Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze2.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (26%)

Memory

51.6MiB live, 924.2MiB allocated; 898ms collecting garbage

Samples

486.0ms	8 256×	0	valid
151.0ms	2 721×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 387.0ms

ival-expm1: 134.0ms (34.7% of total)

ival-mult: 85.0ms (22% of total)

ival-div: 76.0ms (19.7% of total)

ival-sqrt: 70.0ms (18.1% of total)

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

exact: 7.0ms (1.8% of total)

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

adjust: 3.0ms (0.8% of total)

Bogosity

explain121.0ms (2.5%)

Memory

-10.8MiB live, 127.6MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
171	0	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
171	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
1	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	1	(100.41688418669642)	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	171	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	171	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	1	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	1
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	1
↳	`(exp.f64 x)`	overflow	1
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	1
`exp.f64`	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	171	0
-	2	83

Precision

0.9884393063583815

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	171	0	0
-	2	0	83

Precision?

0.9884393063583815

Recall?

1.0

Freqs

test

number	freq
0	83
1	2
2	171

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 106 to 34 computations (67.9% saved)

Precisions

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

ival-exp: 7.0ms (29.3% of total)

ival-expm1: 6.0ms (25.1% of total)

ival-mult: 4.0ms (16.7% of total)

ival-div: 3.0ms (12.5% of total)

ival-sqrt: 3.0ms (12.5% of total)

exact: 1.0ms (4.2% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess178.0ms (3.7%)

Memory

18.6MiB live, 113.4MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	35	27
2	80	27
3	250	27
4	1179	13
0	10	12
0	17	12
1	33	12
2	59	12
3	146	12
4	695	7
5	6520	7
0	8067	7

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 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))

Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	34.0%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify145.0ms (3%)

Memory

4.7MiB live, 95.7MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
0	17	45
1	33	45
2	59	45
3	146	45
4	695	35
5	6520	35
0	8067	31

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

localize69.0ms (1.4%)

Memory

-16.7MiB live, 42.5MiB allocated; 25ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.015625	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
accuracy	0.21484375000000003	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	39.78721676234693	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	39.87511982710014	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

18.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

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

ival-exp: 3.0ms (25.6% of total)

ival-expm1: 3.0ms (25.6% of total)

ival-div: 2.0ms (17.1% of total)

ival-mult: 2.0ms (17.1% of total)

ival-sqrt: 2.0ms (17.1% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

3.1MiB live, 3.1MiB allocated; 0ms collecting garbage

Counts

4 → 20

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

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

1.0ms

-inf

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

simplify155.0ms (3.3%)

Memory

12.1MiB live, 140.4MiB allocated; 27ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	213
1	302	173
2	1041	172
3	3429	170
0	8155	135

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

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

Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) x #s(literal 4/3 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (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 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp x) 1)
(expm1.f64 x)
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))

rewrite66.0ms (1.4%)

Memory

-5.7MiB live, 51.4MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	17	33
1	65	19
0	423	15

Stop Event

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

Counts

4 → 50

Calls

Call 1

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

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

eval8.0ms (0.2%)

Memory: 13.0MiB live, 13.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 189 to 297 computations (75% saved)

prune7.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms collecting garbage

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	10	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Accuracy

100.0%

Counts

70 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
▶	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	67.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	73.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	99.0%	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
▶	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
	68.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 328 to 262 computations (20.1% saved)

simplify124.0ms (2.6%)

Memory

-9.7MiB live, 128.6MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	202
0	51	202
1	85	202
2	176	202
3	491	202
4	1784	172
0	8722	172

Stop Event

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

Calls

Call 1

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

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

localize97.0ms (2%)

Memory

13.0MiB live, 108.2MiB allocated; 18ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.1484375	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.9336471318039575	(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.59181886791829	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.1484375	(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.99609375	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.616586051828797	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy	20.00469712372046	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	17.28173458699075	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0.0	(+.f64 (exp.f64 x) #s(literal 1 binary64))
accuracy	0.0	(exp.f64 x)
accuracy	0.015625	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))

Samples

73.0ms	243×	0	valid
3.0ms	8×	1	valid
2.0ms	4×	2	valid
1.0ms	1×	5	exit

Compiler

Compiled 172 to 31 computations (82% saved)

Precisions

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

ival-mult: 28.0ms (42.7% of total)

const: 12.0ms (18.3% of total)

ival-add: 8.0ms (12.2% of total)

ival-div: 5.0ms (7.6% of total)

ival-sqrt: 5.0ms (7.6% of total)

ival-expm1: 3.0ms (4.6% of total)

adjust: 2.0ms (3.1% of total)

ival-exp: 2.0ms (3.1% of total)

exact: 1.0ms (1.5% of total)

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

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

series18.0ms (0.4%)

Memory

-31.6MiB live, 13.1MiB allocated; 14ms collecting garbage

Counts

18 → 50

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (+ (* 7/192 x) 3/16))
3.0ms	x	@	-inf	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (+ (* 7/192 x) 3/16))
2.0ms	x	@	0	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ 1/2 (sqrt 2)) x) (sqrt 2)) (/ 1/2 (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (+ (* 7/192 x) 3/16))

Time

Variable

Point

Expression

11.0ms

inf

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

3.0ms

-inf

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

2.0ms

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

simplify149.0ms (3.1%)

Memory

4.4MiB live, 105.3MiB allocated; 16ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	584
1	526	474
2	1855	435
3	7231	434
0	8068	387

Stop Event

1×	iter limit
1×	node limit

Counts

50 → 50

Calls

Call 1

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

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

rewrite236.0ms (4.9%)

Memory

19.9MiB live, 150.0MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	185
0	51	185
1	204	143
2	1433	143
0	8147	143

Stop Event

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

Counts

18 → 412

Calls

Call 1

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

Outputs
(*.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.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 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 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 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sinh.f64 (acosh.f64 (exp.f64 x))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (cosh.f64 (asinh.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (sqrt.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (expm1.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (sqrt.f64 (neg.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64)))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (neg.f64 (sinh.f64 (acosh.f64 (exp.f64 x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (cosh.f64 (asinh.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 x)))))
(/.f64 (cosh.f64 (asinh.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64)))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sinh.f64 (acosh.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sinh.f64 (acosh.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sinh.f64 (acosh.f64 (exp.f64 x))) (sqrt.f64 (expm1.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 (cosh.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (expm1.f64 x) (expm1.f64 x)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (/.f64 (expm1.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cosh.f64 x)) (+.f64 #s(literal 1 binary64) (cosh.f64 x))) (pow.f64 (sinh.f64 x) #s(literal 2 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) (cosh.f64 x)) (sinh.f64 x)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64)))) (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (+.f64 (sinh.f64 x) #s(literal 1 binary64)) (+.f64 (sinh.f64 x) #s(literal 1 binary64)))) (-.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)) (*.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)) (.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (cosh.f64 x)) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) (cosh.f64 x)) (+.f64 #s(literal 1 binary64) (cosh.f64 x)) (-.f64 (pow.f64 (sinh.f64 x) #s(literal 2 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (cosh.f64 x)) (sinh.f64 x)))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (-.f64 (.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))) (.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (+.f64 (sinh.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (.f64 (+.f64 (sinh.f64 x) #s(literal 1 binary64)) (+.f64 (sinh.f64 x) #s(literal 1 binary64))) (.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (neg.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (expm1.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (neg.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64)))) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (-.f64 (.f64 (neg.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (neg.f64 (expm1.f64 x))) (.f64 (neg.f64 (expm1.f64 x)) #s(literal -1 binary64))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (neg.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (expm1.f64 x)) (.f64 (neg.f64 (expm1.f64 x)) #s(literal 1 binary64))) (*.f64 (neg.f64 (expm1.f64 x)) (expm1.f64 x)))
(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (neg.f64 (expm1.f64 x))) (.f64 (expm1.f64 x) #s(literal -1 binary64))) (*.f64 (expm1.f64 x) (neg.f64 (expm1.f64 x))))
(/.f64 (fma.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (-.f64 (neg.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x)))
(/.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (expm1.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (neg.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (expm1.f64 x)))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (neg.f64 (expm1.f64 x)))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (expm1.f64 x)))
(neg.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (expm1.f64 x))))
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(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) #s(literal 9/256 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))) (.f64 (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64)) #s(literal 9/256 binary64))) (.f64 (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64)) (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))) (.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))) #s(literal 27/4096 binary64))) (.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64))) (-.f64 #s(literal 3/16 binary64) (.f64 #s(literal 7/192 binary64) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) #s(literal 9/256 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64))) (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) #s(literal 9/256 binary64)) (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64)))
(/.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (fma.f64 #s(literal 343/7077888 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 27/4096 binary64)) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(-.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 #s(literal 3/16 binary64) (.f64 #s(literal 7/192 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))))
(-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal -7/192 binary64) x))
(-.f64 #s(literal 3/16 binary64) (*.f64 (neg.f64 x) #s(literal 7/192 binary64)))
(+.f64 (/.f64 #s(literal 27/4096 binary64) (+.f64 #s(literal 9/256 binary64) (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 7/1024 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 7/1024 binary64))))) (/.f64 #s(literal 27/4096 binary64) (+.f64 #s(literal 9/256 binary64) (-.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(+.f64 (/.f64 #s(literal 27/4096 binary64) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64))))) (/.f64 #s(literal 27/4096 binary64) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(+.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))
(+.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x))

eval118.0ms (2.5%)

Memory: -0.3MiB live, 114.5MiB allocated; 21ms collecting garbage
Compiler: Compiled 19 670 to 2 230 computations (88.7% saved)

prune31.0ms (0.6%)

Memory

0.6MiB live, 46.3MiB allocated; 2ms collecting garbage

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	486	8	494
Fresh	3	2	5
Picked	1	4	5
Done	0	0	0
Total	490	14	504

Accuracy

100.0%

Counts

504 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	67.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
▶	68.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) x))))
	5.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	73.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	68.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶	67.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
	66.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x) (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x))))
▶	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))

Compiler

Compiled 670 to 485 computations (27.6% saved)

simplify152.0ms (3.2%)

Memory

-10.4MiB live, 134.7MiB allocated; 18ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	436
0	70	436
1	122	436
2	284	436
3	933	436
4	2961	388
0	8949	370

Stop Event

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

Calls

Call 1

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

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

localize168.0ms (3.5%)

Memory

17.5MiB live, 102.9MiB allocated; 18ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.15625	(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
accuracy	0.9336471318039575	(/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.59181886791829	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	41.7627806405118	#s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x))
accuracy	0.185878759768442	(/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.22103500976844204	(.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	20.59181886791829	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
accuracy	41.5787801511345	#s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
accuracy	20.00469712372046	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
accuracy	41.755173940951195	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
accuracy	0.0	(+.f64 #s(literal 2 binary64) x)
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	20.63161379588655	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0.00390625	(+.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) x))))
accuracy	0.125	(*.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) x)
accuracy	20.00469712372046	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) x)))

Samples

121.0ms	210×	0	valid
13.0ms	21×	2	valid
11.0ms	24×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 272 to 32 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-add: 17.0ms (29.5% of total)

ival-mult: 16.0ms (27.8% of total)

ival-div: 7.0ms (12.1% of total)

adjust: 6.0ms (10.4% of total)

const: 4.0ms (6.9% of total)

ival-sqrt: 4.0ms (6.9% of total)

ival-expm1: 3.0ms (5.2% of total)

exact: 1.0ms (1.7% of total)

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

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

series34.0ms (0.7%)

Memory

-23.9MiB live, 30.3MiB allocated; 15ms collecting garbage

Counts

22 → 52

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

29.0ms

-inf

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

3.0ms

inf

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

2.0ms

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

simplify144.0ms (3%)

Memory

13.6MiB live, 142.5MiB allocated; 19ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	153	614
1	563	499
2	1957	465
3	7080	463
0	8162	417

Stop Event

1×	iter limit
1×	node limit

Counts

52 → 51

Calls

Call 1

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

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

rewrite293.0ms (6.1%)

Memory

4.7MiB live, 197.9MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	396
0	70	396
1	262	340
2	1916	340
0	8122	326

Stop Event

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

Counts

22 → 335

Calls

Call 1

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

Outputs
(*.f64 (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) x)
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))) x)) (neg.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) x)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 x (-.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))))) (neg.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (*.f64 x (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))) x) (-.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))))
(/.f64 (*.f64 x (-.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(/.f64 (*.f64 x (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 3 binary64)))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x (*.f64 #s(literal 1 binary64) x))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x (*.f64 (/.f64 #s(literal 2 binary64) x) x))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x (*.f64 x (/.f64 #s(literal 2 binary64) x)))
(fma.f64 (/.f64 #s(literal 2 binary64) x) x (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (*.f64 x #s(literal 1 binary64)))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 2 binary64) x) x))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (*.f64 x (/.f64 #s(literal 2 binary64) x)))
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eval72.0ms (1.5%)

Memory: -12.4MiB live, 52.7MiB allocated; 12ms collecting garbage
Compiler: Compiled 18 282 to 1 950 computations (89.3% saved)

prune20.0ms (0.4%)

Memory

-21.9MiB live, 24.6MiB allocated; 3ms collecting garbage

Pruning

16 alts after pruning (9 fresh and 7 done)

	Pruned	Kept	Total
New	377	5	382
Fresh	1	4	5
Picked	2	3	5
Done	0	4	4
Total	380	16	396

Accuracy

100.0%

Counts

396 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	67.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	68.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x (*.f64 #s(literal 1 binary64) x)))))
✓	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
▶	5.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
▶	73.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 #s(approx (+ (/ 2 x) (+ ( 1/2 x) 1)) (/.f64 #s(literal 2 binary64) x)) x))))
✓	73.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
▶	68.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	67.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
	2.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) #s(approx (/ (+ (* 7/192 x) 3/16) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))))))
▶	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) #s(approx (* (* x x) (/ (+ (* 7/192 x) 3/16) (sqrt 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))))

Compiler

Compiled 789 to 558 computations (29.3% saved)

simplify153.0ms (3.2%)

Memory

46.5MiB live, 133.4MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	524
0	79	524
1	146	524
2	340	524
3	1089	524
4	3504	489
0	8349	464

Stop Event

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

Calls

Call 1

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

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

localize146.0ms (3.1%)

Memory

-29.3MiB live, 157.8MiB allocated; 24ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(fma.f64 (/.f64 (fma.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.9336471318039575	(/.f64 (fma.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.59181886791829	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	20.813207342362592	#s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64))
accuracy	0.28125	(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.47265625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.59181886791829	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
accuracy	41.5787801511345	#s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x))
accuracy	0.47265625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	20.59181886791829	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) #s(approx (* (* x x) (/ (+ (* 7/192 x) 3/16) (sqrt 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))))
accuracy	20.97536109589492	#s(approx (* (* x x) (/ (+ (* 7/192 x) 3/16) (sqrt 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
accuracy	41.5787801511345	#s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) #s(approx (* (* x x) (/ (+ (* 7/192 x) 3/16) (sqrt 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
accuracy	0.0	(*.f64 x x)
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
accuracy	20.00469712372046	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	41.645137564386935	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 #s(approx (+ (/ 2 x) (+ ( 1/2 x) 1)) (/.f64 #s(literal 2 binary64) x)) x))))
accuracy	0.125	(.f64 #s(approx (+ (/ 2 x) (+ ( 1/2 x) 1)) (/.f64 #s(literal 2 binary64) x)) x)
accuracy	20.00469712372046	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 #s(approx (+ (/ 2 x) (+ ( 1/2 x) 1)) (/.f64 #s(literal 2 binary64) x)) x)))
accuracy	20.335296813050935	#s(approx (+ (/ 2 x) (+ (* 1/2 x) 1)) (/.f64 #s(literal 2 binary64) x))

Samples

90.0ms	243×	0	valid
25.0ms	4×	2	valid
4.0ms	8×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 292 to 37 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

const: 32.0ms (32.5% of total)

ival-mult: 21.0ms (21.4% of total)

adjust: 19.0ms (19.3% of total)

ival-div: 13.0ms (13.2% of total)

ival-add: 7.0ms (7.1% of total)

ival-sqrt: 3.0ms (3.1% of total)

ival-expm1: 3.0ms (3.1% of total)

exact: 1.0ms (1% of total)

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

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

series10.0ms (0.2%)

Memory

13.5MiB live, 13.5MiB allocated; 0ms collecting garbage

Counts

24 → 50

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

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

3.0ms

inf

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

2.0ms

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

simplify190.0ms (4%)

Memory

15.4MiB live, 200.0MiB allocated; 26ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	151	600
1	554	484
2	1923	444
3	7687	443
0	8680	399

Stop Event

1×	iter limit
1×	node limit

Counts

50 → 50

Calls

Call 1

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

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

rewrite216.0ms (4.5%)

Memory

1.0MiB live, 195.2MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	486
0	79	486
1	288	437
2	2050	437
0	8336	412

Stop Event

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

Counts

24 → 239

Calls

Call 1

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

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

eval60.0ms (1.3%)

Memory: -19.7MiB live, 62.1MiB allocated; 29ms collecting garbage
Compiler: Compiled 13 371 to 1 304 computations (90.2% saved)

prune19.0ms (0.4%)

Memory

-17.0MiB live, 28.4MiB allocated; 4ms collecting garbage

Pruning

17 alts after pruning (5 fresh and 12 done)

	Pruned	Kept	Total
New	289	1	290
Fresh	0	4	4
Picked	0	5	5
Done	0	7	7
Total	289	17	306

Accuracy

100.0%

Counts

306 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	67.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	68.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x (*.f64 #s(literal 1 binary64) x)))))
✓	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
✓	5.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	73.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 #s(approx (+ (/ 2 x) (+ ( 1/2 x) 1)) (/.f64 #s(literal 2 binary64) x)) x))))
✓	73.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
✓	68.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	67.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	67.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
	2.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) #s(approx (/ (+ (* 7/192 x) 3/16) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))))))
	2.6%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 #s(approx ( (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))) x)))
✓	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) #s(approx (* (* x x) (/ (+ (* 7/192 x) 3/16) (sqrt 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))))

Compiler

Compiled 1 227 to 518 computations (57.8% saved)

regimes17.0ms (0.4%)

Memory

21.4MiB live, 21.4MiB allocated; 0ms collecting garbage

Counts

25 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 #s(approx (+ (/ 2 x) (+ ( 1/2 x) 1)) (/.f64 #s(literal 2 binary64) x)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) #s(approx (* (* x x) (/ (+ (* 7/192 x) 3/16) (sqrt 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) x))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 #s(approx ( (+ (* 7/192 x) 3/16) (/ x (sqrt 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) #s(approx (/ (+ (* 7/192 x) 3/16) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 7/192 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) x (*.f64 #s(literal 1 binary64) x)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(approx (+ (* 7/192 x) 3/16) #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x) (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 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))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))

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

Calls

3 calls:

6.0ms

5.0ms

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

5.0ms

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

Results

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

Compiler

Compiled 24 to 20 computations (16.7% saved)

regimes15.0ms (0.3%)

Memory

-29.1MiB live, 17.5MiB allocated; 2ms collecting garbage

Accuracy

Total -46.0b remaining (-269.1%)

Threshold costs -46b (-269.1%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms

4.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
73.3%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
73.3%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
73.3%	1	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify52.0ms (1.1%)

Memory

11.5MiB live, 57.3MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	30	19
2	56	19
3	142	19
4	687	14
5	6543	14

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations159.0ms (3.3%)

Memory

12.3MiB live, 65.6MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	17	33
1	65	19
0	423	15
0	77	213
1	302	173
2	1041	172
3	3429	170
0	8155	135

Stop Event

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

preprocess80.0ms (1.7%)

Memory: -2.1MiB live, 44.6MiB allocated; 2ms collecting garbage
Compiler: Compiled 62 to 52 computations (16.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze2.0ms (0%)

sample1.2s (26%)

explain121.0ms (2.5%)

preprocess178.0ms (3.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify145.0ms (3%)

localize69.0ms (1.4%)

series3.0ms (0.1%)

simplify155.0ms (3.3%)

rewrite66.0ms (1.4%)

eval8.0ms (0.2%)

prune7.0ms (0.1%)

simplify124.0ms (2.6%)

localize97.0ms (2%)

series18.0ms (0.4%)

simplify149.0ms (3.1%)

rewrite236.0ms (4.9%)

eval118.0ms (2.5%)

prune31.0ms (0.6%)

simplify152.0ms (3.2%)

localize168.0ms (3.5%)

series34.0ms (0.7%)

simplify144.0ms (3%)

rewrite293.0ms (6.1%)

eval72.0ms (1.5%)

prune20.0ms (0.4%)

simplify153.0ms (3.2%)

localize146.0ms (3.1%)

series10.0ms (0.2%)

simplify190.0ms (4%)

rewrite216.0ms (4.5%)

eval60.0ms (1.3%)

prune19.0ms (0.4%)

regimes17.0ms (0.4%)

regimes15.0ms (0.3%)

simplify52.0ms (1.1%)

derivations159.0ms (3.3%)

preprocess80.0ms (1.7%)

end0.0ms (0%)

Profiling