Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

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

analyze2.0ms (0%)

Memory

3.0MiB live, 3.0MiB 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 (25.2%)

Memory

44.7MiB live, 918.9MiB allocated; 883ms collecting garbage

Samples

730.0ms	8 256×	0	valid
154.0ms	2 680×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 662.0ms

ival-mult: 337.0ms (50.9% of total)

ival-expm1: 154.0ms (23.3% of total)

ival-div: 81.0ms (12.2% of total)

ival-sqrt: 68.0ms (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

explain125.0ms (2.6%)

Memory

-9.6MiB live, 129.0MiB allocated; 9ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
167	0	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
167	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
3	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	1	(55.727215524563974)	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	167	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	167	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	3	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	3
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	3
↳	`(exp.f64 x)`	overflow	3
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	3
`exp.f64`	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	170	0
-	1	85

Precision

0.9941520467836257

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	170	0	0
-	1	0	85

Precision?

0.9941520467836257

Recall?

1.0

Freqs

test

number	freq
0	85
1	4
2	167

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 106 to 34 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-exp: 8.0ms (31% of total)

ival-expm1: 6.0ms (23.3% of total)

ival-div: 4.0ms (15.5% of total)

ival-mult: 4.0ms (15.5% of total)

ival-sqrt: 3.0ms (11.6% of total)

exact: 1.0ms (3.9% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess174.0ms (3.6%)

Memory

24.3MiB live, 119.0MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.0%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify140.0ms (2.9%)

Memory

3.6MiB live, 93.4MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize113.0ms (2.3%)

Memory

1.2MiB live, 60.9MiB allocated; 20ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
accuracy	0.6210937500000001	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	38.778729614185416	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	38.84361203087737	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

20.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

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

ival-exp: 3.0ms (24.3% of total)

ival-expm1: 3.0ms (24.3% of total)

ival-div: 2.0ms (16.2% of total)

ival-mult: 2.0ms (16.2% of total)

ival-sqrt: 2.0ms (16.2% 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)

series13.0ms (0.3%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Counts

4 → 20

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))
4.0ms	x	@	0	((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))
3.0ms	x	@	-inf	((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

Time

Variable

Point

Expression

5.0ms

inf

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

4.0ms

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

3.0ms

-inf

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

simplify182.0ms (3.8%)

Memory

-5.2MiB live, 124.6MiB allocated; 21ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

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

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

rewrite63.0ms (1.3%)

Memory

-6.8MiB live, 47.4MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 50

Calls

Call 1

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

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

eval8.0ms (0.2%)

Memory: 11.4MiB live, 11.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 189 to 297 computations (75% saved)

prune6.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (8 fresh and 0 done)

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

Accuracy

100.0%

Counts

70 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
▶	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	65.4%	(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))))
▶	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
	65.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	71.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	65.6%	#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))))
▶	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 274 to 218 computations (20.4% saved)

simplify135.0ms (2.8%)

Memory

-9.9MiB live, 125.8MiB allocated; 15ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(expm1.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
cost-diff	3	(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
cost-diff	0	(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
cost-diff	0	(exp.f64 x)
cost-diff	0	(+.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	163
0	52	147
1	90	147
2	175	147
3	485	142
4	1861	132
0	8399	132

Stop Event

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

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)
x
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(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)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
x
#s(literal 2 binary64)
(expm1.f64 x)

localize85.0ms (1.8%)

Memory

2.9MiB live, 102.2MiB allocated; 8ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(expm1.f64 (*.f64 x #s(literal 2 binary64)))
accuracy	0.0	(expm1.f64 x)
accuracy	0.00390625	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
accuracy	0.6210937500000001	(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.04296875	(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)))
accuracy	0.8326950195368841	(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.29144811907435	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy	21.313977329745903	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	18.629907216368352	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(+.f64 (exp.f64 x) #s(literal 1 binary64))
accuracy	0.00390625	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))

Samples

66.0ms	248×	0	valid
2.0ms	5×	1	valid
1.0ms	3×	2	valid

Compiler

Compiled 162 to 29 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-add: 24.0ms (45.5% of total)

ival-mult: 9.0ms (17.1% of total)

ival-sqrt: 6.0ms (11.4% of total)

ival-div: 5.0ms (9.5% of total)

ival-expm1: 4.0ms (7.6% of total)

ival-exp: 2.0ms (3.8% of total)

adjust: 1.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory

11.6MiB live, 11.6MiB allocated; 0ms collecting garbage

Counts

19 → 46

Calls

Call 1

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

Calls

3 calls:

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

Time

Variable

Point

Expression

3.0ms

-inf

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

3.0ms

inf

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

2.0ms

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

simplify171.0ms (3.5%)

Memory

-4.9MiB live, 138.3MiB allocated; 40ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	428
1	470	359
2	1558	346
3	6700	344
0	8024	291

Stop Event

1×	iter limit
1×	node limit

Counts

46 → 45

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* 1/2 x))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

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

rewrite213.0ms (4.4%)

Memory

10.2MiB live, 138.3MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	150
0	52	119
1	198	119
2	1173	119
0	8341	119

Stop Event

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

Counts

19 → 581

Calls

Call 1

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

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

eval136.0ms (2.8%)

Memory: -18.5MiB live, 104.6MiB allocated; 16ms collecting garbage
Compiler: Compiled 16 930 to 2 382 computations (85.9% saved)

prune28.0ms (0.6%)

Memory

-12.5MiB live, 31.6MiB allocated; 5ms collecting garbage

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	522	6	528
Fresh	0	3	3
Picked	1	4	5
Done	0	0	0
Total	523	13	536

Accuracy

100.0%

Counts

536 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	65.4%	(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))))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	65.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	4.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
	5.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	71.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	65.6%	#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))))
✓	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))
	4.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
▶	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 519 to 393 computations (24.3% saved)

simplify141.0ms (2.9%)

Memory

-3.1MiB live, 132.8MiB allocated; 28ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))
cost-diff	1	(neg.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	1	(-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x))
cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
cost-diff	0	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
cost-diff	0	#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
cost-diff	0	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
cost-diff	0	(+.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
cost-diff	0	(+.f64 x x)
cost-diff	0	(expm1.f64 (+.f64 x x))
cost-diff	0	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
cost-diff	3	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	284
0	67	270
1	120	270
2	245	270
3	662	262
4	2295	246
0	8889	237

Stop Event

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

Calls

Call 1

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

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

localize77.0ms (1.6%)

Memory

29.9MiB live, 76.6MiB allocated; 2ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x))
accuracy	0.2890625	(*.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)
accuracy	0.8326950195368841	(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.29144811907435	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))
accuracy	0.171875	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
accuracy	0.4765625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.29144811907435	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
accuracy	40.85567497625212	#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
accuracy	0.01171875	(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	21.313977329745903	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)))
accuracy	40.65079156107183	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
accuracy	0.0	(+.f64 #s(literal 2 binary64) x)
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	22.032249938446395	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0.0	(expm1.f64 (+.f64 x x))
accuracy	0.0	(expm1.f64 x)
accuracy	0.00390625	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
accuracy	0.6210937500000001	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

Samples

53.0ms	248×	0	valid
2.0ms	5×	1	valid
2.0ms	3×	2	valid

Compiler

Compiled 227 to 33 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 14.0ms (33.8% of total)

ival-div: 7.0ms (16.9% of total)

ival-add: 7.0ms (16.9% of total)

ival-sqrt: 5.0ms (12.1% of total)

ival-expm1: 4.0ms (9.7% of total)

adjust: 1.0ms (2.4% of total)

ival-sub: 1.0ms (2.4% of total)

ival-neg: 1.0ms (2.4% of total)

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.6%)

Memory

-30.7MiB live, 14.5MiB allocated; 6ms collecting garbage

Counts

23 → 46

Calls

Call 1

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

Outputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(/ -1/2 (sqrt 2))
(- (* -3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(/ x (sqrt 2))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(* -1/2 (/ x (sqrt 2)))
(* x (- (* -3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(- (exp (* 2 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)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* -3/16 (/ x (sqrt 2)))
(* -1 (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))))
(- (exp x) 1)
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* -3/16 (/ (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(- (exp (neg (* -2 x))) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

Calls

3 calls:

Time

Variable

Point

Expression

20.0ms

inf

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

4.0ms

-inf

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

3.0ms

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

simplify159.0ms (3.3%)

Memory

-2.7MiB live, 142.5MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	134	478
1	493	411
2	1704	394
3	6068	392
0	8153	332

Stop Event

1×	iter limit
1×	node limit

Counts

46 → 45

Calls

Call 1

Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(/ -1/2 (sqrt 2))
(- (* -3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(/ x (sqrt 2))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(* -1/2 (/ x (sqrt 2)))
(* x (- (* -3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(- (exp (* 2 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)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* -3/16 (/ x (sqrt 2)))
(* -1 (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))))
(- (exp x) 1)
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* -3/16 (/ (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2)))))))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(- (exp (neg (* -2 x))) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

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

rewrite260.0ms (5.4%)

Memory

14.9MiB live, 203.9MiB allocated; 33ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	261
0	67	249
1	248	225
2	1475	218
0	8948	211

Stop Event

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

Counts

23 → 702

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 3/2 binary64)))
(*.f64 (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
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(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 3/16 binary64) x) #s(literal 3 binary64)) (.f64 (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 3/32 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 3/16 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 3/32 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (/.f64 (*.f64 #s(literal 3/16 binary64) x) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 3/16 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 3/32 binary64))))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 3/16 binary64) x) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (neg.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (neg.f64 x) (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(*.f64 x (/.f64 (neg.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 x (neg.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) x) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 x (neg.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))

eval185.0ms (3.8%)

Memory: 5.6MiB live, 154.0MiB allocated; 32ms collecting garbage
Compiler: Compiled 19 549 to 2 808 computations (85.6% saved)

prune44.0ms (0.9%)

Memory

-7.4MiB live, 39.3MiB allocated; 2ms collecting garbage

Pruning

14 alts after pruning (6 fresh and 8 done)

	Pruned	Kept	Total
New	654	4	658
Fresh	2	2	4
Picked	1	4	5
Done	0	4	4
Total	657	14	671

Accuracy

100.0%

Counts

671 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
▶	65.4%	(sqrt.f64 #s(approx (/ (- (exp (+ x 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))))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	65.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
✓	4.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
▶	5.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	71.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	65.6%	#s(approx (sqrt (/ (- (exp (+ x 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))))
✓	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
▶	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))
▶	4.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
✓	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 501 to 377 computations (24.8% saved)

simplify125.0ms (2.6%)

Memory

18.3MiB live, 116.3MiB allocated; 14ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	408
0	80	408
1	145	406
2	311	401
3	882	366
4	2740	352
0	8530	342

Stop Event

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

Calls

Call 1

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

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

localize127.0ms (2.6%)

Memory

-27.4MiB live, 158.4MiB allocated; 30ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.0625	(*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)
accuracy	0.406913769536884	(/.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
accuracy	21.29144811907435	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
accuracy	0.2890625	(*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
accuracy	0.8326950195368841	(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.29144811907435	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
accuracy	40.676920859690256	#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x))
accuracy	0.01953125	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0.03125	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.1015625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	21.99333180586125	#s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
accuracy	21.313977329745903	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	40.83919414298023	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.0234375	(-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x))
accuracy	0.2890625	(.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)
accuracy	0.8326950195368841	(/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.29144811907435	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))

Samples

87.0ms	248×	0	valid
3.0ms	5×	1	valid
3.0ms	3×	2	valid

Compiler

Compiled 276 to 47 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 30.0ms (43.1% of total)

ival-add: 12.0ms (17.3% of total)

ival-div: 8.0ms (11.5% of total)

ival-expm1: 5.0ms (7.2% of total)

ival-sqrt: 5.0ms (7.2% of total)

const: 4.0ms (5.8% of total)

ival-sub: 2.0ms (2.9% of total)

ival-neg: 2.0ms (2.9% of total)

adjust: 1.0ms (1.4% of total)

exact: 1.0ms (1.4% of total)

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

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

series14.0ms (0.3%)

Memory

34.9MiB live, 34.9MiB allocated; 0ms collecting garbage

Counts

23 → 55

Calls

Call 1

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

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

6.0ms

-inf

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

4.0ms

inf

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

3.0ms

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

simplify210.0ms (4.3%)

Memory

-20.8MiB live, 168.9MiB allocated; 25ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	143	561
1	497	487
2	1707	461
3	6478	459
0	8132	402

Stop Event

1×	iter limit
1×	node limit

Counts

55 → 55

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

rewrite252.0ms (5.2%)

Memory

-12.2MiB live, 205.2MiB allocated; 45ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	354
0	80	354
1	320	303
2	2177	303
0	9362	293

Stop Event

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

Counts

23 → 381

Calls

Call 1

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

Outputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (neg.f64 #s(approx (neg (/ (+ (* 3/16 x) 1/2) (sqrt 2))) (/.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))))
(/.f64 (+.f64 (pow.f64 (.f64 (neg.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) x) #s(literal 3 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x) #s(literal 2 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (.f64 (neg.f64 #s(approx (neg (/ (+ (* 3/16 x) 1/2) (sqrt 2))) (/.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))))))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (.f64 (neg.f64 x) #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) #s(literal 3 binary64))) (+.f64 #s(literal 2 binary64) (-.f64 (.f64 (.f64 (neg.f64 x) #s(approx (neg (/ (+ (* 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (neg.f64 x) #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 x) #s(approx (neg (/ (+ (* 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (.f64 (neg.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) x) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 2 binary64) (-.f64 (pow.f64 (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 #s(approx (neg (/ (+ (* 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))) x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(approx (neg (/ (+ (* 3/16 x) 1/2) (sqrt 2))) (/.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))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (pow.f64 (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x) (fma.f64 #s(approx (neg (/ (+ (* 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)))))
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(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -3/16 binary64) x) #s(literal 3 binary64)) (.f64 (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 3/32 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1/8 binary64) (.f64 (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -3/16 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 3/32 binary64))))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal -3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (neg.f64 (*.f64 x x)))
(fabs.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (-.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))) (.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) #s(literal 1/8 binary64))) (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 x x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x)))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (*.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 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (-.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 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (.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 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (*.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 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (.f64 x #s(literal 1/12 binary64))))) (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (*.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))
(*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 3/16 binary64) x) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal 3/16 binary64) x) x) (.f64 (.f64 #s(literal 3/16 binary64) x) x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 (.f64 #s(literal 3/16 binary64) x) x) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 #s(literal 3/16 binary64) x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 #s(literal 3/16 binary64) x)) (.f64 x (.f64 #s(literal 3/16 binary64) x)) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 #s(literal 3/16 binary64) x)) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 (.f64 #s(literal 3/16 binary64) x) x) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 (.f64 (.f64 (.f64 #s(literal 3/16 binary64) x) x) (.f64 (.f64 #s(literal 3/16 binary64) x) x)) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 #s(literal 3/16 binary64) x) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 x (.f64 #s(literal 3/16 binary64) x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 #s(literal 3/16 binary64) x)) (.f64 x (.f64 #s(literal 3/16 binary64) x))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 #s(literal 3/16 binary64) x))))))
(/.f64 (neg.f64 (.f64 x (-.f64 (.f64 #s(literal 9/256 binary64) (.f64 x x)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 3/16 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal -27/4096 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 #s(literal 9/256 binary64) (.f64 x x)) #s(literal 1/4 binary64)) x)) (neg.f64 (-.f64 (.f64 #s(literal 3/16 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -27/4096 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) x)) (neg.f64 (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))))
(/.f64 (.f64 x (-.f64 (.f64 #s(literal 9/256 binary64) (.f64 x x)) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 3/16 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal -27/4096 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 9/256 binary64) (.f64 x x)) #s(literal 1/4 binary64)) x) (-.f64 (.f64 #s(literal 3/16 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal -27/4096 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) x) (fma.f64 #s(literal 9/256 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) (.f64 (*.f64 #s(literal 3/16 binary64) x) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) (.f64 x (*.f64 #s(literal 3/16 binary64) x)))
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 (.f64 x #s(literal 1 binary64))) (.f64 (*.f64 #s(literal 3/16 binary64) x) x))
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 (.f64 x #s(literal 1 binary64))) (.f64 x (*.f64 #s(literal 3/16 binary64) x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1 binary64)) (.f64 (*.f64 #s(literal 3/16 binary64) x) x))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1 binary64)) (.f64 x (*.f64 #s(literal 3/16 binary64) x)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 #s(literal 3/16 binary64) x) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 #s(literal 3/16 binary64) x)))
(fma.f64 (.f64 #s(literal 3/16 binary64) x) x (.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x) (.f64 (*.f64 #s(literal 3/16 binary64) x) x))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x) (.f64 x (*.f64 #s(literal 3/16 binary64) x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 3/16 binary64) x) x))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 3/16 binary64) x)))
(fma.f64 x (.f64 #s(literal 3/16 binary64) x) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 (.f64 #s(literal 3/16 binary64) x) x) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 x (.f64 #s(literal 3/16 binary64) x)) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (*.f64 #s(literal 3/16 binary64) x) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (*.f64 #s(literal 3/16 binary64) x)))

eval64.0ms (1.3%)

Memory: 2.6MiB live, 92.5MiB allocated; 9ms collecting garbage
Compiler: Compiled 21 072 to 2 249 computations (89.3% saved)

prune36.0ms (0.7%)

Memory

-13.9MiB live, 32.7MiB allocated; 5ms collecting garbage

Pruning

17 alts after pruning (5 fresh and 12 done)

	Pruned	Kept	Total
New	476	4	480
Fresh	0	1	1
Picked	0	5	5
Done	1	7	8
Total	477	17	494

Accuracy

100.0%

Counts

494 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	65.4%	(sqrt.f64 #s(approx (/ (- (exp (+ x 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))))
	2.5%	(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
	3.3%	(sqrt.f64 #s(approx (/ (- (exp (+ x x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x)))))
✓	67.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	65.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	4.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
✓	5.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	71.6%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	65.6%	#s(approx (sqrt (/ (- (exp (+ x 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))))
✓	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
✓	66.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(approx (neg (/ (+ ( 3/16 x) 1/2) (sqrt 2))) (/.f64 (fma.f64 #s(literal -3/16 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))
	4.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (sqrt.f64 #s(literal 2 binary64)))))
✓	4.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
✓	4.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 991 to 458 computations (53.8% saved)

regimes17.0ms (0.3%)

Memory

20.0MiB live, 20.0MiB allocated; 0ms collecting garbage

Counts

23 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms

5.0ms

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

5.0ms

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

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)

regimes14.0ms (0.3%)

Memory

16.0MiB live, 16.0MiB allocated; 0ms collecting garbage

Accuracy

Total -44.8b remaining (-246.7%)

Threshold costs -44.8b (-246.7%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms

4.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
71.6%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
71.6%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
71.6%	1	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify77.0ms (1.6%)

Memory

-14.1MiB live, 43.0MiB 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)))

derivations161.0ms (3.3%)

Memory

1.8MiB live, 89.2MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

preprocess23.0ms (0.5%)

Memory: -25.6MiB live, 19.7MiB allocated; 3ms 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 (25.2%)

explain125.0ms (2.6%)

preprocess174.0ms (3.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify140.0ms (2.9%)

localize113.0ms (2.3%)

series13.0ms (0.3%)

simplify182.0ms (3.8%)

rewrite63.0ms (1.3%)

eval8.0ms (0.2%)

prune6.0ms (0.1%)

simplify135.0ms (2.8%)

localize85.0ms (1.8%)

series9.0ms (0.2%)

simplify171.0ms (3.5%)

rewrite213.0ms (4.4%)

eval136.0ms (2.8%)

prune28.0ms (0.6%)

simplify141.0ms (2.9%)

localize77.0ms (1.6%)

series28.0ms (0.6%)

simplify159.0ms (3.3%)

rewrite260.0ms (5.4%)

eval185.0ms (3.8%)

prune44.0ms (0.9%)

simplify125.0ms (2.6%)

localize127.0ms (2.6%)

series14.0ms (0.3%)

simplify210.0ms (4.3%)

rewrite252.0ms (5.2%)

eval64.0ms (1.3%)

prune36.0ms (0.7%)

regimes17.0ms (0.3%)

regimes14.0ms (0.3%)

simplify77.0ms (1.6%)

derivations161.0ms (3.3%)

preprocess23.0ms (0.5%)

end0.0ms (0%)

Profiling