Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample865.0ms (23.4%)

Memory

8.6MiB live, 463.2MiB allocated

Samples

402.0ms	8 256×	0	valid
166.0ms	2 542×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 388.0ms

ival-expm1: 118.0ms (30.4% of total)

ival-div: 112.0ms (28.9% of total)

ival-mult: 74.0ms (19.1% of total)

ival-sqrt: 68.0ms (17.5% of total)

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

exact: 6.0ms (1.5% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain109.0ms (2.9%)

Memory

18.1MiB live, 81.0MiB allocated

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

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	158	0
-	0	98

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	158	0	0
-	0	1	97

Precision?

0.9937106918238994

Recall?

1.0

Freqs

test

number	freq
0	98
2	158

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms

512×

valid

Compiler

Compiled 106 to 34 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-exp: 7.0ms (30.5% of total)

ival-expm1: 5.0ms (21.8% of total)

ival-div: 3.0ms (13.1% of total)

ival-mult: 3.0ms (13.1% of total)

ival-sqrt: 3.0ms (13.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess247.0ms (6.7%)

Memory

-32.2MiB live, 73.5MiB allocated

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: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.2%	(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)

simplify138.0ms (3.7%)

Memory

5.4MiB live, 63.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize24.0ms (0.7%)

Memory

15.7MiB live, 15.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(exp.f64 x)
accuracy	0.01171875	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	36.904774547064996	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	36.917094631683945	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

17.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-exp: 3.0ms (27.1% of total)

ival-expm1: 3.0ms (27.1% of total)

ival-div: 2.0ms (18.1% of total)

ival-mult: 2.0ms (18.1% of total)

ival-sqrt: 2.0ms (18.1% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated

Counts

5 → 25

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))))
(exp.f64 x)

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

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))) (exp x))
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))) (exp x))
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))) (exp x))

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))) (exp x))

1.0ms

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

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))) (exp x))

simplify173.0ms (4.7%)

Memory

-1.4MiB live, 67.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	241
1	310	201
2	1070	200
3	3515	198
0	8112	158

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 24

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

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)))
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))
(- (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)))
(exp x)
(exp.f64 x)

rewrite38.0ms (1%)

Memory

-18.1MiB live, 12.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
0	17	35
1	65	21
0	423	17

Stop Event

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

Counts

5 → 57

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))))
(exp.f64 x)

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)))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(/.f64 (-.f64 (.f64 (cosh.f64 x) (cosh.f64 x)) (.f64 (sinh.f64 x) (sinh.f64 x))) (-.f64 (cosh.f64 x) (sinh.f64 x)))
(/.f64 (+.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (pow.f64 (sinh.f64 x) #s(literal 3 binary64))) (fma.f64 (cosh.f64 x) (cosh.f64 x) (-.f64 (.f64 (sinh.f64 x) (sinh.f64 x)) (.f64 (cosh.f64 x) (sinh.f64 x)))))
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(exp.f64 x)

eval9.0ms (0.2%)

Memory: 8.3MiB live, 8.3MiB allocated
Compiler: Compiled 1 410 to 354 computations (74.9% saved)

prune4.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	6	82

Accuracy

100.0%

Counts

82 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
▶	62.3%	(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))))
▶	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	62.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	62.7%	#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))))

Compiler

Compiled 210 to 168 computations (20% saved)

simplify148.0ms (4%)

Memory

9.3MiB live, 74.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
cost-diff	0	(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	(+.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
cost-diff	0	#s(approx (/ (- (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	28	202
0	46	202
1	74	202
2	151	202
3	422	202
4	1490	162
5	7953	162
0	8111	162

Stop Event

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

Calls

Call 1

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

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

localize64.0ms (1.7%)

Memory

-3.7MiB live, 53.9MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0625	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0.06640625	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.11328125	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.94438690762853	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0.0	(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	0.0	(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))))
accuracy	23.1333472013189	#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	0.0	(+.f64 #s(literal 2 binary64) x)
accuracy	0.0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	24.01741591903097	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0.0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	20.15165851914354	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0.0	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	0.0	(exp.f64 x)
accuracy	0.0078125	(+.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

41.0ms

256×

valid

Compiler

Compiled 163 to 26 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 8.0ms (27.5% of total)

ival-add: 7.0ms (24.1% of total)

ival-expm1: 3.0ms (10.3% of total)

const: 3.0ms (10.3% of total)

ival-sqrt: 3.0ms (10.3% of total)

ival-div: 2.0ms (6.9% of total)

ival-exp: 2.0ms (6.9% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

17 → 39

Calls

Call 1

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

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))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
1/2
(+ 1/2 (* 1/6 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))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	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)) (+ 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) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))
2.0ms	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)) (+ 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) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))
1.0ms	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)) (+ 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) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))

Time

Variable

Point

Expression

2.0ms

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

2.0ms

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

1.0ms

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

simplify152.0ms (4.1%)

Memory

-12.5MiB live, 86.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	334
1	361	288
2	1263	282
3	5716	280
0	8446	238

Stop Event

1×	iter limit
1×	node limit

Counts

39 → 38

Calls

Call 1

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

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

rewrite225.0ms (6.1%)

Memory

-19.6MiB live, 87.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	188
0	46	188
1	177	132
2	1256	132
0	8169	132

Stop Event

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

Counts

17 → 333

Calls

Call 1

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

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 #s(literal 2 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(.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 (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 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/2 binary64)))
(*.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 (sinh.f64 (acosh.f64 (exp.f64 x)))) (neg.f64 (sqrt.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 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (sqrt.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (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 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (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 (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 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.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 (-.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 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sinh.f64 (acosh.f64 (exp.f64 x))) (sqrt.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)))))
(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)) (+.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 (+.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)))
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(.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)))
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(+.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (neg.f64 x) #s(literal 1/6 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (neg.f64 x) #s(literal 1/6 binary64)) (.f64 (neg.f64 x) #s(literal 1/6 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 x) #s(literal 1/6 binary64))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (-.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) #s(literal 1/8 binary64))) (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))
(-.f64 #s(literal 1/2 binary64) (*.f64 (neg.f64 x) #s(literal 1/6 binary64)))
(+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 1/12 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (*.f64 x #s(literal 1/12 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (.f64 x #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) (*.f64 x #s(literal 1/12 binary64))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(+.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))

eval48.0ms (1.3%)

Memory: 8.4MiB live, 38.0MiB allocated
Compiler: Compiled 12 550 to 1 718 computations (86.3% saved)

prune9.0ms (0.2%)

Memory

-10.7MiB live, 19.9MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	367	7	374

Accuracy

100.0%

Counts

374 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	62.3%	(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))))
✓	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
✓	62.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	62.7%	#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))))

Compiler

Compiled 126 to 101 computations (19.8% saved)

simplify137.0ms (3.7%)

Memory

3.6MiB live, 68.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	132
0	37	132
1	68	132
2	151	132
3	454	132
4	1730	117
0	8605	114

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

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

localize51.0ms (1.4%)

Memory

21.7MiB live, 21.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
accuracy	0.00390625	(+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))
accuracy	0.00390625	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	23.1333472013189	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64)))
accuracy	0.0625	(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
accuracy	0.1875	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.703125	(/.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	23.87980719584232	#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))))

Samples

34.0ms	243×	0	valid
3.0ms	7×	2	valid
2.0ms	6×	1	valid

Compiler

Compiled 112 to 25 computations (77.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 9.0ms (31.3% of total)

ival-add: 5.0ms (17.4% of total)

const: 4.0ms (13.9% of total)

ival-div: 3.0ms (10.4% of total)

ival-sqrt: 3.0ms (10.4% of total)

ival-expm1: 3.0ms (10.4% of total)

adjust: 1.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory

2.7MiB live, 2.7MiB allocated

Counts

9 → 39

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify140.0ms (3.8%)

Memory

-0.5MiB live, 87.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	137	512
1	493	410
2	1746	374
3	6752	370
0	8062	330

Stop Event

1×	iter limit
1×	node limit

Counts

39 → 38

Calls

Call 1

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

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

rewrite159.0ms (4.3%)

Memory

12.8MiB live, 106.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	117
0	37	117
1	168	96
2	1212	96
0	8196	93

Stop Event

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

Counts

9 → 193

Calls

Call 1

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

Outputs
#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))))
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(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (.f64 x (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64)) x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(fma.f64 x (.f64 #s(literal 1/2 binary64) x) (.f64 x #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/2 binary64) x)))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (*.f64 #s(literal 1 binary64) x))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (*.f64 #s(literal 1/2 binary64) x) x))
(+.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (*.f64 x #s(literal 1 binary64)))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.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))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))) #s(literal 3 binary64))) (fma.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 (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))) (fma.f64 (/.f64 #s(literal 9/256 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 (/.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 (-.f64 #s(literal 27/4096 binary64) (pow.f64 (.f64 #s(literal -7/192 binary64) x) #s(literal 3 binary64))) (+.f64 #s(literal 9/256 binary64) (fma.f64 (.f64 #s(literal -7/192 binary64) x) (.f64 #s(literal -7/192 binary64) x) (.f64 #s(literal 3/16 binary64) (*.f64 #s(literal -7/192 binary64) x)))))
(/.f64 (-.f64 #s(literal 27/4096 binary64) (pow.f64 (.f64 (neg.f64 x) #s(literal 7/192 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 9/256 binary64) (fma.f64 (.f64 (neg.f64 x) #s(literal 7/192 binary64)) (.f64 (neg.f64 x) #s(literal 7/192 binary64)) (.f64 #s(literal 3/16 binary64) (*.f64 (neg.f64 x) #s(literal 7/192 binary64))))))
(/.f64 (+.f64 (pow.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))))) #s(literal 3 binary64)) (pow.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))))) #s(literal 3 binary64))) (fma.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 (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 (/.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 #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 (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 (neg.f64 (-.f64 #s(literal 9/256 binary64) (pow.f64 (.f64 #s(literal 7/192 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (.f64 #s(literal 7/192 binary64) x))))
(/.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))

eval64.0ms (1.7%)

Memory: -38.1MiB live, 36.0MiB allocated
Compiler: Compiled 10 924 to 1 206 computations (89% saved)

prune6.0ms (0.2%)

Memory

10.2MiB live, 10.2MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	227	9	236

Accuracy

100.0%

Counts

236 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	62.3%	(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))))
✓	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
✓	62.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	62.7%	#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))))
▶	33.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶	62.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+.f64 (*.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))))

Compiler

Compiled 196 to 153 computations (21.9% saved)

simplify112.0ms (3%)

Memory

11.7MiB live, 67.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	231
0	49	231
1	87	231
2	189	231
3	551	231
4	1929	221
0	8274	213

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

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

localize79.0ms (2.1%)

Memory

-19.1MiB live, 52.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.15234375	(.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)
accuracy	0.703125	(/.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)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	18.21084644812197	(fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64))
accuracy	23.87980719584232	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 7/192 binary64)) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.078125	(*.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))))
accuracy	0.1875	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.38671875	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.87980719584232	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+.f64 (*.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))))

Samples

44.0ms	243×	0	valid
4.0ms	7×	2	valid
2.0ms	6×	1	valid

Compiler

Compiled 166 to 29 computations (82.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 12.0ms (32.3% of total)

ival-div: 6.0ms (16.2% of total)

ival-add: 6.0ms (16.2% of total)

ival-sqrt: 5.0ms (13.5% of total)

const: 4.0ms (10.8% of total)

ival-expm1: 3.0ms (8.1% of total)

adjust: 1.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

11 → 38

Calls

Call 1

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

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

2.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify154.0ms (4.2%)

Memory

13.7MiB live, 72.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	130	462
1	460	403
2	1631	367
3	5890	361
0	8406	331

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 38

Calls

Call 1

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

rewrite202.0ms (5.4%)

Memory

7.7MiB live, 102.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	182
0	49	182
1	202	168
2	1450	168
0	8324	166

Stop Event

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

Counts

11 → 264

Calls

Call 1

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

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

eval44.0ms (1.2%)

Memory: 0.5MiB live, 56.3MiB allocated
Compiler: Compiled 20 706 to 1 695 computations (91.8% saved)

prune12.0ms (0.3%)

Memory

-23.9MiB live, 20.2MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	0	0	0
Picked	1	1	2
Done	0	7	7
Total	300	9	309

Accuracy

100.0%

Counts

309 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	62.3%	(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))))
✓	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	64.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x) #s(literal 2 binary64))))
✓	62.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	62.7%	#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))))
	62.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 #s(approx (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (.f64 #s(approx (+ ( (+ (/ 1/2 (* x x)) 7/192) x) 3/16) (fma.f64 #s(literal 7/192 binary64) x (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -3/16 binary64)))) x)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	62.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+.f64 (*.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))))

Compiler

Compiled 466 to 242 computations (48.1% saved)

regimes9.0ms (0.2%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

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

3.0ms

2.0ms

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

2.0ms

(/.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)

regimes8.0ms (0.2%)

Memory

13.9MiB live, 13.9MiB allocated

Accuracy

Total -23.8b remaining (-121%)

Threshold costs -23.8b (-121%)

Counts

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

3.0ms

2.0ms

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

2.0ms

(/.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
69.3%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
69.3%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
69.3%	1	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify51.0ms (1.4%)

Memory

-11.4MiB live, 48.7MiB allocated

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)))

soundness182.0ms (4.9%)

Memory

1.2MiB live, 67.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	241
1	310	201
2	1070	200
3	3515	198
0	8112	158
0	10	35
0	17	35
1	65	21
0	423	17

Stop Event

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

Compiler

Compiled 38 to 31 computations (18.4% saved)

preprocess18.0ms (0.5%)

Memory: -6.3MiB live, 22.6MiB allocated
Compiler: Compiled 62 to 52 computations (16.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze1.0ms (0%)

sample865.0ms (23.4%)

explain109.0ms (2.9%)

preprocess247.0ms (6.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify138.0ms (3.7%)

localize24.0ms (0.7%)

series3.0ms (0.1%)

simplify173.0ms (4.7%)

rewrite38.0ms (1%)

eval9.0ms (0.2%)

prune4.0ms (0.1%)

simplify148.0ms (4%)

localize64.0ms (1.7%)

series5.0ms (0.1%)

simplify152.0ms (4.1%)

rewrite225.0ms (6.1%)

eval48.0ms (1.3%)

prune9.0ms (0.2%)

simplify137.0ms (3.7%)

localize51.0ms (1.4%)

series6.0ms (0.2%)

simplify140.0ms (3.8%)

rewrite159.0ms (4.3%)

eval64.0ms (1.7%)

prune6.0ms (0.2%)

simplify112.0ms (3%)

localize79.0ms (2.1%)

series6.0ms (0.2%)

simplify154.0ms (4.2%)

rewrite202.0ms (5.4%)

eval44.0ms (1.2%)

prune12.0ms (0.3%)

regimes9.0ms (0.2%)

regimes8.0ms (0.2%)

simplify51.0ms (1.4%)

soundness182.0ms (4.9%)

preprocess18.0ms (0.5%)

end0.0ms (0%)

Profiling