Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

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

analyze2.0ms (0%)

Memory

4.5MiB live, 4.5MiB 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 (26.4%)

Memory

62.8MiB live, 929.3MiB allocated; 913ms collecting garbage

Samples

476.0ms	8 256×	0	valid
425.0ms	2 545×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 710.0ms

ival-mult: 408.0ms (57.4% of total)

ival-expm1: 128.0ms (18% of total)

ival-sqrt: 80.0ms (11.3% of total)

ival-div: 73.0ms (10.3% of total)

ival-true: 7.0ms (1% of total)

exact: 6.0ms (0.8% of total)

ival-assert: 4.0ms (0.6% of total)

adjust: 3.0ms (0.4% of total)

Bogosity

explain128.0ms (2.7%)

Memory

-15.2MiB live, 131.1MiB allocated; 15ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	158	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	158	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	2	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	2
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	2
↳	`(exp.f64 x)`	overflow	2
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	2

Confusion

	Predicted +	Predicted -
+	160	0
-	0	96

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	160	0	0
-	0	0	96

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	96
1	2
2	158

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

47.0ms

512×

valid

Compiler

Compiled 106 to 34 computations (67.9% saved)

Precisions

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

ival-exp: 14.0ms (45.1% of total)

ival-expm1: 6.0ms (19.3% of total)

ival-mult: 4.0ms (12.9% of total)

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

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

exact: 1.0ms (3.2% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess182.0ms (3.9%)

Memory

0.1MiB live, 137.6MiB allocated; 17ms 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
▶	38.5%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify141.0ms (3%)

Memory

6.8MiB live, 97.0MiB allocated; 8ms 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)

localize28.0ms (0.6%)

Memory

-19.3MiB live, 26.4MiB allocated; 3ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(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	0.40234375000000006	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	36.89379922316474	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	36.9071031601878	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

19.0ms

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 (25.2% of total)

ival-expm1: 3.0ms (25.2% of total)

ival-div: 2.0ms (16.8% of total)

ival-mult: 2.0ms (16.8% of total)

ival-sqrt: 2.0ms (16.8% 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

2.9MiB live, 2.9MiB 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))))

simplify198.0ms (4.2%)

Memory

10.9MiB live, 150.0MiB allocated; 42ms 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)))

rewrite38.0ms (0.8%)

Memory

38.5MiB live, 38.5MiB allocated; 0ms 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)))

eval17.0ms (0.4%)

Memory: -30.5MiB live, 14.1MiB allocated; 8ms collecting garbage
Compiler: Compiled 1 189 to 297 computations (75% saved)

prune6.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Accuracy

100.0%

Counts

70 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	61.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	63.7%	(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))))
	61.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	69.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	62.1%	#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))))
	63.4%	#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))))
▶	62.2%	#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 300 to 236 computations (21.3% saved)

simplify143.0ms (3%)

Memory

-34.2MiB live, 120.9MiB allocated; 19ms 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)

localize73.0ms (1.6%)

Memory

34.5MiB live, 80.7MiB allocated; 3ms 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	0.1953125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.697597509768442	(/.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	24.0406035299444	#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	0.171875	(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	23.976731085434796	#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	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy	23.218202400052473	#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	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	19.99161282891588	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	0.01171875	(+.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

50.0ms	243×	0	valid
3.0ms	5×	2	valid
3.0ms	7×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 172 to 31 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 11.0ms (26.1% of total)

ival-add: 10.0ms (23.8% of total)

ival-div: 5.0ms (11.9% of total)

ival-sqrt: 5.0ms (11.9% of total)

const: 4.0ms (9.5% of total)

ival-expm1: 3.0ms (7.1% of total)

adjust: 2.0ms (4.8% of total)

ival-exp: 2.0ms (4.8% of total)

exact: 1.0ms (2.4% of total)

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

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

series9.0ms (0.2%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms 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
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))
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

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))

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))

simplify156.0ms (3.3%)

Memory

-18.4MiB live, 120.1MiB allocated; 30ms 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)))))

rewrite199.0ms (4.2%)

Memory

24.1MiB live, 168.9MiB allocated; 29ms 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))

eval99.0ms (2.1%)

Memory: -5.7MiB live, 82.2MiB allocated; 11ms collecting garbage
Compiler: Compiled 19 670 to 2 230 computations (88.7% saved)

prune43.0ms (0.9%)

Memory

-41.8MiB live, 28.7MiB allocated; 12ms collecting garbage

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	488	6	494
Fresh	1	2	3
Picked	1	4	5
Done	0	0	0
Total	490	12	502

Accuracy

100.0%

Counts

502 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	61.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	63.7%	(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))))
▶	61.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	4.1%	(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))))
	4.9%	(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)))))
✓	69.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	62.1%	#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))))
▶	62.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
✓	62.2%	#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))))
	61.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)) x (sqrt.f64 #s(literal 2 binary64))))
▶	2.8%	#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 532 to 397 computations (25.4% saved)

simplify131.0ms (2.8%)

Memory

9.8MiB live, 140.6MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	380
0	71	378
1	132	366
2	329	366
3	1186	366
4	4376	366
0	8087	335

Stop Event

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

Calls

Call 1

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

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

localize138.0ms (2.9%)

Memory

20.1MiB live, 123.2MiB allocated; 11ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
accuracy	0.1953125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.41796875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	24.0406035299444	#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))))
accuracy	0.22722626953688405	(/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.25	(.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	24.0406035299444	#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	38.25653185314458	#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	0.00390625	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	0.00390625	(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	23.218202400052473	#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	38.31821816200419	#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	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	23.977035466307743	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0.11394501953688405	(fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy	0.1484375	(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
accuracy	0.1953125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	24.0406035299444	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))

Samples

71.0ms	219×	0	valid
12.0ms	16×	2	valid
10.0ms	20×	1	valid
4.0ms	1×	5	exit

Compiler

Compiled 283 to 38 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-mult: 37.0ms (47.5% of total)

ival-add: 11.0ms (14.1% of total)

ival-div: 9.0ms (11.6% of total)

adjust: 9.0ms (11.6% of total)

const: 4.0ms (5.1% of total)

ival-sqrt: 4.0ms (5.1% of total)

ival-expm1: 3.0ms (3.9% of total)

exact: 1.0ms (1.3% of total)

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

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

series15.0ms (0.3%)

Memory

-21.7MiB live, 22.4MiB allocated; 5ms collecting garbage

Counts

22 → 68

Calls

Call 1

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

Outputs
(* 1/2 (sqrt 2))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(* 1/4 (sqrt 2))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 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
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
3/16
(+ 3/16 (* 7/192 x))
(* 3/16 x)
(* x (+ 3/16 (* 7/192 x)))
(/ 3/16 (sqrt 2))
(+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))
(/ x (sqrt 2))
(* 7/192 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/384 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(* 7/384 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* x (+ 1 (* 2 (/ 1 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 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))
(* (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))))
(* 7/192 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (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

7.0ms

inf

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

4.0ms

-inf

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

3.0ms

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

simplify183.0ms (3.9%)

Memory

27.8MiB live, 126.5MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	232	909
1	856	779
2	3220	709
0	8631	648

Stop Event

1×	iter limit
1×	node limit

Counts

68 → 67

Calls

Call 1

Inputs
(* 1/2 (sqrt 2))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(* 1/4 (sqrt 2))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 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
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
3/16
(+ 3/16 (* 7/192 x))
(* 3/16 x)
(* x (+ 3/16 (* 7/192 x)))
(/ 3/16 (sqrt 2))
(+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))
(/ x (sqrt 2))
(* 7/192 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/384 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(* 7/384 (* (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* x (+ 1 (* 2 (/ 1 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 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))
(* (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))))
(* 7/192 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (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
(* 1/2 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(+ (* 1/2 (sqrt 2)) (* x (+ (* 7/192 (* x (sqrt 2))) (* 3/16 (sqrt 2)))))
(*.f64 (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 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)))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 7/384 binary64) x) x (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 7/384 binary64) x) x (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 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))
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
#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))
(* 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)
(/ 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)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (* (pow x 2) (sqrt 2)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) #s(literal 7/192 binary64))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (* 3/16 (/ (sqrt 2) x))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -7/192 binary64))) (*.f64 x x))
(* (pow x 2) (+ (* 7/192 (sqrt 2)) (+ (* 3/16 (/ (sqrt 2) x)) (* 1/2 (/ (sqrt 2) (pow x 2))))))
(.f64 (.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64))) x) x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(* 7/384 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 7/384 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 3/32 binary64) x) #s(literal -7/384 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -3/32 binary64)) (.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 3/32 binary64) x) #s(literal -7/384 binary64)) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (.f64 x x))) (pow.f64 x #s(literal 3 binary64)))
(* 7/384 (* (pow x 2) (sqrt 2)))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) #s(literal 7/384 binary64))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 3/32 binary64) x) #s(literal -7/384 binary64))) (*.f64 x x))
(* (pow x 2) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -3/32 binary64)) (.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x 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))
(* 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 x (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) x)) x #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 (+.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))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* 7/192 (pow x 2))
(.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 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64)))
(* 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))
(* 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)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2))) x)) (* 7/192 (sqrt 2))))
(.f64 (.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 7/192 binary64))) x) x)
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 3/32 binary64) x) #s(literal -7/384 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -3/32 binary64)) (.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 3/32 binary64) x) #s(literal -7/384 binary64)) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (.f64 x x))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (/ (sqrt 2) x)) (* -3/32 (sqrt 2))) x)) (* 7/384 (sqrt 2))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -3/32 binary64)) (.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x))
(* -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)) (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 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)))))

rewrite225.0ms (4.8%)

Memory

-24.9MiB live, 162.1MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	339
0	71	347
1	283	270
2	2000	270
0	8162	267

Stop Event

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

Counts

22 → 468

Calls

Call 1

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

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

eval83.0ms (1.8%)

Memory: 9.9MiB live, 140.1MiB allocated; 18ms collecting garbage
Compiler: Compiled 25 953 to 2 634 computations (89.9% saved)

prune16.0ms (0.3%)

Memory

32.9MiB live, 32.9MiB allocated; 0ms collecting garbage

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	540	6	546
Fresh	1	2	3
Picked	3	2	5
Done	1	3	4
Total	545	13	558

Accuracy

100.0%

Counts

558 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	61.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	63.7%	(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))))
✓	61.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	4.1%	(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))))
▶	4.9%	(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)))))
✓	69.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	62.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 7/384 binary64) x) x (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64))))) x (sqrt.f64 #s(literal 2 binary64))))
▶	30.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #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))))
▶	2.8%	#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 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
	2.3%	#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))))))
▶	4.1%	#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)))))
▶	62.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 738 to 525 computations (28.9% saved)

simplify188.0ms (4%)

Memory

-21.5MiB live, 173.3MiB allocated; 30ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64))))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #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)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #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))))
cost-diff	0	(*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(.f64 (.f64 (fma.f64 x #s(literal 7/192 binary64) #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 x #s(literal 7/192 binary64) #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 x #s(literal 7/192 binary64) #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	(fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 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) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	551
0	88	539
1	182	533
2	445	533
3	1480	531
4	5669	531
0	8723	486

Stop Event

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

Calls

Call 1

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

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

localize186.0ms (4%)

Memory

21.8MiB live, 213.4MiB allocated; 23ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3669924193427587	(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
accuracy	0.41796875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	19.356243650062922	(fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64))
accuracy	24.0406035299444	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #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))))
accuracy	0.2109375	(*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.41796875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	24.0406035299444	#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 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
accuracy	38.25653185314458	#s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x))
accuracy	0.41796875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	24.0406035299444	#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	24.300723178039906	#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	38.25653185314458	#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	0.00390625	(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	0.0078125	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	23.218202400052473	#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	38.436416330349054	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.1796875	(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.7012668409528	#s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	24.0406035299444	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

Samples

111.0ms	243×	0	valid
13.0ms	5×	2	valid
5.0ms	7×	1	valid
2.0ms	1×	5	exit

Compiler

Compiled 315 to 53 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-mult: 33.0ms (30% of total)

ival-expm1: 32.0ms (29.1% of total)

ival-add: 17.0ms (15.4% of total)

adjust: 10.0ms (9.1% of total)

ival-div: 9.0ms (8.2% of total)

const: 4.0ms (3.6% of total)

ival-sqrt: 3.0ms (2.7% of total)

exact: 1.0ms (0.9% of total)

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

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

series37.0ms (0.8%)

Memory

-41.3MiB live, 15.4MiB allocated; 6ms collecting garbage

Counts

24 → 59

Calls

Call 1

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

Outputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
1
(+ 1 (* 1/4 x))
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
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(/ x (sqrt 2))
(/ 1/2 x)
(/ (+ 1/2 (* 3/16 x)) x)
(/ (+ 1/2 (* x (+ 3/16 (* 7/192 x)))) x)
(/ 1/2 (pow x 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/384 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(* 1/4 (* x (sqrt 2)))
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(* 1/4 x)
(* x (+ 1/4 (/ 1 x)))
(/ (- (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))))))
(* 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))))
(* x (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (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 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))

Calls

3 calls:

Time

Variable

Point

Expression

30.0ms

inf

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

3.0ms

-inf

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

3.0ms

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

simplify157.0ms (3.3%)

Memory

44.3MiB live, 132.4MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	212	779
1	778	647
2	2910	608
0	8555	554

Stop Event

1×	iter limit
1×	node limit

Counts

59 → 59

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
1
(+ 1 (* 1/4 x))
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
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(/ x (sqrt 2))
(/ 1/2 x)
(/ (+ 1/2 (* 3/16 x)) x)
(/ (+ 1/2 (* x (+ 3/16 (* 7/192 x)))) x)
(/ 1/2 (pow x 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/384 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(* 1/4 (* x (sqrt 2)))
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(* 1/4 x)
(* x (+ 1/4 (/ 1 x)))
(/ (- (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))))))
(* 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))))
(* x (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (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 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))

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)))
(+ (sqrt 2) (* 1/4 (* x (sqrt 2))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/32 (* x (sqrt 2))) (* 1/4 (sqrt 2)))))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/4 (sqrt 2)) (* x (+ (* 7/384 (* x (sqrt 2))) (* 3/32 (sqrt 2)))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/384 binary64) x #s(literal 3/32 binary64))) x (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 x))
(fma.f64 #s(literal 1/4 binary64) x #s(literal 1 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
#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))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 3/16 x)) x)
(-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -3/16 binary64))
(/ (+ 1/2 (* x (+ 3/16 (* 7/192 x)))) x)
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal -7/192 binary64) x #s(literal -3/16 binary64)))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(* 7/384 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 7/384 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (* 3/32 (/ (sqrt 2) x))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 3/32 binary64) x) #s(literal -7/384 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (* 1/4 (/ (sqrt 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -3/32 binary64)) (.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/384 (sqrt 2)) (+ (* 3/32 (/ (sqrt 2) x)) (+ (* 1/4 (/ (sqrt 2) (pow x 2))) (/ (sqrt 2) (pow x 3))))))
(*.f64 (fma.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -3/32 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64))))) (pow.f64 x #s(literal 3 binary64)))
(* 1/4 (* x (sqrt 2)))
(.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(* x (+ (* 1/4 (sqrt 2)) (/ (sqrt 2) x)))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)
(* 1/4 x)
(*.f64 #s(literal 1/4 binary64) x)
(* x (+ 1/4 (/ 1 x)))
(fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))
(/ (- (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)))))
(.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) x #s(literal 1 binary64)) x)
(* 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 (+.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))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 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)
(* 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 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 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))
(* x (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64))
(* -1 (* (pow x 3) (+ (* -3/32 (/ (sqrt 2) x)) (* -7/384 (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 3/32 binary64) x) #s(literal -7/384 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) x))) x)) (* -7/384 (sqrt 2)))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -3/32 binary64)) (.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2))) x)) (* 3/32 (sqrt 2))) x)) (* -7/384 (sqrt 2)))))
(*.f64 (fma.f64 #s(literal 7/384 binary64) (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -3/32 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64))))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* x (+ (* -1 (/ (sqrt 2) x)) (* -1/4 (sqrt 2)))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)
(* -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)) (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64))) (/.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 (/ (+ 3/16 (* 1/2 (/ 1 x))) x)) 7/192)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -3/16 binary64)) x) #s(literal 7/192 binary64)))

rewrite217.0ms (4.6%)

Memory

-25.4MiB live, 165.4MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	496
0	88	484
1	371	432
2	2580	432
0	8451	411

Stop Event

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

Counts

24 → 268

Calls

Call 1

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

Outputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) x)))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) x)))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) x))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1 binary64))) (-.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64)))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) x))))
(fma.f64 (.f64 #s(literal 1/4 binary64) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) x)))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (.f64 #s(literal 1/4 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 #s(literal 1/4 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal 1 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) x))) (.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) x))) #s(literal 1 binary64))) (.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) x))) (fma.f64 #s(literal 1/16 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) x)))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) #s(literal 9/256 binary64))) (neg.f64 (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3 binary64)) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3 binary64)) #s(literal 27/4096 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) #s(literal 9/256 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) #s(literal 9/256 binary64)) (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3 binary64)) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3 binary64)) #s(literal 27/4096 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) #s(literal 9/256 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64))
(fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x 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 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x))) (/.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 3/16 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64))))
(-.f64 #s(literal 3/16 binary64) (.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64))) x))
(-.f64 #s(literal 3/16 binary64) (.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) #s(literal 9/256 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64)))) (/.f64 #s(literal 27/4096 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 2 binary64)) #s(literal 9/256 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64)))))
(+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x) #s(literal 3/16 binary64))
(+.f64 #s(literal 3/16 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x))
(/.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x))) (neg.f64 (neg.f64 x)))
(/.f64 (fabs.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 x))) x)
(/.f64 (fabs.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x))) x)
(/.f64 (fabs.f64 (/.f64 #s(literal 1/2 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 x)) (neg.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) x)
(/.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(sqrt.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fabs.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(fabs.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))

eval65.0ms (1.4%)

Memory: 15.9MiB live, 60.8MiB allocated; 6ms collecting garbage
Compiler: Compiled 19 662 to 1 771 computations (91% saved)

prune66.0ms (1.4%)

Memory

-64.0MiB live, 23.5MiB allocated; 29ms collecting garbage

Pruning

13 alts after pruning (4 fresh and 9 done)

	Pruned	Kept	Total
New	381	1	382
Fresh	0	3	3
Picked	1	4	5
Done	0	5	5
Total	382	13	395

Accuracy

100.0%

Counts

395 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	61.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	63.7%	(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))))
✓	61.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	4.1%	(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))))
✓	4.9%	(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)))))
✓	69.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	62.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 7/384 binary64) x) x (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64))))) x (sqrt.f64 #s(literal 2 binary64))))
	62.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x #s(approx (+ ( (+ (/ 1/2 (* x x)) 7/192) x) 3/16) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #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))))
✓	2.8%	#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 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)))
	2.3%	#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))))))
✓	4.1%	#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)))))
✓	62.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 1 108 to 453 computations (59.1% saved)

regimes16.0ms (0.3%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

Counts

22 → 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)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (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) (*.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)) (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)))))
#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 x #s(literal 7/192 binary64) #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))))
#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 #s(approx (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 7/384 binary64) x) x (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64))))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)) 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))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x #s(approx (+ ( (+ (/ 1/2 (* x x)) 7/192) x) 3/16) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #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(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #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(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

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

Calls

3 calls:

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

12.0MiB live, 12.0MiB allocated; 0ms collecting garbage

Accuracy

Total -43.5b remaining (-220.9%)

Threshold costs -43.5b (-220.9%)

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)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) x) (sqrt 2)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (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) (*.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)) (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)))))
#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 x #s(literal 7/192 binary64) #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))))
#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 #s(approx (/ (+ (* (* (+ (* 7/192 x) 3/16) x) (sqrt 2)) (* (sqrt 2) 1/2)) 2) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 7/384 binary64) x) x (fma.f64 #s(literal 3/32 binary64) x #s(literal 1/4 binary64))))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)) 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))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x #s(approx (+ ( (+ (/ 1/2 (* x x)) 7/192) x) 3/16) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #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(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #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(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (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

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

4.0ms

(/.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
69.2%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
69.2%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
69.2%	1	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify51.0ms (1.1%)

Memory

2.9MiB live, 48.2MiB allocated; 5ms 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)))

derivations184.0ms (3.9%)

Memory

-21.7MiB live, 163.3MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

preprocess19.0ms (0.4%)

Memory: 25.0MiB live, 25.0MiB allocated; 0ms 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 (26.4%)

explain128.0ms (2.7%)

preprocess182.0ms (3.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify141.0ms (3%)

localize28.0ms (0.6%)

series3.0ms (0.1%)

simplify198.0ms (4.2%)

rewrite38.0ms (0.8%)

eval17.0ms (0.4%)

prune6.0ms (0.1%)

simplify143.0ms (3%)

localize73.0ms (1.6%)

series9.0ms (0.2%)

simplify156.0ms (3.3%)

rewrite199.0ms (4.2%)

eval99.0ms (2.1%)

prune43.0ms (0.9%)

simplify131.0ms (2.8%)

localize138.0ms (2.9%)

series15.0ms (0.3%)

simplify183.0ms (3.9%)

rewrite225.0ms (4.8%)

eval83.0ms (1.8%)

prune16.0ms (0.3%)

simplify188.0ms (4%)

localize186.0ms (4%)

series37.0ms (0.8%)

simplify157.0ms (3.3%)

rewrite217.0ms (4.6%)

eval65.0ms (1.4%)

prune66.0ms (1.4%)

regimes16.0ms (0.3%)

regimes15.0ms (0.3%)

simplify51.0ms (1.1%)

derivations184.0ms (3.9%)

preprocess19.0ms (0.4%)

end0.0ms (0%)

Profiling