Metrics for sqrtexp (problem 3.4.4)

analyze1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample906.0ms (10.7%)

Memory

43.0MiB live, 921.7MiB allocated

Samples

456.0ms	8 256×	0	valid
138.0ms	2 568×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 364.0ms

ival-expm1: 126.0ms (34.6% of total)

ival-mult: 76.0ms (20.9% of total)

ival-div: 72.0ms (19.8% of total)

ival-sqrt: 72.0ms (19.8% of total)

ival-true: 8.0ms (2.2% of total)

exact: 7.0ms (1.9% of total)

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

Bogosity

preprocess394.0ms (4.6%)

Memory

7.0MiB live, 359.5MiB 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)))

explain188.0ms (2.2%)

Memory

2.8MiB live, 168.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
169	0	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
169	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
3	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
1	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	1	(-125.68157372664184)	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	169	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	169	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	3	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	3
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	3
↳	`(exp.f64 x)`	overflow	3
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	3
`sqrt.f64`	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`	oflow-rescue	1	0
↳	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	overflow	3
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	3
↳	`(exp.f64 x)`	overflow	3
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	3
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	3
↳	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`	overflow	2
`exp.f64`	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	172	0
-	1	83

Precision

0.9942196531791907

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	172	0	0
-	1	0	83

Precision?

0.9942196531791907

Recall?

1.0

Freqs

test

number	freq
0	83
1	3
2	170

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

91.0ms

512×

valid

Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-exp: 60.0ms (77.9% of total)

ival-expm1: 6.0ms (7.8% of total)

ival-div: 3.0ms (3.9% of total)

ival-mult: 3.0ms (3.9% of total)

ival-sqrt: 3.0ms (3.9% of total)

exact: 1.0ms (1.3% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB 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
▶	33.5%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify401.0ms (4.7%)

Memory

1.1MiB live, 397.5MiB 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)

localize34.0ms (0.4%)

Memory

-7.0MiB live, 31.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
✓	accuracy	99.1%	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	accuracy	38.1%	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	accuracy	38.0%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

22.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-sqrt: 5.0ms (33.4% of total)

ival-exp: 3.0ms (20% of total)

ival-expm1: 3.0ms (20% of total)

ival-div: 2.0ms (13.4% of total)

ival-mult: 2.0ms (13.4% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB 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 (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
#<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 (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)))>

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	(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
0.0ms	x	@	0	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms	x	@	0	(- (exp (* 2 x)) 1)

simplify422.0ms (5%)

Memory

-11.0MiB live, 315.7MiB allocated

Algorithm

1×	egg-herbie

Rules

15 504×	`lower-fma.f64`
15 504×	`lower-fma.f32`
4 704×	`lower-*.f64`
4 704×	`lower-*.f32`
2 492×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	480
1	252	446
2	663	446
3	1429	440
4	2558	360
5	5941	325
0	8294	270

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)
(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)))

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

rewrite327.0ms (3.9%)

Memory

-2.0MiB live, 434.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 562×	`lower-fma.f64`
4 562×	`lower-fma.f32`
3 484×	`lower-*.f32`
3 482×	`lower-*.f64`
2 734×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
0	17	36
1	63	22
2	429	22
3	4997	22
0	8103	18

Stop Event

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

Counts

5 → 711

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

eval105.0ms (1.2%)

Memory: 8.3MiB live, 157.3MiB allocated
Compiler: Compiled 17 442 to 2 477 computations (85.8% saved)

prune89.0ms (1.1%)

Memory

7.7MiB live, 207.0MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	763	7	770
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	764	7	771

Accuracy

99.6%

Counts

771 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	66.4%	(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))))
▶	68.0%	(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))))
▶	66.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	72.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	67.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))

Compiler

Compiled 136 to 92 computations (32.4% saved)

simplify420.0ms (4.9%)

Memory

19.7MiB live, 538.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

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: 5 (0.0ms)

Iter	Nodes	Cost
0	29	202
0	47	202
1	86	202
2	138	202
3	239	202
4	312	162
5	373	146
6	450	146
7	853	146
8	3187	146
9	7165	146
0	8190	146

Stop Event

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

Calls

Call 1

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

localize84.0ms (1%)

Memory

7.2MiB live, 122.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(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 #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	99.6%	(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	66.6%	#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 #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	99.6%	(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	67.7%	#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	99.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	accuracy	66.5%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
✓	accuracy	99.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	accuracy	71.8%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓	accuracy	99.6%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Samples

50.0ms

256×

valid

Compiler

Compiled 163 to 27 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-add: 10.0ms (27.7% of total)

ival-mult: 9.0ms (24.9% of total)

const: 4.0ms (11.1% of total)

ival-sqrt: 4.0ms (11.1% of total)

ival-expm1: 3.0ms (8.3% of total)

ival-div: 2.0ms (5.5% of total)

ival-exp: 2.0ms (5.5% of total)

ival-sub: 1.0ms (2.8% of total)

exact: 1.0ms (2.8% of total)

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

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

series10.0ms (0.1%)

Memory

-26.6MiB live, 12.2MiB allocated

Counts

17 → 204

Calls

Call 1

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

51 calls:

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

simplify404.0ms (4.8%)

Memory

-5.6MiB live, 499.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 534×	`lower-fma.f64`
16 534×	`lower-fma.f32`
4 720×	`lower-*.f64`
4 720×	`lower-*.f32`
2 888×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	1818
1	322	1640
2	923	1632
3	3250	1602
4	6491	1602
0	8177	1222

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 202

Calls

Call 1

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

rewrite356.0ms (4.2%)

Memory

-2.5MiB live, 430.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 360×	`lower-fma.f32`
5 350×	`lower-fma.f64`
4 328×	`lower-/.f64`
4 328×	`lower-/.f32`
3 452×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	188
0	47	188
1	194	132
2	1435	132
0	8413	132

Stop Event

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

Counts

17 → 478

Calls

Call 1

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

eval83.0ms (1%)

Memory: 13.7MiB live, 165.8MiB allocated
Compiler: Compiled 13 789 to 1 793 computations (87% saved)

prune99.0ms (1.2%)

Memory

-1.5MiB live, 152.7MiB allocated

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	674	6	680
Fresh	0	2	2
Picked	0	5	5
Done	0	0	0
Total	674	13	687

Accuracy

99.6%

Counts

687 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	66.4%	(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))))
✓	68.0%	(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))))
✓	66.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	2.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))))
	3.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))))
▶	2.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))))
	4.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))))
▶	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	72.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	67.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
▶	66.7%	#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 245 to 146 computations (40.4% saved)

simplify335.0ms (3.9%)

Memory

16.2MiB live, 427.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

12 754×	`lower-fma.f32`
12 740×	`lower-fma.f64`
2 220×	`lower-*.f32`
2 210×	`lower-*.f64`
2 206×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	423
0	74	413
1	154	407
2	307	405
3	594	405
4	839	361
5	1123	345
6	1239	345
7	1634	345
8	3848	345
9	7416	345
0	8310	330

Stop Event

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

Calls

Call 1

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

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

localize171.0ms (2%)

Memory

2.2MiB live, 262.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	98.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.1%	#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))))
✓	accuracy	99.9%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	99.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))))
✓	accuracy	67.0%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)))
✓	accuracy	34.9%	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
✓	accuracy	99.8%	(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
✓	accuracy	99.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))))
✓	accuracy	67.0%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))))
✓	accuracy	33.7%	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	99.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	accuracy	68.1%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
✓	accuracy	34.2%	#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.9%	(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)))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	68.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))

Samples

83.0ms	234×	0	valid
7.0ms	13×	1	valid
6.0ms	8×	2	valid
1.0ms	1×	5	exit

Compiler

Compiled 266 to 43 computations (83.8% saved)

Precisions

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

ival-mult: 24.0ms (38% of total)

ival-add: 16.0ms (25.3% of total)

const: 8.0ms (12.7% of total)

ival-div: 5.0ms (7.9% of total)

adjust: 3.0ms (4.7% of total)

ival-sqrt: 3.0ms (4.7% of total)

ival-expm1: 3.0ms (4.7% of total)

exact: 1.0ms (1.6% of total)

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

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

series22.0ms (0.3%)

Memory

-15.9MiB live, 23.0MiB allocated

Counts

22 → 240

Calls

Call 1

Inputs
#<alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))>
#<alt (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)))>
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))>
#<alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))>
#<alt #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))>
#<alt (.f64 #s(literal 1/2 binary64) (.f64 x x))>
#<alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))))>
#<alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))))>
#<alt #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))>
#<alt (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))>
#<alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))))>
#<alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)))>
#<alt #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))>
#<alt (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)>
#<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 #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))))>
#<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 x #s(literal 1/6 binary64) #s(literal 1/2 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 (+ (* 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 (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 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 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>
#<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 (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (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 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>
#<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 (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<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 (/ (- (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>
#<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 x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 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)))))>
#<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)) x)) 1/6)))>
#<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 (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 (+ (* 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>
#<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))))>
#<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

60 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))
1.0ms	x	@	0	(+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))
0.0ms	x	@	inf	(/ x (sqrt 2))
0.0ms	x	@	0	(+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))
0.0ms	x	@	-inf	(+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))

simplify707.0ms (8.3%)

Memory

18.2MiB live, 741.7MiB allocated

Algorithm

1×	egg-herbie

Rules

20 114×	`lower-fma.f64`
20 114×	`lower-fma.f32`
5 022×	`lower-*.f64`
5 022×	`lower-*.f32`
3 400×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	2616
1	531	2393
2	1620	2252
3	4912	2220
0	8143	1824

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 239

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

rewrite707.0ms (8.3%)

Memory

-32.1MiB live, 395.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 920×	`lower-*.f32`
4 910×	`lower-*.f64`
3 966×	`lower-/.f32`
3 962×	`lower-/.f64`
3 798×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	380
0	74	372
1	330	310
2	2783	306
0	8894	294

Stop Event

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

Counts

22 → 555

Calls

Call 1

Inputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
(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)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
#s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)))
#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 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))))
#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)))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 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
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(+.f64 (*.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)))
(+.f64 (/.f64 (.f64 x (.f64 x #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))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (.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)))) (/.f64 #s(literal 2 binary64) (-.f64 (.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)))))
(fma.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 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 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x #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 x (*.f64 (/.f64 #s(literal 1 binary64) (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)))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #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 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #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 #s(literal 3/16 binary64) (*.f64 x (/.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 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x #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 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
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(/.f64 (-.f64 #s(literal 9/256 binary64) (.f64 (.f64 x x) #s(literal 49/36864 binary64))) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (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))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #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 (*.f64 x x) #s(literal 49/36864 binary64) #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 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))

eval226.0ms (2.7%)

Memory: -5.6MiB live, 104.3MiB allocated
Compiler: Compiled 25 266 to 2 353 computations (90.7% saved)

prune119.0ms (1.4%)

Memory

21.3MiB live, 144.1MiB allocated

Pruning

21 alts after pruning (13 fresh and 8 done)

	Pruned	Kept	Total
New	839	11	850
Fresh	1	2	3
Picked	2	3	5
Done	0	5	5
Total	842	21	863

Accuracy

99.6%

Counts

863 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	66.4%	(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))))
✓	68.0%	(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))))
✓	66.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	2.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))))
▶	4.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x))))
	2.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) x))))
▶	3.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
	3.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))))
✓	2.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))))
✓	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	72.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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)))))
▶	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	66.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (/.f64 (-.f64 (.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))))
	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
	66.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x #s(approx (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))))
	4.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)))))
▶	2.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2)) (/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
	3.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))

Compiler

Compiled 480 to 276 computations (42.5% saved)

simplify398.0ms (4.7%)

Memory

12.8MiB live, 367.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64)))
✓	cost-diff	0	(/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2)) (/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2)) (/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	0	(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
✓	cost-diff	0	(fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x)
✓	cost-diff	0	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x))
✓	cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x)))
✓	cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x))))
✓	cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
✓	cost-diff	0	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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)))))
✓	cost-diff	1664	(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))))

Rules

12 778×	`lower-fma.f32`
12 764×	`lower-fma.f64`
2 256×	`lower-*.f32`
2 244×	`lower-*.f64`
2 182×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	480
0	84	490
1	180	452
2	373	452
3	770	452
4	1137	417
5	1356	403
6	1433	403
7	1827	403
8	4030	403
9	7631	403
0	8151	391

Stop Event

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

Calls

Call 1

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

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

localize159.0ms (1.9%)

Memory

11.0MiB live, 324.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.8%	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.8%	(/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.3%	(.f64 (.f64 x x) #s(literal 7/192 binary64))
✓	accuracy	67.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2)) (/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	33.6%	#s(approx (+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2)) (/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.9%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	99.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
✓	accuracy	67.0%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓	accuracy	34.7%	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓	accuracy	99.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x))))
✓	accuracy	67.0%	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x)))
✓	accuracy	66.7%	#s(approx (+ (* x 1/6) 1/2) #s(literal 1/2 binary64))
✓	accuracy	34.9%	#s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x))
✓	accuracy	99.8%	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	98.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	67.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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)))))

Samples

81.0ms	240×	0	valid
6.0ms	10×	1	valid
4.0ms	5×	2	valid
1.0ms	1×	5	exit

Compiler

Compiled 304 to 45 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 26.0ms (39.1% of total)

ival-add: 15.0ms (22.6% of total)

const: 8.0ms (12% of total)

ival-div: 7.0ms (10.5% of total)

ival-expm1: 4.0ms (6% of total)

ival-sqrt: 3.0ms (4.5% of total)

adjust: 2.0ms (3% of total)

exact: 1.0ms (1.5% of total)

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

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

series16.0ms (0.2%)

Memory

-32.9MiB live, 16.0MiB allocated

Counts

25 → 276

Calls

Call 1

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

Calls

69 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/ (* x (* (* x x) 7/192)) (sqrt 2))
0.0ms	x	@	inf	(/ (* x (* (* x x) 7/192)) (sqrt 2))
0.0ms	x	@	-inf	(/ (* x (* (* x x) 7/192)) (sqrt 2))
0.0ms	x	@	inf	(* x (* (* x x) 7/192))
0.0ms	x	@	-inf	(* x (* (* x x) 7/192))

simplify466.0ms (5.5%)

Memory

44.6MiB live, 775.1MiB allocated

Algorithm

1×	egg-herbie

Rules

22 524×	`lower-fma.f64`
22 524×	`lower-fma.f32`
4 896×	`lower-*.f64`
4 896×	`lower-*.f32`
3 146×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	2614
1	500	2611
2	1470	2493
3	4434	2403
0	8190	2011

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 275

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

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

rewrite294.0ms (3.5%)

Memory

-5.2MiB live, 463.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 230×	`lower-*.f32`
6 218×	`lower-*.f64`
3 706×	`lower-/.f32`
3 700×	`lower-/.f64`
2 858×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	428
0	84	438
1	364	351
2	3113	350
0	9575	338

Stop Event

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

Counts

25 → 332

Calls

Call 1

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

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

eval122.0ms (1.4%)

Memory: -35.5MiB live, 110.1MiB allocated
Compiler: Compiled 15 449 to 959 computations (93.8% saved)

prune66.0ms (0.8%)

Memory

30.5MiB live, 117.7MiB allocated

Pruning

22 alts after pruning (10 fresh and 12 done)

	Pruned	Kept	Total
New	695	5	700
Fresh	3	5	8
Picked	1	4	5
Done	0	8	8
Total	699	22	721

Accuracy

99.6%

Counts

721 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	66.4%	(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))))
✓	68.0%	(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))))
✓	66.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	2.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))))
✓	4.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (fma.f64 x (.f64 x #s(approx (+ ( x 1/6) 1/2) #s(literal 1/2 binary64))) x))))
	3.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))))
	2.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) x))))
✓	3.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
✓	2.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))))
✓	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* x (+ (* x 1/2) 1)) 2) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
✓	72.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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)))))
✓	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	66.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 x (/.f64 (fma.f64 (.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (/.f64 (-.f64 (.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))))
	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
	3.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (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)))))
	3.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))))
	4.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2)) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)))))
	2.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* x (+ (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)) (/ 1/2 (sqrt 2)))) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64)) x) x)))

Compiler

Compiled 663 to 262 computations (60.5% saved)

regimes27.0ms (0.3%)

Memory

-33.9MiB live, 44.0MiB allocated

Counts

30 → 1

Calls

Call 1

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

10.0ms

7.0ms

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

7.0ms

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

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	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))))`
99.6%	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)

regimes23.0ms (0.3%)

Memory

36.0MiB live, 36.0MiB allocated

Accuracy

Total -45.5b remaining (-257.9%)

Threshold costs -45.5b (-257.9%)

Counts

28 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms

7.0ms

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

7.0ms

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

Results

Accuracy	Segments	Branch
72.5%	1	`x`
72.5%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
72.5%	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)

simplify7.0ms (0.1%)

Memory

-28.6MiB live, 10.1MiB 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)))

soundness248.0ms (2.9%)

Memory

-4.2MiB live, 152.2MiB allocated

Rules

15 504×	`lower-fma.f64`
15 504×	`lower-fma.f32`
4 704×	`lower-*.f64`
4 704×	`lower-*.f32`
4 562×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
0	17	36
1	63	22
2	429	22
3	4997	22
0	8103	18
0	77	480
1	252	446
2	663	446
3	1429	440
4	2558	360
5	5941	325
0	8294	270

Stop Event

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

Compiler

Compiled 30 to 23 computations (23.3% saved)

preprocess48.0ms (0.6%)

Memory: 29.2MiB live, 68.3MiB allocated
Compiler: Compiled 44 to 34 computations (22.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

sample906.0ms (10.7%)

preprocess394.0ms (4.6%)

explain188.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify401.0ms (4.7%)

localize34.0ms (0.4%)

series4.0ms (0.1%)

simplify422.0ms (5%)

rewrite327.0ms (3.9%)

eval105.0ms (1.2%)

prune89.0ms (1.1%)

simplify420.0ms (4.9%)

localize84.0ms (1%)

series10.0ms (0.1%)

simplify404.0ms (4.8%)

rewrite356.0ms (4.2%)

eval83.0ms (1%)

prune99.0ms (1.2%)

simplify335.0ms (3.9%)

localize171.0ms (2%)

series22.0ms (0.3%)

simplify707.0ms (8.3%)

rewrite707.0ms (8.3%)

eval226.0ms (2.7%)

prune119.0ms (1.4%)

simplify398.0ms (4.7%)

localize159.0ms (1.9%)

series16.0ms (0.2%)

simplify466.0ms (5.5%)

rewrite294.0ms (3.5%)

eval122.0ms (1.4%)

prune66.0ms (0.8%)

regimes27.0ms (0.3%)

regimes23.0ms (0.3%)

simplify7.0ms (0.1%)

soundness248.0ms (2.9%)

preprocess48.0ms (0.6%)

end0.0ms (0%)

Profiling