5%)

Memory

22.4MiB live, 459.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 464×	`lower-/.f64`
4 464×	`lower-/.f32`
4 164×	`lower-fma.f32`
4 154×	`lower-fma.f64`
3 262×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	94
0	45	66
1	192	66
2	1447	66
0	8313	66

Stop Event

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

Counts

13 → 642

Calls

Call 1

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

Outputs
(exp.f64 x)
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) x)
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(-.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(-.f64 (/.f64 (/.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 x))) (neg.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))
(-.f64 (/.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (.f64 (expm1.f64 x) (+.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 x) (+.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))))))
(-.f64 (/.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (/.f64 (expm1.f64 x) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x))))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x))))))
(-.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(fma.f64 (neg.f64 (exp.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (.f64 (exp.f64 (+.f64 x x)) #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) #s(literal 1 binary64)) (/.f64 (exp.f64 x) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (expm1.f64 (+.f64 x x))) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (/.f64 (exp.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(neg.f64 (neg.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (expm1.f64 x) (+.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))) (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (expm1.f64 x)) (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x)) (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x)))) (-.f64 (.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (expm1.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (.f64 (+.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (.f64 (expm1.f64 x) (+.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x)))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64)))) (neg.f64 (.f64 (expm1.f64 x) (+.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64)))) (neg.f64 (.f64 (+.f64 (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (expm1.f64 x))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64)))) (neg.f64 (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 2 binary64)))) (neg.f64 (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(/.f64 (/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (expm1.f64 x)) (+.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))))
(/.f64 (/.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 2 binary64))) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))
(/.f64 (-.f64 (neg.f64 (exp.f64 (+.f64 x x))) #s(literal -1 binary64)) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 (.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))) (.f64 (expm1.f64 x) #s(literal -1 binary64))) (*.f64 (expm1.f64 x) (neg.f64 (expm1.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 x))) (.f64 (/.f64 (expm1.f64 x) (exp.f64 (+.f64 x x))) #s(literal -1 binary64))) (*.f64 (/.f64 (expm1.f64 x) (exp.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
(/.f64 (-.f64 (expm1.f64 x) (.f64 (/.f64 (expm1.f64 x) (exp.f64 (+.f64 x x))) #s(literal 1 binary64))) (.f64 (/.f64 (expm1.f64 x) (exp.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (-.f64 (.f64 (neg.f64 (exp.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))) (.f64 (neg.f64 (expm1.f64 x)) #s(literal -1 binary64))) (pow.f64 (neg.f64 (expm1.f64 x)) #s(literal 2 binary64)))
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(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/36 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/12 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/12 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/12 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x #s(literal 1/12 binary64))))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/12 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))

eval50.0ms (0.5%)

Memory: -10.3MiB live, 103.5MiB allocated
Compiler: Compiled 6 922 to 657 computations (90.5% saved)

prune27.0ms (0.3%)

Memory

28.8MiB live, 65.5MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	467	2	469
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	467	7	474

Accuracy

100.0%

Counts

474 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	69.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	70.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	69.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	75.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	69.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 60 to 45 computations (25% saved)

simplify607.0ms (5.7%)

Memory

-10.6MiB live, 384.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

13 944×	`lower-fma.f32`
13 938×	`lower-fma.f64`
2 750×	`lower-*.f64`
2 750×	`lower-*.f32`
1 734×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	117
0	37	117
1	71	117
2	165	111
3	326	110
4	487	81
5	731	81
6	1409	81
7	5684	81
0	8125	79

Stop Event

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

Calls

Call 1

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

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

localize120.0ms (1.1%)

Memory

9.8MiB live, 92.2MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))))
✓	accuracy	99.9%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.8%	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	accuracy	99.3%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	98.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))

Samples

86.0ms	248×	0	valid
2.0ms	4×	2	valid
1.0ms	3×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 125 to 25 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-mult: 55.0ms (69.5% of total)

ival-div: 8.0ms (10.1% of total)

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

const: 4.0ms (5.1% of total)

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

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

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

series795.0ms (7.5%)

Memory

-27.2MiB live, 11.6MiB allocated

Counts

9 → 84

Calls

Call 1

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

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (/ 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt 3/16>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2))
1.0ms	x	@	inf	(sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))
1.0ms	x	@	0	(+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2))
1.0ms	x	@	-inf	(sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))
1.0ms	x	@	-inf	(+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2))

simplify1.0s (9.8%)

Memory

12.9MiB live, 664.2MiB allocated

Algorithm

1×	egg-herbie

Rules

19 008×	`lower-fma.f64`
19 008×	`lower-fma.f32`
5 072×	`lower-*.f64`
5 072×	`lower-*.f32`
2 854×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	902
1	467	897
2	1356	844
3	3358	818
0	8335	668

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(.f64 x (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (.f64 x (*.f64 x x)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) x)))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 x #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (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 x (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/96 binary64) (/.f64 #s(literal -1/1024 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (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 (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))

rewrite346.0ms (3.3%)

Memory

10.3MiB live, 448.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 766×	`lower-/.f32`
4 758×	`lower-/.f64`
4 440×	`lower-*.f64`
4 440×	`lower-*.f32`
3 192×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	87
0	35	87
1	166	61
2	1473	58
0	8585	57

Stop Event

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

Counts

9 → 706

Calls

Call 1

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

Outputs
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(+.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (-.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (-.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (/.f64 (.f64 x (.f64 (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(fma.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal -2 binary64)))))
(/.f64 (fma.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 3 binary64))) (-.f64 (fma.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(/.f64 (fma.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 2 binary64) (-.f64 (.f64 x (.f64 (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))))
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(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (-.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (-.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))) (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (.f64 #s(literal 49/36864 binary64) (.f64 x x))) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (.f64 #s(literal 49/36864 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(pow.f64 (/.f64 (-.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))

eval30.0ms (0.3%)

Memory: -19.5MiB live, 55.1MiB allocated
Compiler: Compiled 3 751 to 804 computations (78.6% saved)

prune31.0ms (0.3%)

Memory

28.0MiB live, 71.8MiB allocated

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	239	6	245
Fresh	0	0	0
Picked	2	0	2
Done	0	5	5
Total	241	11	252

Accuracy

100.0%

Counts

252 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	73.3%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))))))
▶	69.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
▶	68.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
▶	70.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
▶	74.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
▶	69.1%	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	69.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	70.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	69.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	75.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

Compiler

Compiled 179 to 134 computations (25.1% saved)

simplify323.0ms (3%)

Memory

-7.9MiB live, 387.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(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)))
✓	cost-diff	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))
✓	cost-diff	(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
✓	cost-diff	(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
✓	cost-diff	(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
✓	cost-diff	(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
✓	cost-diff	(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))

Rules

13 736×	`lower-fma.f32`
13 720×	`lower-fma.f64`
2 724×	`lower-*.f32`
2 718×	`lower-*.f64`
1 714×	`lower-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	44	309
0	72	309
1	132	309
2	232	281
3	360	281
4	592	211
5	815	211
6	1463	211
7	5709	211
0	8138	211

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
x
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
(*.f64 x #s(literal 1/48 binary64))
#s(literal 1/48 binary64)
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(*.f64 x #s(literal -1/480 binary64))
#s(literal -1/480 binary64)
#s(literal 1/48 binary64)
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))
#s(literal 1 binary64)
#s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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))))
(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)))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 x #s(literal -1/64 binary64) #s(literal -1/8 binary64))
#s(literal -1/64 binary64)
#s(literal -1/8 binary64)

Outputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
x
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
(*.f64 x #s(literal 1/48 binary64))
#s(literal 1/48 binary64)
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))
(fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (fma.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)) (.f64 x x) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)) (.f64 x x) #s(literal -1/4 binary64))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(*.f64 x #s(literal -1/480 binary64))
#s(literal -1/480 binary64)
#s(literal 1/48 binary64)
#s(literal -1/4 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
#s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
(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)))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 x #s(literal -1/64 binary64) #s(literal -1/8 binary64))
#s(literal -1/64 binary64)
#s(literal -1/8 binary64)

localize126.0ms (1.2%)

Memory

-1.0MiB live, 190.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.9%	(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)))
✓	accuracy	99.3%	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
✓	accuracy	99.9%	(*.f64 x #s(literal -1/480 binary64))
✓	accuracy	99.6%	(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
✓	accuracy	99.9%	(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/48 binary64))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))

Samples

68.0ms

256×

valid

Compiler

Compiled 325 to 39 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 18.0ms (36.3% of total)

const: 10.0ms (20.2% of total)

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

ival-div: 6.0ms (12.1% of total)

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

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

exact: 1.0ms (2% of total)

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

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

series14.0ms (0.1%)

Memory

23.2MiB live, 23.2MiB allocated

Counts

21 → 240

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))>
#<alt (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))>
#<alt (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))>
#<alt (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))>
#<alt (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))>
#<alt (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))>
#<alt (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))>
#<alt (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))>
#<alt (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64))>
#<alt (/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))>
#<alt (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)))>
#<alt (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 #s(literal 1/2 binary64))>
#<alt (*.f64 x #s(literal 1/48 binary64))>
#<alt (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))>
#<alt (*.f64 x #s(literal -1/480 binary64))>
#<alt (fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (* 1/48 (pow x 3))>
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/48 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))>
#<alt -1/4>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (* 1/48 (pow x 2))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/48 (pow x 2))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))>
#<alt (* -1/480 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))>
#<alt (* (pow x 5) (- (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 5)))) (+ 1/480 (/ 1/4 (pow x 4)))))>
#<alt (* -1/480 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/480 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/480 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 5)))))))>
#<alt -1/4>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)>
#<alt (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)>
#<alt (* -1/480 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))>
#<alt (* -1/480 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/64 (/ x (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/64 (/ x (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* -1/64 (/ (pow x 2) (sqrt 1/2)))>
#<alt (* -1 (* (pow x 2) (+ (* 1/64 (/ 1 (sqrt 1/2))) (* 1/8 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* (pow x 2) (- (/ (sqrt 1/2) (pow x 2)) (+ (* 1/64 (/ 1 (sqrt 1/2))) (/ 1/8 (* x (sqrt 1/2))))))>
#<alt (* (pow x 2) (- (/ (sqrt 1/2) (pow x 2)) (+ (* 1/64 (/ 1 (sqrt 1/2))) (/ 1/8 (* x (sqrt 1/2))))))>
#<alt (* -1/64 (/ (pow x 2) (sqrt 1/2)))>
#<alt (* -1 (* (pow x 2) (+ (* 1/64 (/ 1 (sqrt 1/2))) (* 1/8 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* (pow x 2) (- (* -1 (/ (+ (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/64 (/ 1 (sqrt 1/2)))))>
#<alt (* (pow x 2) (- (* -1 (/ (+ (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/64 (/ 1 (sqrt 1/2)))))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* x (+ 1/48 (* -1/480 (pow x 2))))>
#<alt (* x (+ 1/48 (* -1/480 (pow x 2))))>
#<alt (* x (+ 1/48 (* -1/480 (pow x 2))))>
#<alt (* -1/480 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt (* -1/480 x)>
#<alt 1/48>
#<alt (+ 1/48 (* -1/480 (pow x 2)))>
#<alt (+ 1/48 (* -1/480 (pow x 2)))>
#<alt (+ 1/48 (* -1/480 (pow x 2)))>
#<alt (* -1/480 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* -1/480 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>
#<alt (* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))>

Calls

60 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(+ (* (/ x (sqrt 1/2)) (+ (* x -1/64) -1/8)) (sqrt 1/2))
1.0ms	x	@	inf	(+ (* (/ x (sqrt 1/2)) (+ (* x -1/64) -1/8)) (sqrt 1/2))
0.0ms	x	@	inf	(/ x (sqrt 1/2))
0.0ms	x	@	0	(/ x (sqrt 1/2))
0.0ms	x	@	-inf	(+ (* x (+ (* x (* x 1/48)) -1/4)) 1/2)

simplify734.0ms (6.9%)

Memory

-44.1MiB live, 644.1MiB allocated

Algorithm

1×	egg-herbie

Rules

22 486×	`lower-fma.f64`
22 486×	`lower-fma.f32`
5 010×	`lower-*.f64`
5 010×	`lower-*.f32`
4 106×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	182	2541
1	497	2351
2	1459	2349
3	4037	2275
0	8326	1866

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 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 (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(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 (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 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 (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(* 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)))))
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 3))
(* -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))))))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))
-1/4
(- (* 1/48 (pow x 2)) 1/4)
(- (* 1/48 (pow x 2)) 1/4)
(- (* 1/48 (pow x 2)) 1/4)
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 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 (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(sqrt (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
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)))
(* -1/480 (pow x 5))
(* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(* (pow x 5) (- (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 5)))) (+ 1/480 (/ 1/4 (pow x 4)))))
(* -1/480 (pow x 5))
(* -1 (* (pow x 5) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/480 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/480 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 5)))))))
-1/4
(- (* 1/48 (pow x 2)) 1/4)
(- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)
(- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)
(* -1/480 (pow x 4))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(* -1/480 (pow x 4))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/64 (/ x (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* -1/64 (/ x (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* -1/64 (/ (pow x 2) (sqrt 1/2)))
(* -1 (* (pow x 2) (+ (* 1/64 (/ 1 (sqrt 1/2))) (* 1/8 (/ 1 (* x (sqrt 1/2)))))))
(* (pow x 2) (- (/ (sqrt 1/2) (pow x 2)) (+ (* 1/64 (/ 1 (sqrt 1/2))) (/ 1/8 (* x (sqrt 1/2))))))
(* (pow x 2) (- (/ (sqrt 1/2) (pow x 2)) (+ (* 1/64 (/ 1 (sqrt 1/2))) (/ 1/8 (* x (sqrt 1/2))))))
(* -1/64 (/ (pow x 2) (sqrt 1/2)))
(* -1 (* (pow x 2) (+ (* 1/64 (/ 1 (sqrt 1/2))) (* 1/8 (/ 1 (* x (sqrt 1/2)))))))
(* (pow x 2) (- (* -1 (/ (+ (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/64 (/ 1 (sqrt 1/2)))))
(* (pow x 2) (- (* -1 (/ (+ (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/64 (/ 1 (sqrt 1/2)))))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* x (+ 1/48 (* -1/480 (pow x 2))))
(* x (+ 1/48 (* -1/480 (pow x 2))))
(* x (+ 1/48 (* -1/480 (pow x 2))))
(* -1/480 (pow x 3))
(* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* -1/480 (pow x 3))
(* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
(* -1/480 x)
1/48
(+ 1/48 (* -1/480 (pow x 2)))
(+ 1/48 (* -1/480 (pow x 2)))
(+ 1/48 (* -1/480 (pow x 2)))
(* -1/480 (pow x 2))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* -1/480 (pow x 2))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
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(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(fma.f64 x (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(* -1/480 (pow x 5))
(*.f64 #s(literal -1/480 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/480 binary64) (/.f64 #s(literal 1/48 binary64) (.f64 x x))))
(* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/480 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (.f64 x x)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 5) (- (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 5)))) (+ 1/480 (/ 1/4 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/480 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (*.f64 x x))))))))
(* -1/480 (pow x 5))
(*.f64 #s(literal -1/480 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/480 binary64) (/.f64 #s(literal 1/48 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (+ 1/480 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/480 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (.f64 x x)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* -1 (* (pow x 5) (- (+ 1/480 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 5)))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/480 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (*.f64 x x))))))))
-1/4
#s(literal -1/4 binary64)
(- (* 1/48 (pow x 2)) 1/4)
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
(- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
(* -1/480 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/480 binary64)))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(.f64 (+.f64 #s(literal -1/480 binary64) (/.f64 #s(literal 1/48 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/480 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (.f64 x x)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/480 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (.f64 x x)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* -1/480 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/480 binary64)))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(.f64 (+.f64 #s(literal -1/480 binary64) (/.f64 #s(literal 1/48 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/480 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (.f64 x x)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* (pow x 4) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/480 (/ 1/4 (pow x 4)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/480 binary64) (+.f64 (/.f64 #s(literal 1/48 binary64) (.f64 x x)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (- (* -1/64 (/ x (sqrt 1/2))) (* 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 (- (* -1/64 (/ x (sqrt 1/2))) (* 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)))
(* -1/64 (/ (pow x 2) (sqrt 1/2)))
(/.f64 (.f64 x (.f64 x #s(literal -1/64 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (pow x 2) (+ (* 1/64 (/ 1 (sqrt 1/2))) (* 1/8 (/ 1 (* x (sqrt 1/2)))))))
(.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* (pow x 2) (- (/ (sqrt 1/2) (pow x 2)) (+ (* 1/64 (/ 1 (sqrt 1/2))) (/ 1/8 (* x (sqrt 1/2))))))
(.f64 (.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/8 binary64) x)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x x))))
(* (pow x 2) (- (/ (sqrt 1/2) (pow x 2)) (+ (* 1/64 (/ 1 (sqrt 1/2))) (/ 1/8 (* x (sqrt 1/2))))))
(.f64 (.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/8 binary64) x)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x x))))
(* -1/64 (/ (pow x 2) (sqrt 1/2)))
(/.f64 (.f64 x (.f64 x #s(literal -1/64 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (pow x 2) (+ (* 1/64 (/ 1 (sqrt 1/2))) (* 1/8 (/ 1 (* x (sqrt 1/2)))))))
(.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(* (pow x 2) (- (* -1 (/ (+ (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/64 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/8 binary64) x)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x x))))
(* (pow x 2) (- (* -1 (/ (+ (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/64 (/ 1 (sqrt 1/2)))))
(.f64 (.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/8 binary64) x)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x x))))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* x (+ 1/48 (* -1/480 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* x (+ 1/48 (* -1/480 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* x (+ 1/48 (* -1/480 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* -1/480 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64))
(* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* (pow x 3) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* -1/480 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64))
(* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* -1 (* (pow x 3) (- 1/480 (* 1/48 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
(* -1/480 x)
(*.f64 x #s(literal -1/480 binary64))
1/48
#s(literal 1/48 binary64)
(+ 1/48 (* -1/480 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(+ 1/48 (* -1/480 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(+ 1/48 (* -1/480 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(* -1/480 (pow x 2))
(.f64 x (.f64 x #s(literal -1/480 binary64)))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(* -1/480 (pow x 2))
(.f64 x (.f64 x #s(literal -1/480 binary64)))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(* (pow x 2) (- (* 1/48 (/ 1 (pow x 2))) 1/480))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))

rewrite304.0ms (2.9%)

Memory

40.2MiB live, 392.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 902×	`lower-/.f32`
3 898×	`lower-/.f64`
3 880×	`lower-*.f32`
3 874×	`lower-*.f64`
3 792×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	217
0	72	217
1	282	130
2	2066	130
0	8168	130

Stop Event

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

Counts

21 → 851

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))
(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)))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/48 binary64))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(*.f64 x #s(literal -1/480 binary64))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))

Outputs
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 #s(approx (/ 1 (/ (- (exp ( 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (neg.f64 (log.f64 #s(approx (/ 1 (/ (- (exp ( 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))
(exp.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(approx (/ 1 (/ (- (exp ( 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
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(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(*.f64 x #s(literal 1/48 binary64))
(*.f64 #s(literal 1/48 binary64) x)
(+.f64 (.f64 x #s(literal 1/48 binary64)) (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))))
(+.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x #s(literal 1/48 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x)))) (-.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x #s(literal 1/48 binary64)))) (/.f64 (.f64 (.f64 x #s(literal 1/48 binary64)) (.f64 x #s(literal 1/48 binary64))) (-.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x #s(literal 1/48 binary64)))))
(fma.f64 x #s(literal 1/48 binary64) (.f64 x (.f64 #s(literal -1/480 binary64) (*.f64 x x))))
(fma.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x)) (*.f64 x #s(literal 1/48 binary64)))
(fma.f64 #s(literal 1/48 binary64) x (.f64 x (.f64 #s(literal -1/480 binary64) (*.f64 x x))))
(fma.f64 (.f64 x #s(literal -1/480 binary64)) (.f64 x x) (*.f64 x #s(literal 1/48 binary64)))
(fma.f64 (.f64 #s(literal -1/480 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/48 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/480 binary64)) (*.f64 x #s(literal 1/48 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/480 binary64) (*.f64 x #s(literal 1/48 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64)) (.f64 x (.f64 x x)) (.f64 #s(literal 1/110592 binary64) (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 x #s(literal 1/48 binary64)) (.f64 x #s(literal 1/48 binary64))) (.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (*.f64 x #s(literal 1/48 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x)))) (.f64 (.f64 x #s(literal 1/48 binary64)) (.f64 x #s(literal 1/48 binary64)))) (-.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x #s(literal 1/48 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64))) (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (*.f64 x x) #s(literal -1/23040 binary64))))
(/.f64 (.f64 x (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64))) (fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64)) x) (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (*.f64 x x) #s(literal -1/23040 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64)) x) (fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64)) (.f64 x (.f64 x x)) (.f64 #s(literal 1/110592 binary64) (.f64 x (.f64 x x))))) (neg.f64 (fma.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 x #s(literal 1/48 binary64)) (.f64 x #s(literal 1/48 binary64))) (.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (*.f64 x #s(literal 1/48 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x)))) (.f64 (.f64 x #s(literal 1/48 binary64)) (.f64 x #s(literal 1/48 binary64))))) (neg.f64 (-.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x #s(literal 1/48 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64)))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (*.f64 x x) #s(literal -1/23040 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64)))) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64)) x)) (neg.f64 (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (*.f64 x x) #s(literal -1/23040 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64))))
(/.f64 (fma.f64 #s(literal 1/110592 binary64) (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64)) (.f64 x (.f64 x x)))) (fma.f64 (.f64 x #s(literal 1/48 binary64)) (.f64 x #s(literal 1/48 binary64)) (-.f64 (.f64 (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal -1/480 binary64) (.f64 x x)))) (.f64 (.f64 x #s(literal 1/48 binary64)) (.f64 x (.f64 #s(literal -1/480 binary64) (*.f64 x x)))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64)) x)
(*.f64 x #s(literal -1/480 binary64))
(*.f64 #s(literal -1/480 binary64) x)
(+.f64 #s(literal 1/48 binary64) (.f64 #s(literal -1/480 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal -1/480 binary64) (.f64 x x)) #s(literal 1/48 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64))) (/.f64 #s(literal 1/2304 binary64) (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64))))
(-.f64 (/.f64 #s(literal 1/2304 binary64) (-.f64 #s(literal 1/48 binary64) (.f64 #s(literal -1/480 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 1/48 binary64) (.f64 #s(literal -1/480 binary64) (.f64 x x)))))
(fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal 1/48 binary64))
(fma.f64 (*.f64 x #s(literal -1/480 binary64)) x #s(literal 1/48 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/480 binary64) #s(literal 1/48 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (.f64 x x) #s(literal -1/23040 binary64))) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)) (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (.f64 x x) #s(literal -1/23040 binary64))) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)) (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64)) (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (.f64 x x) #s(literal -1/23040 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64)) (+.f64 #s(literal 1/2304 binary64) (-.f64 (.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1/23040 binary64)))))
(/.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64)) (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (.f64 x x) #s(literal -1/23040 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64))) (neg.f64 (+.f64 #s(literal 1/2304 binary64) (-.f64 (.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1/23040 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64))) (neg.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64))))
(/.f64 (-.f64 #s(literal 1/2304 binary64) (.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/48 binary64) (.f64 #s(literal -1/480 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2304 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)) (fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (.f64 x x) #s(literal -1/23040 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2304 binary64) (.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 1/48 binary64) (.f64 #s(literal -1/480 binary64) (.f64 x x)))))
(pow.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (.f64 x x) #s(literal -1/23040 binary64))) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64)) (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64) #s(literal 1/110592 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2304 binary64)) (.f64 (*.f64 x x) #s(literal -1/23040 binary64)))))
(.f64 (fma.f64 #s(literal 1/230400 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2304 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/480 binary64)) #s(literal -1/48 binary64))))

eval65.0ms (0.6%)

Memory: -16.2MiB live, 97.7MiB allocated
Compiler: Compiled 8 102 to 425 computations (94.8% saved)

prune39.0ms (0.4%)

Memory

-6.4MiB live, 32.9MiB allocated

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	667	2	669
Fresh	1	0	1
Picked	1	4	5
Done	0	5	5
Total	669	11	680

Accuracy

100.0%

Counts

680 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	73.3%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 #s(approx (/ 1 (/ (- (exp ( 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))))
✓	69.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
✓	68.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
✓	70.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
✓	74.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
	69.1%	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (fma.f64 x (/.f64 (fma.f64 x #s(literal -1/64 binary64) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	69.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	70.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
✓	69.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	75.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

Compiler

Compiled 257 to 150 computations (41.6% saved)

regimes13.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

16 → 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)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (fma.f64 x (/.f64 (fma.f64 x #s(literal -1/64 binary64) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 #s(approx (/ 1 (/ (- (exp ( 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

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

Calls

3 calls:

5.0ms

4.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
100.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes12.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Accuracy

Total -5.1b remaining (-31.7%)

Threshold costs -5.1b (-31.7%)

Counts

14 → 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)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/480 binary64)) #s(literal 1/48 binary64))) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (fma.f64 x (/.f64 (fma.f64 x #s(literal -1/64 binary64) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))) (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)))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 #s(approx (/ 1 (/ (- (exp ( 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 #s(approx (/ 1 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))))))

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

Calls

3 calls:

4.0ms

3.0ms

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

3.0ms

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

Results

Accuracy	Segments	Branch
75.0%	1	`x`
75.0%	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))))`
75.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify26.0ms (0.2%)

Memory

-25.4MiB live, 14.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness352.0ms (3.3%)

Memory

15.6MiB live, 249.9MiB allocated

Rules

18 226×	`lower-fma.f64`
18 226×	`lower-fma.f32`
5 402×	`lower-fma.f64`
5 402×	`lower-fma.f32`
4 492×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
0	15	26
1	56	19
2	378	19
3	4533	19
0	8161	15
0	49	342
1	155	342
2	335	342
3	752	342
4	1201	302
5	1536	286
6	2025	286
7	2949	286
8	4633	286
0	8302	232

Stop Event

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

Compiler

Compiled 17 to 15 computations (11.8% saved)

preprocess51.0ms (0.5%)

Memory: 0.1MiB live, 38.9MiB allocated
Compiler: Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

sample914.0ms (8.6%)

preprocess481.0ms (4.5%)

explain133.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify408.0ms (3.9%)

localize33.0ms (0.3%)

series4.0ms (0%)

simplify505.0ms (4.8%)

rewrite358.0ms (3.4%)

eval93.0ms (0.9%)

prune84.0ms (0.8%)

simplify822.0ms (7.8%)

localize141.0ms (1.3%)

series7.0ms (0.1%)

simplify398.0ms (3.8%)

rewrite1.1s (10.5%)

eval50.0ms (0.5%)

prune27.0ms (0.3%)

simplify607.0ms (5.7%)

localize120.0ms (1.1%)

series795.0ms (7.5%)

simplify1.0s (9.8%)

rewrite346.0ms (3.3%)

eval30.0ms (0.3%)

prune31.0ms (0.3%)

simplify323.0ms (3%)

localize126.0ms (1.2%)

series14.0ms (0.1%)

simplify734.0ms (6.9%)

rewrite304.0ms (2.9%)

eval65.0ms (0.6%)

prune39.0ms (0.4%)

regimes13.0ms (0.1%)

regimes12.0ms (0.1%)

simplify26.0ms (0.2%)

soundness352.0ms (3.3%)

preprocess51.0ms (0.5%)

end0.0ms (0%)

Profiling