Metrics for Rust f32::acosh

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample623.0ms (22.9%)

Memory

-7.9MiB live, 753.4MiB allocated; 150ms collecting garbage

Samples

442.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 241.0ms

ival-acosh: 193.0ms (80% of total)

ival->=: 35.0ms (14.5% of total)

exact: 6.0ms (2.5% of total)

ival-assert: 4.0ms (1.7% of total)

adjust: 3.0ms (1.2% of total)

Bogosity

explain135.0ms (5%)

Memory

21.2MiB live, 110.2MiB allocated; 21ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
129	-	-	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`
2	-	-	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
0	-	-	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`
0	-	-	`(*.f32 x x)`
0	-	-	`#s(literal 1 binary32)`
0	-	-	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f32`	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`	oflow-rescue	129	0
↳	`(*.f32 x x)`	overflow	129
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	129
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	2	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	2
↳	`(*.f32 x x)`	overflow	129
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	129

Confusion

	Predicted +	Predicted -
+	129	0
-	0	127

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	129	0	0
-	0	0	127

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	127
1	127
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

59.0ms

512×

valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-log: 35.0ms (73.1% of total)

ival-mult: 4.0ms (8.4% of total)

ival-sub: 3.0ms (6.3% of total)

ival-sqrt: 3.0ms (6.3% of total)

ival-add: 2.0ms (4.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess193.0ms (7.1%)

Memory

-23.0MiB live, 118.4MiB allocated; 33ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	7	9
0	12	9
1	22	9
2	49	9
3	121	9
4	383	9
5	2335	9
6	7889	9
0	8019	8

Stop Event

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

Calls

Call 1

Inputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Outputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))

Compiler

Compiled 9 to 7 computations (22.2% 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

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.8%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify173.0ms (6.3%)

Memory

0.3MiB live, 144.2MiB allocated; 30ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))
cost-diff	0	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
cost-diff	0	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
cost-diff	1	(-.f32 (*.f32 x x) #s(literal 1 binary32))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	33
1	22	33
2	49	33
3	121	33
4	383	33
5	2335	33
6	7889	33
0	8019	29

Stop Event

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

Calls

Call 1

Inputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
x
(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(*.f32 x x)
#s(literal 1 binary32)

Outputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
x
(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(fma.f32 x x #s(literal -1 binary32))
(*.f32 x x)
#s(literal 1 binary32)

localize58.0ms (2.1%)

Memory

-14.3MiB live, 28.9MiB allocated; 13ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f32 (*.f32 x x) #s(literal 1 binary32))
accuracy	0.03125	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
accuracy	0.2337977767045218	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
accuracy	13.96359580965167	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Samples

14.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 2.0ms (22.6% of total)

ival-log: 2.0ms (22.6% of total)

ival-sqrt: 2.0ms (22.6% of total)

ival-add: 1.0ms (11.3% of total)

ival-sub: 1.0ms (11.3% 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)

series5.0ms (0.2%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Counts

4 → 39

Calls

Call 1

Inputs
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Outputs
-1
(- (pow x 2) 1)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
1.0ms	x	@	-inf	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
1.0ms	x	@	inf	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

Time

Variable

Point

Expression

2.0ms

((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

1.0ms

-inf

((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

1.0ms

inf

((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

simplify287.0ms (10.6%)

Memory

24.1MiB live, 258.7MiB allocated; 62ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	525
1	470	499
2	1771	482
0	7736	463

Stop Event

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

Counts

39 → 38

Calls

Call 1

Inputs
-1
(- (pow x 2) 1)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))

Outputs
-1
#s(literal -1 binary32)
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 (fma.f32 #s(literal 1/6 binary32) (*.f32 x x) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 #s(literal 3/40 binary32) x) (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 (sqrt.f32 #s(literal -1 binary32)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (/.f32 (fma.f32 #s(literal 1/8 binary32) (*.f32 x x) #s(literal 1/2 binary32)) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) x) #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (/.f32 (fma.f32 #s(literal 1/8 binary32) (.f32 x x) #s(literal 1/2 binary32)) (sqrt.f32 #s(literal -1 binary32))) (.f32 x x) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (pow.f32 x #s(literal 4 binary32)) (fma.f32 (.f32 #s(literal 1/16 binary32) x) (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (/.f32 #s(literal 1/8 binary32) (sqrt.f32 #s(literal -1 binary32)))) (fma.f32 (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) x) #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 x x))) x) x)
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (-.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal -3/32 binary32)) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal 1/4 binary32) (.f32 x x)))
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(.f32 (-.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (pow.f32 x #s(literal 4 binary32))) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 x x)) #s(literal 2 binary32))) x)
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 (/.f32 x x) (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (-.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (pow.f32 x #s(literal 4 binary32))) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x x)
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(-.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(-.f32 (-.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x))) (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(-.f32 (-.f32 (-.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x))) (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal -5/96 binary32) (pow.f32 x #s(literal 6 binary32))))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (-.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal -1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (+.f32 (/.f32 (/.f32 (-.f32 (/.f32 #s(literal 1/16 binary32) (*.f32 x x)) #s(literal -1/8 binary32)) x) x) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 #s(literal -5/128 binary32) (.f32 x x)) #s(literal 1/16 binary32)) (pow.f32 x #s(literal 4 binary32))) (-.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) #s(literal -1/2 binary32))) (neg.f32 x))
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 x x)) #s(literal -1 binary32)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(.f32 (-.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 x x)) #s(literal -1 binary32)) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(.f32 (+.f32 (/.f32 (-.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal -1/8 binary32)) (pow.f32 x #s(literal 4 binary32))) (+.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 x x)) #s(literal -1 binary32))) x)

rewrite109.0ms (4%)

Memory

-13.0MiB live, 180.8MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
0	12	15
1	53	15
0	400	14

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

4 → 64

Calls

Call 1

Inputs
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Outputs
(expm1.f32 (*.f32 (log.f32 x) #s(literal 2 binary32)))
(*.f32 (+.f32 (neg.f32 x) #s(literal 1 binary32)) (-.f32 (neg.f32 x) #s(literal 1 binary32)))
(*.f32 (+.f32 (fabs.f32 x) #s(literal 1 binary32)) (-.f32 (fabs.f32 x) #s(literal 1 binary32)))
(*.f32 (neg.f32 (sinh.f32 (acosh.f32 x))) (neg.f32 (sinh.f32 (acosh.f32 x))))
(*.f32 (fabs.f32 (sinh.f32 (acosh.f32 x))) (fabs.f32 (sinh.f32 (acosh.f32 x))))
(*.f32 (-.f32 x #s(literal 1 binary32)) (-.f32 x #s(literal -1 binary32)))
(*.f32 (-.f32 x #s(literal -1 binary32)) (-.f32 x #s(literal 1 binary32)))
(*.f32 (sinh.f32 (acosh.f32 x)) (sinh.f32 (acosh.f32 x)))
(sqrt.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))))
(/.f32 (neg.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (neg.f32 (fma.f32 x x #s(literal 1 binary32))))
(/.f32 (neg.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32))) (neg.f32 (+.f32 (fma.f32 x x #s(literal 1 binary32)) (pow.f32 x #s(literal 4 binary32)))))
(/.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 x x #s(literal 1 binary32)))
(/.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (+.f32 (fma.f32 x x #s(literal 1 binary32)) (pow.f32 x #s(literal 4 binary32))))
(-.f32 (/.f32 (pow.f32 x #s(literal 4 binary32)) (fma.f32 x x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))))
(-.f32 (/.f32 (pow.f32 x #s(literal 6 binary32)) (+.f32 (fma.f32 x x #s(literal 1 binary32)) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 x x #s(literal 1 binary32)) (pow.f32 x #s(literal 4 binary32)))))
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(fma.f32 (.f32 (neg.f32 x) #s(literal 1 binary32)) (.f32 (neg.f32 x) #s(literal 1 binary32)) #s(literal -1 binary32))
(fma.f32 (.f32 (fabs.f32 x) #s(literal 1 binary32)) (.f32 (fabs.f32 x) #s(literal 1 binary32)) #s(literal -1 binary32))
(fma.f32 (pow.f32 x #s(literal 1 binary32)) (pow.f32 x #s(literal 1 binary32)) #s(literal -1 binary32))
(fma.f32 (.f32 x #s(literal 1 binary32)) (.f32 x #s(literal 1 binary32)) #s(literal -1 binary32))
(fma.f32 (neg.f32 (neg.f32 x)) (neg.f32 (neg.f32 x)) #s(literal -1 binary32))
(fma.f32 (neg.f32 (fabs.f32 x)) (neg.f32 (fabs.f32 x)) #s(literal -1 binary32))
(fma.f32 (fabs.f32 (fabs.f32 x)) (fabs.f32 (fabs.f32 x)) #s(literal -1 binary32))
(fma.f32 (neg.f32 x) (*.f32 (neg.f32 x) #s(literal 1 binary32)) #s(literal -1 binary32))
(fma.f32 (neg.f32 x) (neg.f32 x) #s(literal -1 binary32))
(fma.f32 (fabs.f32 x) (*.f32 (fabs.f32 x) #s(literal 1 binary32)) #s(literal -1 binary32))
(fma.f32 (fabs.f32 x) (fabs.f32 x) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 x x) #s(literal -1 binary32))
(fma.f32 (*.f32 x x) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 x (*.f32 x #s(literal 1 binary32)) #s(literal -1 binary32))
(fma.f32 x x #s(literal -1 binary32))
(pow.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32))
(pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 2 binary32))
(pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1 binary32))
(+.f32 (*.f32 x x) #s(literal -1 binary32))
(acosh.f32 x)
(log.f32 (+.f32 (sinh.f32 (acosh.f32 x)) x))
(-.f32 (log.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (-.f32 x (sinh.f32 (acosh.f32 x)))))
(-.f32 (log.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))) (log.f32 (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (*.f32 x x))))
(/.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x)) (-.f32 (sinh.f32 (acosh.f32 x)) x))
(/.f32 (neg.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (neg.f32 (-.f32 x (sinh.f32 (acosh.f32 x)))))
(/.f32 (neg.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))) (neg.f32 (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (*.f32 x x))))
(/.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32))) (-.f32 x (sinh.f32 (acosh.f32 x))))
(/.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32))) (+.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 (.f32 x x) (.f32 (sinh.f32 (acosh.f32 x)) x))))
(/.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32))) (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (*.f32 x x)))
(-.f32 (/.f32 (*.f32 x x) (-.f32 x (sinh.f32 (acosh.f32 x)))) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sinh.f32 (acosh.f32 x)))))
(fma.f32 (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)) (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)) x)
(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
(fma.f32 (pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/2 binary32)) (pow.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1/2 binary32)) x)
(+.f32 (/.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (.f32 x x))) (/.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (.f32 x x))))
(+.f32 (sinh.f32 (acosh.f32 x)) x)
(+.f32 x (sinh.f32 (acosh.f32 x)))
(*.f32 (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)) (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)))
(*.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))))
(*.f32 (pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/2 binary32)) (pow.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1/2 binary32)))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (sqrt.f32 (fma.f32 x x #s(literal 1 binary32))))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32))) (sqrt.f32 (+.f32 (fma.f32 x x #s(literal 1 binary32)) (pow.f32 x #s(literal 4 binary32)))))
(/.f32 (-.f32 (exp.f32 (acosh.f32 x)) (exp.f32 (neg.f32 (acosh.f32 x)))) #s(literal 2 binary32))
(pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/2 binary32))
(exp.f32 (*.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32)))
(sinh.f32 (acosh.f32 (neg.f32 x)))
(sinh.f32 (acosh.f32 (fabs.f32 x)))
(sinh.f32 (acosh.f32 x))

eval10.0ms (0.4%)

Memory: 24.2MiB live, 24.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 699 to 485 computations (71.5% saved)

prune2.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	3	103

Accuracy

100.0%

Counts

103 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
▶	96.8%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
▶	99.3%	(acosh.f32 x)

Status

Accuracy

Program

▶

99.3%

(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))

▶

96.8%

(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))

▶

99.3%

(acosh.f32 x)

Compiler

Compiled 26 to 21 computations (19.2% saved)

simplify126.0ms (4.6%)

Memory

-1.5MiB live, 185.8MiB allocated; 14ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f32 x #s(literal -1 binary32))
cost-diff	0	(sqrt.f32 (-.f32 x #s(literal -1 binary32)))
cost-diff	0	(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
cost-diff	0	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
cost-diff	0	(*.f32 #s(literal 2 binary32) x)
cost-diff	0	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
cost-diff	0	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
cost-diff	0	(acosh.f32 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	71
0	28	71
1	42	71
2	79	71
3	179	71
4	618	71
5	4153	71
0	8238	69

Stop Event

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

Calls

Call 1

Inputs
(acosh.f32 x)
x
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(*.f32 #s(literal 2 binary32) x)
#s(literal 2 binary32)
x
(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
(sqrt.f32 (-.f32 x #s(literal -1 binary32)))
(-.f32 x #s(literal -1 binary32))
x
#s(literal -1 binary32)
(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
(-.f32 x #s(literal 1 binary32))
#s(literal 1 binary32)

Outputs
(acosh.f32 x)
x
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(*.f32 #s(literal 2 binary32) x)
#s(literal 2 binary32)
x
(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (-.f32 x #s(literal -1 binary32))) x))
(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
(fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (-.f32 x #s(literal -1 binary32))) x)
(sqrt.f32 (-.f32 x #s(literal -1 binary32)))
(-.f32 x #s(literal -1 binary32))
x
#s(literal -1 binary32)
(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
(-.f32 x #s(literal 1 binary32))
#s(literal 1 binary32)

localize58.0ms (2.1%)

Memory

-32.6MiB live, 111.1MiB allocated; 13ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
accuracy	0.00390625	(sqrt.f32 (-.f32 x #s(literal -1 binary32)))
accuracy	0.07421875	(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
accuracy	0.2337977767045218	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
accuracy	0.0	(*.f32 #s(literal 2 binary32) x)
accuracy	0.2337977767045218	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
accuracy	0.9544242509920478	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
accuracy	0.21484375	(acosh.f32 x)

Samples

45.0ms

256×

valid

Compiler

Compiled 67 to 20 computations (70.1% saved)

Precisions

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

ival-sub: 13.0ms (34.9% of total)

ival-sqrt: 9.0ms (24.1% of total)

ival-mult: 5.0ms (13.4% of total)

ival-log: 4.0ms (10.7% of total)

ival-acosh: 3.0ms (8% of total)

ival-add: 2.0ms (5.4% 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)

series9.0ms (0.3%)

Memory

18.8MiB live, 18.8MiB allocated; 0ms collecting garbage

Counts

9 → 56

Calls

Call 1

Inputs
(acosh.f32 x)
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(*.f32 #s(literal 2 binary32) x)
(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
(sqrt.f32 (-.f32 x #s(literal -1 binary32)))
(-.f32 x #s(literal -1 binary32))
(sqrt.f32 (-.f32 x #s(literal 1 binary32)))

Outputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x)) (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x) (sqrt (- x -1)) (- x -1) (sqrt (- x 1)))
2.0ms	x	@	inf	((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x)) (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x) (sqrt (- x -1)) (- x -1) (sqrt (- x 1)))
1.0ms	x	@	0	((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x)) (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x) (sqrt (- x -1)) (- x -1) (sqrt (- x 1)))

Time

Variable

Point

Expression

5.0ms

-inf

((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x)) (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x) (sqrt (- x -1)) (- x -1) (sqrt (- x 1)))

2.0ms

inf

((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x)) (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x) (sqrt (- x -1)) (- x -1) (sqrt (- x 1)))

1.0ms

((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x)) (+ (* (sqrt (- x -1)) (sqrt (- x 1))) x) (sqrt (- x -1)) (- x -1) (sqrt (- x 1)))

simplify246.0ms (9%)

Memory

-11.7MiB live, 220.3MiB allocated; 145ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	291	1042
1	911	837
2	3927	809
0	8628	769

Stop Event

1×	iter limit
1×	node limit

Counts

56 → 55

Calls

Call 1

Inputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Outputs
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal -1 binary32))) (sqrt.f32 #s(literal -1 binary32))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) #s(literal 3/40 binary32) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 (sqrt.f32 #s(literal -1 binary32)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (.f32 #s(literal -1/8 binary32) x) x) #s(literal -1 binary32))) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
1
#s(literal 1 binary32)
(+ 1 (* 1/2 x))
(fma.f32 #s(literal 1/2 binary32) x #s(literal 1 binary32))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f32 (fma.f32 #s(literal -1/8 binary32) x #s(literal 1/2 binary32)) x #s(literal 1 binary32))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f32 (fma.f32 (fma.f32 #s(literal 1/16 binary32) x #s(literal -1/8 binary32)) x #s(literal 1/2 binary32)) x #s(literal 1 binary32))
(+ 1 x)
(-.f32 x #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 #s(literal 1/8 binary32) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 (fma.f32 (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32) (/.f32 #s(literal 1/8 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (sqrt.f32 #s(literal -1 binary32)))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (/.f32 (-.f32 (/.f32 #s(literal 3/32 binary32) (*.f32 x x)) #s(literal -1/4 binary32)) x) x))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (-.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal -3/32 binary32)) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal 1/4 binary32) (.f32 x x)))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 (/.f32 (-.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) #s(literal -1/2 binary32)) x) x)) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal -1/16 binary32) (.f32 x x)) #s(literal -1/8 binary32)) (pow.f32 x #s(literal 4 binary32))) (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (*.f32 x x)))) x)
(sqrt x)
(sqrt.f32 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 7 binary32)))) #s(literal 1/16 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))) x)
x
(* x (+ 1 (/ 1 x)))
(-.f32 x #s(literal -1 binary32))
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(*.f32 (fma.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(.f32 (+.f32 (fma.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 7 binary32)))) (fma.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))) x)
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(-.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32))) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))) (log.f32 #s(literal -1/2 binary32)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f32 (-.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32))) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))) (/.f32 #s(literal -5/96 binary32) (pow.f32 x #s(literal 6 binary32)))) (log.f32 #s(literal -1/2 binary32)))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (-.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal -1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (+.f32 (/.f32 (/.f32 (-.f32 (/.f32 #s(literal 1/16 binary32) (*.f32 x x)) #s(literal -1/8 binary32)) x) x) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal -5/128 binary32) (.f32 x x)) #s(literal -1/16 binary32)) (pow.f32 x #s(literal 4 binary32))) (-.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) #s(literal -1/2 binary32))) (neg.f32 x))
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f32 (-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+.f32 (+.f32 (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32))) (-.f32 (/.f32 #s(literal -1/4 binary32) (*.f32 x x)) (log.f32 (/.f32 #s(literal -1 binary32) x)))) (log.f32 #s(literal -2 binary32)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(+.f32 (-.f32 (-.f32 (-.f32 (/.f32 #s(literal -5/96 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -2 binary32)))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(*.f32 #s(literal 2 binary32) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(.f32 (+.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) x)
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(.f32 (neg.f32 x) (+.f32 (/.f32 #s(literal 1/16 binary32) (pow.f32 x #s(literal 6 binary32))) (-.f32 (+.f32 #s(literal -2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f32 (sqrt.f32 x) #s(literal 1 binary32))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f32 (fma.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f32 (fma.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 7 binary32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) x)) #s(literal 1 binary32))))) x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) x)) #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 7 binary32)))) #s(literal 1/16 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32))))) x)

rewrite82.0ms (3%)

Memory

22.8MiB live, 67.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	62
0	28	47
1	101	42
0	846	42

Stop Event

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

Counts

9 → 68

Calls

Call 1

Inputs
(acosh.f32 x)
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(*.f32 #s(literal 2 binary32) x)
(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
(sqrt.f32 (-.f32 x #s(literal -1 binary32)))
(-.f32 x #s(literal -1 binary32))
(sqrt.f32 (-.f32 x #s(literal 1 binary32)))

Outputs
(acosh.f32 x)
(log.f32 (+.f32 (sinh.f32 (acosh.f32 x)) x))
(-.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (log.f32 (-.f32 (sinh.f32 (acosh.f32 x)) x)))
(-.f32 (log.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (-.f32 x (sinh.f32 (acosh.f32 x)))))
(-.f32 (log.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))) (log.f32 (fma.f32 x (-.f32 x (sinh.f32 (acosh.f32 x))) (fma.f32 x x #s(literal -1 binary32)))))
(-.f32 (log.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))) (log.f32 (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (*.f32 x x))))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(*.f32 #s(literal 2 binary32) x)
(*.f32 x #s(literal 2 binary32))
(/.f32 (-.f32 (.f32 x x) (.f32 x x)) (-.f32 x x))
(/.f32 (+.f32 (pow.f32 x #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32))) (fma.f32 x x (-.f32 (.f32 x x) (.f32 x x))))
(+.f32 x x)
(acosh.f32 x)
(log.f32 (+.f32 (sinh.f32 (acosh.f32 x)) x))
(-.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (log.f32 (-.f32 (sinh.f32 (acosh.f32 x)) x)))
(-.f32 (log.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (-.f32 x (sinh.f32 (acosh.f32 x)))))
(-.f32 (log.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))) (log.f32 (fma.f32 x (-.f32 x (sinh.f32 (acosh.f32 x))) (fma.f32 x x #s(literal -1 binary32)))))
(-.f32 (log.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))) (log.f32 (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (*.f32 x x))))
(/.f32 (neg.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (neg.f32 (-.f32 x (sinh.f32 (acosh.f32 x)))))
(/.f32 (neg.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))) (neg.f32 (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (*.f32 x x))))
(/.f32 (neg.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))) (neg.f32 (fma.f32 x (-.f32 x (sinh.f32 (acosh.f32 x))) (fma.f32 x x #s(literal -1 binary32)))))
(/.f32 (neg.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (neg.f32 (-.f32 (sinh.f32 (acosh.f32 x)) x)))
(/.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32))) (-.f32 x (sinh.f32 (acosh.f32 x))))
(/.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x)) (-.f32 (sinh.f32 (acosh.f32 x)) x))
(/.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32))) (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (*.f32 x x)))
(/.f32 (+.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32))) (fma.f32 x (-.f32 x (sinh.f32 (acosh.f32 x))) (fma.f32 x x #s(literal -1 binary32))))
(-.f32 (/.f32 (*.f32 x x) (-.f32 x (sinh.f32 (acosh.f32 x)))) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sinh.f32 (acosh.f32 x)))))
(-.f32 (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 (sinh.f32 (acosh.f32 x)) x)) (/.f32 (*.f32 x x) (-.f32 (sinh.f32 (acosh.f32 x)) x)))
(-.f32 x (*.f32 (neg.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32)))) (sqrt.f32 (-.f32 x #s(literal -1 binary32)))))
(-.f32 x (*.f32 (neg.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32)))) (sqrt.f32 (-.f32 x #s(literal 1 binary32)))))
(fma.f32 (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)) (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)) x)
(fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (-.f32 x #s(literal -1 binary32))) x)
(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
(+.f32 (/.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (.f32 x x))) (/.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (fma.f32 (sinh.f32 (acosh.f32 x)) (-.f32 (sinh.f32 (acosh.f32 x)) x) (.f32 x x))))
(+.f32 (/.f32 (pow.f32 (sinh.f32 (acosh.f32 x)) #s(literal 3 binary32)) (fma.f32 x (-.f32 x (sinh.f32 (acosh.f32 x))) (fma.f32 x x #s(literal -1 binary32)))) (/.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 x (-.f32 x (sinh.f32 (acosh.f32 x))) (fma.f32 x x #s(literal -1 binary32)))))
(+.f32 (sinh.f32 (acosh.f32 x)) x)
(+.f32 x (sinh.f32 (acosh.f32 x)))
(*.f32 (pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/4 binary32)) (pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/4 binary32)))
(sqrt.f32 (-.f32 x #s(literal -1 binary32)))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 3 binary32)) #s(literal -1 binary32))) (sqrt.f32 (fma.f32 x x (fma.f32 #s(literal -1 binary32) x #s(literal 1 binary32)))))
(/.f32 (sinh.f32 (acosh.f32 x)) (sqrt.f32 (-.f32 x #s(literal 1 binary32))))
(pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/2 binary32))
(exp.f32 (*.f32 (log1p.f32 x) #s(literal 1/2 binary32)))
(*.f32 (-.f32 x #s(literal -1 binary32)) (/.f32 (-.f32 x #s(literal 1 binary32)) (-.f32 x #s(literal 1 binary32))))
(*.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (-.f32 x #s(literal -1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 x x)) (-.f32 #s(literal 1 binary32) x))
(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 x x) x)))
(/.f32 (+.f32 (pow.f32 x #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 x x (-.f32 #s(literal 1 binary32) x)))
(/.f32 (neg.f32 (-.f32 (pow.f32 x #s(literal 3 binary32)) #s(literal -1 binary32))) (neg.f32 (fma.f32 x x (fma.f32 #s(literal -1 binary32) x #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 x x #s(literal -1 binary32))) (neg.f32 (-.f32 x #s(literal 1 binary32))))
(/.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (*.f32 (fma.f32 x x #s(literal 1 binary32)) (-.f32 x #s(literal 1 binary32))))
(/.f32 (-.f32 (pow.f32 x #s(literal 3 binary32)) #s(literal -1 binary32)) (fma.f32 x x (fma.f32 #s(literal -1 binary32) x #s(literal 1 binary32))))
(/.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (fma.f32 x x #s(literal 1 binary32)) (pow.f32 x #s(literal 4 binary32))) (-.f32 x #s(literal 1 binary32))))
(/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x #s(literal 1 binary32)))
(-.f32 (/.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 x x (fma.f32 #s(literal -1 binary32) x #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (fma.f32 x x (fma.f32 #s(literal -1 binary32) x #s(literal 1 binary32)))))
(-.f32 (/.f32 (*.f32 x x) (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 x #s(literal 1 binary32))))
(-.f32 #s(literal 1 binary32) (*.f32 (neg.f32 x) #s(literal 1 binary32)))
(-.f32 x #s(literal -1 binary32))
(+.f32 #s(literal 1 binary32) x)
(+.f32 x #s(literal 1 binary32))
(*.f32 (pow.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1/4 binary32)) (pow.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1/4 binary32)))
(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
(/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 3 binary32)) #s(literal 1 binary32))) (sqrt.f32 (fma.f32 x x (-.f32 x #s(literal -1 binary32)))))
(/.f32 (sinh.f32 (acosh.f32 x)) (sqrt.f32 (-.f32 x #s(literal -1 binary32))))
(pow.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1/2 binary32))
(exp.f32 (*.f32 (log.f32 (-.f32 x #s(literal 1 binary32))) #s(literal 1/2 binary32)))

eval31.0ms (1.1%)

Memory: -28.1MiB live, 29.5MiB allocated; 20ms collecting garbage
Compiler: Compiled 2 346 to 553 computations (76.4% saved)

prune2.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	116	3	119

Accuracy

100.0%

Counts

119 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
▶	96.8%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
✓	99.3%	(acosh.f32 x)

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify176.0ms (6.5%)

Memory

31.0MiB live, 121.4MiB allocated; 15ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f32 x x)
cost-diff	0	#s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x))
cost-diff	0	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
0	11	29
1	23	29
2	52	29
3	130	29
4	431	29
5	2677	29
6	6902	29
0	8193	27

Stop Event

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

Calls

Call 1

Inputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x))
(+.f32 x x)
x

Outputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(+.f32 x x)
(*.f32 #s(literal 2 binary32) x)
x

localize25.0ms (0.9%)

Memory

-6.0MiB live, 38.4MiB allocated; 7ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f32 x x)
accuracy	0.2337977767045218	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
accuracy	0.9544242509920478	#s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x))

Samples

19.0ms

256×

valid

Compiler

Compiled 23 to 10 computations (56.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 5.0ms (35.8% of total)

ival-log: 3.0ms (21.5% of total)

ival-add: 2.0ms (14.3% of total)

ival-sqrt: 2.0ms (14.3% of total)

ival-sub: 1.0ms (7.2% 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)

series2.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated; 0ms collecting garbage

Counts

3 → 24

Calls

Call 1

Inputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x))
(+.f32 x x)

Outputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))

1.0ms

-inf

((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))

0.0ms

((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))

simplify185.0ms (6.8%)

Memory

-6.6MiB live, 232.5MiB allocated; 42ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	339
1	386	321
2	1414	310
0	7718	301

Stop Event

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

Counts

24 → 24

Calls

Call 1

Inputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))

Outputs
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 (fma.f32 #s(literal 1/6 binary32) (*.f32 x x) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 #s(literal 3/40 binary32) x) (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 (sqrt.f32 #s(literal -1 binary32)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (/.f32 (fma.f32 #s(literal 1/8 binary32) (*.f32 x x) #s(literal 1/2 binary32)) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (-.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal -3/32 binary32)) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal 1/4 binary32) (.f32 x x)))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(.f32 (-.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (pow.f32 x #s(literal 4 binary32))) (-.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 x x)) #s(literal 2 binary32))) x)
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(-.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(-.f32 (-.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x))) (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(-.f32 (-.f32 (-.f32 (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x))) (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (/.f32 #s(literal -5/96 binary32) (pow.f32 x #s(literal 6 binary32))))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (-.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal -1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (+.f32 (/.f32 (/.f32 (-.f32 (/.f32 #s(literal 1/16 binary32) (*.f32 x x)) #s(literal -1/8 binary32)) x) x) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 #s(literal -5/128 binary32) (.f32 x x)) #s(literal 1/16 binary32)) (pow.f32 x #s(literal 4 binary32))) (-.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) #s(literal -1/2 binary32))) (neg.f32 x))

rewrite57.0ms (2.1%)

Memory

18.9MiB live, 65.4MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
0	11	22
1	59	22
0	489	22

Stop Event

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

Counts

3 → 10

Calls

Call 1

Inputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x))
(+.f32 x x)

Outputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(*.f32 #s(literal 2 binary32) x)
(*.f32 x #s(literal 2 binary32))
(/.f32 (neg.f32 (*.f32 #s(literal 2 binary32) (pow.f32 x #s(literal 3 binary32)))) (neg.f32 (fma.f32 x x #s(literal 0 binary32))))
(/.f32 (*.f32 #s(literal 2 binary32) (pow.f32 x #s(literal 3 binary32))) (fma.f32 x x #s(literal 0 binary32)))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
(-.f32 (/.f32 (.f32 x x) #s(literal 0 binary32)) (/.f32 (.f32 x x) #s(literal 0 binary32)))
(+.f32 (/.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 x x #s(literal 0 binary32))) (/.f32 (pow.f32 x #s(literal 3 binary32)) (fma.f32 x x #s(literal 0 binary32))))
(+.f32 x x)

eval7.0ms (0.3%)

Memory: -24.4MiB live, 19.1MiB allocated; 5ms collecting garbage
Compiler: Compiled 713 to 174 computations (75.6% saved)

prune2.0ms (0.1%)

Memory

10.3MiB live, 10.3MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	34	3	37

Accuracy

100.0%

Counts

37 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
✓	96.8%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
✓	99.3%	(acosh.f32 x)

Compiler

Compiled 74 to 47 computations (36.5% saved)

regimes8.0ms (0.3%)

Memory

-20.7MiB live, 25.7MiB allocated; 2ms collecting garbage

Accuracy

Total -15.7b remaining (-7306.7%)

Threshold costs -15.7b (-7306.7%)

Counts

5 → 1

Calls

Call 1

Inputs
(acosh.f32 x)
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))

Outputs
(acosh.f32 x)

Calls

3 calls:

4.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
2.0ms	x
2.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Results

Accuracy	Segments	Branch
99.3%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`
99.3%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
99.3%	1	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify9.0ms (0.3%)

Memory

31.7MiB live, 31.7MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2

Stop Event

1×

saturated

Calls

Call 1

Inputs
(acosh.f32 x)

Outputs
(acosh.f32 x)

derivations84.0ms (3.1%)

Memory

-40.5MiB live, 110.3MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
0	12	15
1	53	15
0	400	14

Stop Event

1×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 2 to 2 computations (0% saved)

preprocess17.0ms (0.6%)

Memory: 36.5MiB live, 36.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 46 to 36 computations (21.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample623.0ms (22.9%)

explain135.0ms (5%)

preprocess193.0ms (7.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify173.0ms (6.3%)

localize58.0ms (2.1%)

series5.0ms (0.2%)

simplify287.0ms (10.6%)

rewrite109.0ms (4%)

eval10.0ms (0.4%)

prune2.0ms (0.1%)

simplify126.0ms (4.6%)

localize58.0ms (2.1%)

series9.0ms (0.3%)

simplify246.0ms (9%)

rewrite82.0ms (3%)

eval31.0ms (1.1%)

prune2.0ms (0.1%)

simplify176.0ms (6.5%)

localize25.0ms (0.9%)

series2.0ms (0.1%)

simplify185.0ms (6.8%)

rewrite57.0ms (2.1%)

eval7.0ms (0.3%)

prune2.0ms (0.1%)

regimes8.0ms (0.3%)

simplify9.0ms (0.3%)

derivations84.0ms (3.1%)

preprocess17.0ms (0.6%)

end0.0ms (0%)

Profiling