Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

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

analyze2.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (35.1%)

Memory

21.5MiB live, 897.1MiB allocated; 894ms collecting garbage

Samples

449.0ms	8 256×	0	valid
441.0ms	2 665×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 652.0ms

ival-mult: 365.0ms (56% of total)

ival-expm1: 123.0ms (18.9% of total)

ival-div: 76.0ms (11.7% of total)

ival-sqrt: 67.0ms (10.3% of total)

ival-true: 7.0ms (1.1% of total)

exact: 6.0ms (0.9% of total)

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

adjust: 3.0ms (0.5% of total)

Bogosity

explain112.0ms (3.2%)

Memory

31.0MiB live, 124.4MiB allocated; 4ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	176	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	176	0

Confusion

	Predicted +	Predicted -
+	176	0
-	0	80

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	176	0	0
-	0	0	80

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	80
2	176

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms

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 (30.3% of total)

ival-expm1: 5.0ms (21.7% of total)

ival-div: 3.0ms (13% of total)

ival-mult: 3.0ms (13% of total)

ival-sqrt: 3.0ms (13% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess178.0ms (5.1%)

Memory

-3.0MiB live, 136.9MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	32.8%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify0.0ms (0%)

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

series5.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

10 → 29

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (exp (* 2 x)) (* 2 x) 2 x 1 (- (exp x) 1) (exp x))
2.0ms	x	@	inf	((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (exp (* 2 x)) (* 2 x) 2 x 1 (- (exp x) 1) (exp x))
1.0ms	x	@	0	((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (exp (* 2 x)) (* 2 x) 2 x 1 (- (exp x) 1) (exp x))

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify212.0ms (6%)

Memory

7.8MiB live, 152.1MiB allocated; 28ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	272
1	321	232
2	1122	231
3	3760	229
0	8381	183

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

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

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

rewrite40.0ms (1.1%)

Memory

-16.3MiB live, 29.3MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
0	17	45
1	65	31
0	423	27

Stop Event

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

Counts

10 → 84

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
(*.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 (/.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 (+.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 (pow.f64 (exp.f64 #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64))))
(*.f64 (neg.f64 (exp.f64 x)) (neg.f64 (exp.f64 x)))
(*.f64 (fabs.f64 (exp.f64 x)) (fabs.f64 (exp.f64 x)))
(*.f64 (exp.f64 x) (exp.f64 x))
(*.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) x)
(pow.f64 (exp.f64 x) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 x #s(literal 2 binary64))) (cosh.f64 (.f64 x #s(literal 2 binary64)))) (.f64 (sinh.f64 (.f64 x #s(literal 2 binary64))) (sinh.f64 (.f64 x #s(literal 2 binary64))))) (-.f64 (cosh.f64 (.f64 x #s(literal 2 binary64))) (sinh.f64 (.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 x #s(literal 2 binary64))) (cosh.f64 (.f64 x #s(literal 2 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 x #s(literal 2 binary64))) (sinh.f64 (.f64 x #s(literal 2 binary64)))) (.f64 (cosh.f64 (.f64 x #s(literal 2 binary64))) (sinh.f64 (.f64 x #s(literal 2 binary64)))))))
(fma.f64 (cosh.f64 x) (exp.f64 x) (*.f64 (sinh.f64 x) (exp.f64 x)))
(fma.f64 (exp.f64 x) (cosh.f64 x) (*.f64 (exp.f64 x) (sinh.f64 x)))
(fma.f64 #s(literal 2 binary64) (.f64 (sinh.f64 x) (cosh.f64 x)) (cosh.f64 (.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 (cosh.f64 x) (exp.f64 x)) (.f64 (sinh.f64 x) (exp.f64 x)))
(+.f64 (.f64 (exp.f64 x) (cosh.f64 x)) (.f64 (exp.f64 x) (sinh.f64 x)))
(+.f64 (sinh.f64 (.f64 x #s(literal 2 binary64))) (cosh.f64 (.f64 x #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 x #s(literal 2 binary64))) (sinh.f64 (.f64 x #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) x))
(exp.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))))
(+.f64 x x)
#s(literal 2 binary64)
x
#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 (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)

eval11.0ms (0.3%)

Memory: 17.0MiB live, 17.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 986 to 484 computations (75.6% saved)

prune5.0ms (0.2%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Accuracy

100.0%

Counts

115 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
▶	68.8%	(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))))
▶	70.2%	(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))))
▶	68.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	74.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	99.0%	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
	69.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 222 to 180 computations (18.9% saved)

simplify0.0ms (0%)

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

series10.0ms (0.3%)

Memory

-36.3MiB live, 7.3MiB allocated; 4ms collecting garbage

Counts

22 → 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)
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)
(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)
(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)

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))))))
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 (+ 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
5.0ms	x	@	0	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) x 1 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) 2 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) 1/2 (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) 1/6)
2.0ms	x	@	inf	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) x 1 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) 2 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) 1/2 (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) 1/6)
2.0ms	x	@	-inf	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) x 1 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) 2 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ 2 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) 1/2 (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) 1/6)

Time

Variable

Point

Expression

5.0ms

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

2.0ms

inf

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

2.0ms

-inf

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

simplify161.0ms (4.6%)

Memory

38.6MiB live, 132.3MiB allocated; 26ms collecting garbage

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))))))
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 (+ 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))
x
(+ 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 (+ 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)))

rewrite170.0ms (4.8%)

Memory

-27.5MiB live, 167.6MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	193
0	46	193
1	177	137
2	1256	137
0	8169	137

Stop Event

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

Counts

22 → 343

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)
(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)
(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)

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

eval55.0ms (1.6%)

Memory: 26.4MiB live, 71.8MiB allocated; 3ms collecting garbage
Compiler: Compiled 13 776 to 1 852 computations (86.6% saved)

prune24.0ms (0.7%)

Memory

-16.1MiB live, 29.6MiB allocated; 4ms collecting garbage

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	418	2	420
Fresh	1	1	2
Picked	0	5	5
Done	0	0	0
Total	419	8	427

Accuracy

100.0%

Counts

427 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
▶	68.4%	(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	68.8%	(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))))
✓	70.2%	(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))))
✓	68.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	23.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.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))))))
✓	74.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	69.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 160 to 125 computations (21.9% saved)

simplify0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

series11.0ms (0.3%)

Memory

14.9MiB live, 14.9MiB allocated; 0ms collecting garbage

Counts

32 → 81

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (+ (* 7/192 x) 3/16) 7/192 x 3/16 1/2 (sqrt 2) 2 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (pow (neg x) 3) (- (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) 1/6)) (pow (neg x) 3) (neg x) 3 (- (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) 1/6) (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) (neg (+ (/ (/ (- x -2) x) x) 1/2)) (+ (/ (/ (- x -2) x) x) 1/2) (/ (/ (- x -2) x) x) (/ (- x -2) x) (- x -2) -2 1/6 (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) 1)
3.0ms	x	@	-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) (+ (* 7/192 x) 3/16) 7/192 x 3/16 1/2 (sqrt 2) 2 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (pow (neg x) 3) (- (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) 1/6)) (pow (neg x) 3) (neg x) 3 (- (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) 1/6) (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) (neg (+ (/ (/ (- x -2) x) x) 1/2)) (+ (/ (/ (- x -2) x) x) 1/2) (/ (/ (- x -2) x) x) (/ (- x -2) x) (- x -2) -2 1/6 (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) 1)
3.0ms	x	@	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) (+ (* 7/192 x) 3/16) 7/192 x 3/16 1/2 (sqrt 2) 2 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (pow (neg x) 3) (- (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) 1/6)) (pow (neg x) 3) (neg x) 3 (- (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) 1/6) (/ (neg (+ (/ (/ (- x -2) x) x) 1/2)) x) (neg (+ (/ (/ (- x -2) x) x) 1/2)) (+ (/ (/ (- x -2) x) x) 1/2) (/ (/ (- x -2) x) x) (/ (- x -2) x) (- x -2) -2 1/6 (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) 1)

Time

Variable

Point

Expression

4.0ms

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

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

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

simplify145.0ms (4.1%)

Memory

8.9MiB live, 100.7MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	205	849
1	686	724
2	2435	684
3	7999	684
0	8009	639

Stop Event

1×	iter limit
1×	node limit

Counts

81 → 80

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

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

rewrite276.0ms (7.9%)

Memory

-30.9MiB live, 174.7MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	308
0	67	308
1	296	287
2	2104	282
0	9529	273

Stop Event

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

Counts

32 → 410

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

eval85.0ms (2.4%)

Memory: 2.6MiB live, 130.9MiB allocated; 18ms collecting garbage
Compiler: Compiled 27 440 to 3 479 computations (87.3% saved)

prune11.0ms (0.3%)

Memory

31.2MiB live, 31.2MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	579	1	580
Fresh	0	0	0
Picked	1	2	3
Done	0	5	5
Total	580	8	588

Accuracy

100.0%

Counts

588 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	68.4%	(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	68.8%	(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))))
✓	70.2%	(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))))
✓	68.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	23.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (-.f64 (/.f64 (+.f64 (/.f64 (/.f64 (-.f64 x #s(literal -2 binary64)) x) x) #s(literal 1/2 binary64)) (neg.f64 x)) #s(literal 1/6 binary64)) (*.f64 x x)) (neg.f64 x)))))
✓	74.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	69.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 162 to 124 computations (23.5% saved)

simplify0.0ms (0%)

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

series35.0ms (1%)

Memory

-58.0MiB live, 5.8MiB allocated; 7ms collecting garbage

Counts

17 → 54

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

32.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify144.0ms (4.1%)

Memory

22.3MiB live, 152.8MiB allocated; 18ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	521
1	412	466
2	1474	434
3	5642	432
0	8268	404

Stop Event

1×	iter limit
1×	node limit

Counts

54 → 53

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

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

rewrite198.0ms (5.7%)

Memory

25.7MiB live, 167.4MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	228
0	42	228
1	195	206
2	1395	206
0	8077	197

Stop Event

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

Counts

17 → 230

Calls

Call 1

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

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

eval91.0ms (2.6%)

Memory: -25.4MiB live, 79.7MiB allocated; 13ms collecting garbage
Compiler: Compiled 23 967 to 3 169 computations (86.8% saved)

prune13.0ms (0.4%)

Memory

-12.0MiB live, 34.1MiB allocated; 2ms collecting garbage

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	392	2	394
Fresh	0	0	0
Picked	1	0	1
Done	0	7	7
Total	393	9	402

Accuracy

100.0%

Counts

402 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	68.4%	(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	68.8%	(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))))
✓	70.2%	(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))))
✓	68.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	74.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 #s(approx ( (- (/ (+ (/ (/ (- x -2) x) x) 1/2) (neg x)) 1/6) (* x x)) (/.f64 #s(literal -2 binary64) x)) (neg.f64 x)))))
	68.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 #s(approx ( (- (/ (+ (/ (/ (- x -2) x) x) 1/2) (neg x)) 1/6) (* x x)) (-.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x))) (neg.f64 x)))))
✓	74.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	69.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 568 to 280 computations (50.7% saved)

regimes10.0ms (0.3%)

Memory

15.8MiB live, 15.8MiB allocated; 0ms collecting garbage

Counts

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

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

Calls

3 calls:

4.0ms

3.0ms

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

3.0ms

(/.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

10.2MiB live, 10.2MiB allocated; 0ms collecting garbage

Accuracy

Total -33.2b remaining (-202.5%)

Threshold costs -33.2b (-202.5%)

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

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
74.4%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
74.4%	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))))`
74.4%	1	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify72.0ms (2%)

Memory

9.2MiB live, 53.2MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations175.0ms (5%)

Memory

-25.2MiB live, 120.1MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	272
1	321	232
2	1122	231
3	3760	229
0	8381	183
0	10	45
0	17	45
1	65	31
0	423	27

Stop Event

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

preprocess16.0ms (0.5%)

Memory: 32.7MiB live, 32.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 62 to 52 computations (16.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze2.0ms (0%)

sample1.2s (35.1%)

explain112.0ms (3.2%)

preprocess178.0ms (5.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

series5.0ms (0.1%)

simplify212.0ms (6%)

rewrite40.0ms (1.1%)

eval11.0ms (0.3%)

prune5.0ms (0.2%)

simplify0.0ms (0%)

series10.0ms (0.3%)

simplify161.0ms (4.6%)

rewrite170.0ms (4.8%)

eval55.0ms (1.6%)

prune24.0ms (0.7%)

simplify0.0ms (0%)

series11.0ms (0.3%)

simplify145.0ms (4.1%)

rewrite276.0ms (7.9%)

eval85.0ms (2.4%)

prune11.0ms (0.3%)

simplify0.0ms (0%)

series35.0ms (1%)

simplify144.0ms (4.1%)

rewrite198.0ms (5.7%)

eval91.0ms (2.6%)

prune13.0ms (0.4%)

regimes10.0ms (0.3%)

regimes8.0ms (0.2%)

simplify72.0ms (2%)

derivations175.0ms (5%)

preprocess16.0ms (0.5%)

end0.0ms (0%)

Profiling