Metrics for Hyperbolic arc-cosine

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze68.0ms (1.5%)

Memory

34.1MiB live, 107.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample2.5s (54.4%)

Memory

42.9MiB live, 2 275.0MiB allocated

Samples

1.1s	7 291×	1	invalid
574.0ms	8 256×	0	valid
67.0ms	1 157×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-mult: 271.0ms (21.5% of total)

ival-log: 260.0ms (20.7% of total)

ival-add: 211.0ms (16.8% of total)

ival-sqrt: 187.0ms (14.9% of total)

adjust: 166.0ms (13.2% of total)

ival-sub: 135.0ms (10.7% of total)

ival-true: 12.0ms (1% of total)

exact: 10.0ms (0.8% of total)

ival-assert: 6.0ms (0.5% of total)

Bogosity

explain162.0ms (3.6%)

Memory

-4.4MiB live, 166.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
133	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`
1	-	-	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
0	-	-	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 x x)`
0	-	-	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	133	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	133
↳	`(*.f64 x x)`	overflow	133
`log.f64`	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`	oflow-rescue	1	0
↳	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`	overflow	1
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	133
↳	`(*.f64 x x)`	overflow	133

Confusion

	Predicted +	Predicted -
+	133	0
-	0	123

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	133	0	0
-	0	0	123

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	123
1	132
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

46.0ms

512×

valid

Compiler

Compiled 112 to 32 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-sub: 16.0ms (48.2% of total)

ival-log: 6.0ms (18.1% of total)

ival-mult: 4.0ms (12% of total)

ival-sqrt: 4.0ms (12% of total)

ival-add: 2.0ms (6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess310.0ms (6.8%)

Memory

-1.5MiB live, 199.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	32	19
2	87	19
3	255	19
4	801	19
5	1503	19
6	2966	19
7	4674	19
8	5717	19
9	7138	19
10	7891	19
0	7	9
0	12	9
1	26	9
2	53	9
3	167	9
4	584	9
5	1218	9
6	2582	9
7	4612	9
8	5688	9
9	6759	9
10	7572	9
0	8003	8

Stop Event

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

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.7%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify133.0ms (2.9%)

Memory

-7.6MiB live, 104.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
cost-diff	128	(-.f64 (*.f64 x x) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	33
1	26	33
2	53	33
3	167	33
4	584	33
5	1218	33
6	2582	33
7	4612	33
8	5688	33
9	6759	33
10	7572	33
0	8003	29

Stop Event

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

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
x
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
x
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x x #s(literal -1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

localize22.0ms (0.5%)

Memory

18.6MiB live, 18.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0.01171875	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.2460418520454816	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	30.999112050906476	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

15.0ms

256×

valid

Compiler

Compiled 68 to 16 computations (76.5% saved)

Precisions

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

ival-log: 3.0ms (32.3% of total)

ival-mult: 2.0ms (21.5% of total)

ival-sqrt: 2.0ms (21.5% of total)

ival-sub: 1.0ms (10.8% of total)

ival-add: 1.0ms (10.8% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

4 → 39

Calls

Call 1

Inputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

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)))

simplify66.0ms (1.4%)

Memory

-24.2MiB live, 26.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	525
0	489	508

Stop Event

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

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 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (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.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) (*.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(+ (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.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) (.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x))
(+ (log 2) (* -1 (log (/ 1 x))))
(fma.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (log.f64 x)) (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x x))) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (fma.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (log.f64 x)) (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -1 binary64) #s(literal 2 binary64)) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (+.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(neg.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1 binary64) #s(literal -1/2 binary64)) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(.f64 (neg.f64 x) (-.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))

rewrite241.0ms (5.3%)

Memory

-33.0MiB live, 163.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
0	12	15
1	57	15
2	408	13
3	5453	13
0	8310	12

Stop Event

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

Counts

4 → 450

Calls

Call 1

Inputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Outputs
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (.f64 (sinh.f64 (acosh.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(.f64 (.f64 (sinh.f64 (acosh.f64 x)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64))) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) x)) (fabs.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
(*.f64 (fabs.f64 (-.f64 x #s(literal 1 binary64))) (fabs.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (fabs.f64 (+.f64 #s(literal 1 binary64) x)) (fabs.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fabs.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))))
(*.f64 (pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sinh.f64 (neg.f64 (acosh.f64 x))) #s(literal 1 binary64)) (pow.f64 (sinh.f64 (neg.f64 (acosh.f64 x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (exp.f64 (.f64 (neg.f64 (log1p.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))))
(*.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64)) (.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64)) (sinh.f64 (acosh.f64 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (sinh.f64 (neg.f64 (acosh.f64 x))) (sinh.f64 (neg.f64 (acosh.f64 x))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sinh.f64 (acosh.f64 x))))
(*.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal 1 binary64)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (tanh.f64 (log.f64 x)))
(.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (sinh.f64 (acosh.f64 x)) (sinh.f64 (acosh.f64 x)))
(*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (fabs.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (sinh.f64 (neg.f64 (acosh.f64 x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (+.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (.f64 (sinh.f64 (acosh.f64 (.f64 x x))) (sinh.f64 (acosh.f64 x))) (cosh.f64 (asinh.f64 x)))
(/.f64 (*.f64 (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3 binary64)))) (sinh.f64 (acosh.f64 x))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (acosh.f64 x))) (sinh.f64 (acosh.f64 x))) #s(literal 2 binary64))
(/.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (sinh.f64 (acosh.f64 x)) (sinh.f64 (acosh.f64 (.f64 x x)))) (cosh.f64 (asinh.f64 x)))
(/.f64 (*.f64 (sinh.f64 (acosh.f64 x)) (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (.f64 (sinh.f64 (acosh.f64 x)) (.f64 #s(literal 2 binary64) (sinh.f64 (acosh.f64 x)))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64))) (-.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) #s(literal 3 binary64)) (exp.f64 (.f64 (neg.f64 (log1p.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) #s(literal 3 binary64)))) (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
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(/.f64 (fabs.f64 (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (fabs.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (acosh.f64 x)))) #s(literal 2 binary64))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (sinh.f64 (acosh.f64 (*.f64 (sinh.f64 (acosh.f64 x)) x))))
(/.f64 (sin.f64 (acos.f64 (*.f64 x x))) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(/.f64 (sinh.f64 (acosh.f64 (*.f64 x x))) (cosh.f64 (asinh.f64 x)))
(/.f64 (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (acosh.f64 x))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (cosh.f64 (asinh.f64 x)) (sinh.f64 (acosh.f64 (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 (acosh.f64 x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))))
(sinh.f64 (neg.f64 (neg.f64 (acosh.f64 (neg.f64 x)))))
(sinh.f64 (acosh.f64 (sqrt.f64 (*.f64 (neg.f64 x) x))))
(sinh.f64 (acosh.f64 (exp.f64 (log.f64 x))))
(sinh.f64 (acosh.f64 (neg.f64 x)))
(sinh.f64 (acosh.f64 x))
(neg.f64 (sinh.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (sinh.f64 (-.f64 (acosh.f64 x) (acosh.f64 x))) x (*.f64 (cosh.f64 (-.f64 (acosh.f64 x) (acosh.f64 x))) (sinh.f64 (acosh.f64 x))))
(fma.f64 (sinh.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (cosh.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))) (*.f64 (cosh.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sinh.f64 (neg.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))))
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(-.f64 (.f64 (sinh.f64 (+.f64 (acosh.f64 (neg.f64 x)) (acosh.f64 x))) (cosh.f64 (acosh.f64 (neg.f64 x)))) (.f64 (cosh.f64 (+.f64 (acosh.f64 (neg.f64 x)) (acosh.f64 x))) (sinh.f64 (acosh.f64 x))))
(-.f64 (.f64 (sinh.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))))) (cosh.f64 (log.f64 (neg.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))) (.f64 (cosh.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))))) (sinh.f64 (log.f64 (neg.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))))
(-.f64 (.f64 #s(literal 0 binary64) x) (.f64 #s(literal 1 binary64) (sinh.f64 (neg.f64 (acosh.f64 x)))))
(-.f64 (/.f64 (exp.f64 (acosh.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 (acosh.f64 x))) #s(literal 2 binary64)))
(-.f64 (.f64 (sinh.f64 (-.f64 (acosh.f64 x) (acosh.f64 x))) x) (.f64 (cosh.f64 (-.f64 (acosh.f64 x) (acosh.f64 x))) (sinh.f64 (neg.f64 (acosh.f64 x)))))
(-.f64 (.f64 (sinh.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (cosh.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))) (.f64 (cosh.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sinh.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))))
(fabs.f64 (sinh.f64 (neg.f64 (acosh.f64 x))))
(fabs.f64 (sinh.f64 (acosh.f64 x)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 4 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sinh.f64 (acosh.f64 x))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sinh.f64 (acosh.f64 x))))
(+.f64 (cosh.f64 (log.f64 (sinh.f64 (acosh.f64 x)))) (sinh.f64 (log.f64 (sinh.f64 (acosh.f64 x)))))
(+.f64 (.f64 (sinh.f64 (-.f64 (acosh.f64 x) (acosh.f64 x))) x) (.f64 (cosh.f64 (-.f64 (acosh.f64 x) (acosh.f64 x))) (sinh.f64 (acosh.f64 x))))
(+.f64 (.f64 (sinh.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (cosh.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))) (.f64 (cosh.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sinh.f64 (neg.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))))

eval74.0ms (1.6%)

Memory: 0.8MiB live, 108.2MiB allocated
Compiler: Compiled 10 625 to 2 080 computations (80.4% saved)

prune14.0ms (0.3%)

Memory

-19.3MiB live, 31.8MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	486	2	488
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	487	2	489

Accuracy

100.0%

Counts

489 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.3%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	99.7%	(acosh.f64 x)

Compiler

Compiled 15 to 12 computations (20% saved)

simplify155.0ms (3.4%)

Memory

38.4MiB live, 147.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
cost-diff	0	(acosh.f64 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
0	14	33
1	31	33
2	58	33
3	174	33
4	623	33
5	1293	33
6	2642	33
7	4651	33
8	5699	33
9	6757	33
10	7568	33
0	8016	31

Stop Event

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

Calls

Call 1

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

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

localize69.0ms (1.5%)

Memory

-29.5MiB live, 21.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.2460418520454816	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	0.9633915082111679	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
accuracy	0.1875	(acosh.f64 x)

Samples

63.0ms

256×

valid

Compiler

Compiled 60 to 23 computations (61.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 31.0ms (55% of total)

ival-log: 18.0ms (31.9% of total)

ival-acosh: 4.0ms (7.1% of total)

ival-sqrt: 2.0ms (3.5% of total)

ival-add: 1.0ms (1.8% of total)

ival-sub: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

3.3MiB live, 3.3MiB allocated

Counts

4 → 24

Calls

Call 1

Inputs
(acosh.f64 x)
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) 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	x	@	-inf	((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x))
1.0ms	x	@	inf	((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x))
1.0ms	x	@	0	((acosh x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x))

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify28.0ms (0.6%)

Memory

-11.9MiB live, 24.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	339
0	397	328

Stop Event

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

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.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (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.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) (*.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ (log 2) (* -1 (log (/ 1 x))))
(fma.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (log.f64 x)) (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x x))) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (fma.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (log.f64 x)) (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -1 binary64) #s(literal 2 binary64)) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (+.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(neg.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1 binary64) #s(literal -1/2 binary64)) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x))

rewrite169.0ms (3.7%)

Memory

27.4MiB live, 180.4MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	30
0	14	24
1	61	24
2	417	20
3	5623	20
0	8210	20

Stop Event

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

Counts

4 → 88

Calls

Call 1

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

Outputs
(*.f64 #s(literal -1 binary64) (neg.f64 (acosh.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (acosh.f64 x)) (neg.f64 (acosh.f64 x)))) (neg.f64 (acosh.f64 x)))
(/.f64 (-.f64 (.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))) (log.f64 (*.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 (acosh.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (neg.f64 (acosh.f64 x)) (neg.f64 (acosh.f64 x)) #s(literal 0 binary64))))
(/.f64 (-.f64 (pow.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 3 binary64)) (pow.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) #s(literal 3 binary64))) (fma.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (*.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))))
(neg.f64 (log.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (exp.f64 (acosh.f64 x))))))
(neg.f64 (neg.f64 (acosh.f64 x)))
(fma.f64 #s(literal -1 binary64) (neg.f64 (acosh.f64 x)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(acosh.f64 x)
(-.f64 (log.f64 (.f64 (.f64 (fma.f64 x x (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (exp.f64 (acosh.f64 x)))) (log.f64 (fma.f64 x x (fma.f64 x x #s(literal -1 binary64)))))
(-.f64 (log.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64))) (exp.f64 (acosh.f64 x)))) (log.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x (fma.f64 x x #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (log.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64))) (pow.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))) (log.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)))))
(-.f64 (log.f64 (.f64 (+.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))) (log.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64))) (pow.f64 (.f64 (sinh.f64 (acosh.f64 x)) x) #s(literal 3 binary64)))))
(-.f64 (log.f64 (-.f64 (.f64 (.f64 (.f64 x x) (exp.f64 (acosh.f64 x))) (.f64 (.f64 x x) (exp.f64 (acosh.f64 x)))) (.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x)))))) (log.f64 (fma.f64 (.f64 x x) (exp.f64 (acosh.f64 x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x))))))
(-.f64 (log.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))) (.f64 (/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))) (log.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))))
(-.f64 (log.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) (exp.f64 (acosh.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x))) #s(literal 3 binary64)))) (log.f64 (fma.f64 (.f64 (.f64 x x) (exp.f64 (acosh.f64 x))) (.f64 (.f64 x x) (exp.f64 (acosh.f64 x))) (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x))) (.f64 (.f64 (.f64 x x) (exp.f64 (acosh.f64 x))) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x))))))))
(-.f64 (log.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) #s(literal 3 binary64)))) (log.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (-.f64 (.f64 (/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))))))
(-.f64 (log.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))))) (log.f64 (neg.f64 (neg.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))))
(-.f64 (log.f64 (.f64 (.f64 (fma.f64 x x (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))) (log.f64 (*.f64 (fma.f64 x x (fma.f64 x x #s(literal -1 binary64))) (exp.f64 (neg.f64 (acosh.f64 x))))))
(-.f64 (log.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64))) #s(literal 1 binary64))) (log.f64 (.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x (fma.f64 x x #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) (exp.f64 (neg.f64 (acosh.f64 x))))))
(-.f64 (log.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64))) #s(literal 1 binary64))) (log.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (log.f64 (.f64 (+.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64))) (log.f64 (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64))) (pow.f64 (*.f64 (sinh.f64 (acosh.f64 x)) x) #s(literal 3 binary64))) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (log.f64 (*.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))
(-.f64 (log.f64 (-.f64 (.f64 (.f64 x x) (exp.f64 (neg.f64 (acosh.f64 x)))) (.f64 (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))) (log.f64 (.f64 (exp.f64 (neg.f64 (acosh.f64 x))) (exp.f64 (neg.f64 (acosh.f64 x))))))
(-.f64 (log.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) (.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))))) (log.f64 (.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (log.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (log.f64 (exp.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))))
(-.f64 (log.f64 (fma.f64 (sinh.f64 (acosh.f64 x)) (exp.f64 (acosh.f64 x)) (*.f64 x x))) (log.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)))))
(-.f64 (+.f64 (log.f64 (fma.f64 x x (fma.f64 x x #s(literal -1 binary64)))) #s(literal 0 binary64)) (log.f64 (*.f64 (fma.f64 x x (fma.f64 x x #s(literal -1 binary64))) (exp.f64 (neg.f64 (acosh.f64 x))))))
(-.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64)))) (log.f64 (*.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x (fma.f64 x x #s(literal -1 binary64))) (pow.f64 x #s(literal 4 binary64))) (exp.f64 (neg.f64 (acosh.f64 x))))))
(-.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64)))) (log.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (log.f64 #s(literal -1 binary64)) (acosh.f64 (neg.f64 x)))
(-.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)))) (log.f64 (neg.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (log.f64 (+.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) (log.f64 (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 6 binary64))) (pow.f64 (.f64 (sinh.f64 (acosh.f64 x)) x) #s(literal 3 binary64))) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))))
(-.f64 #s(literal 0 binary64) (log.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (exp.f64 (acosh.f64 x))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (acosh.f64 x)))
(-.f64 (acosh.f64 x) #s(literal 0 binary64))
(+.f64 (log.f64 (/.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal -1 binary64) (.f64 x (exp.f64 (neg.f64 (acosh.f64 x))))) #s(literal 2 binary64))))) (log1p.f64 (.f64 (sinh.f64 (acosh.f64 x)) x)))
(+.f64 (log.f64 (/.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (.f64 x (exp.f64 (neg.f64 (acosh.f64 x))))) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (log.f64 (fma.f64 (+.f64 #s(literal -1 binary64) (.f64 x (exp.f64 (neg.f64 (acosh.f64 x))))) (-.f64 (+.f64 #s(literal -1 binary64) (.f64 x (exp.f64 (neg.f64 (acosh.f64 x))))) (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (log.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))) #s(literal -1 binary64))) (log.f64 (fma.f64 (sinh.f64 (acosh.f64 x)) (exp.f64 (acosh.f64 x)) (*.f64 x x))))
(+.f64 (neg.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))) (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(+.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (acosh.f64 (neg.f64 x))))
(+.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)))) (log.f64 (pow.f64 (neg.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64))))
(+.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (/.f64 (exp.f64 (acosh.f64 x)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(+.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (*.f64 (exp.f64 (acosh.f64 x)) (pow.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))))
(+.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (log.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))))))
(+.f64 (acosh.f64 (neg.f64 x)) (log.f64 (/.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (acosh.f64 x))) (exp.f64 (neg.f64 (acosh.f64 x))))))
(+.f64 (acosh.f64 (neg.f64 x)) (log.f64 (*.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (acosh.f64 x))) (exp.f64 (acosh.f64 x)))))
(+.f64 #s(literal 0 binary64) (acosh.f64 x))
(+.f64 (acosh.f64 x) #s(literal 0 binary64))
(log.f64 (exp.f64 (acosh.f64 x)))
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 0 binary64) (pow.f64 #s(literal 0 binary64) #s(literal -1 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(pow.f64 (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (/.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal -1 binary64) (.f64 x (exp.f64 (neg.f64 (acosh.f64 x))))) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (sinh.f64 (acosh.f64 x)) x)) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (/.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (.f64 x (exp.f64 (neg.f64 (acosh.f64 x))))) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (+.f64 #s(literal -1 binary64) (.f64 x (exp.f64 (neg.f64 (acosh.f64 x))))) (-.f64 (+.f64 #s(literal -1 binary64) (.f64 x (exp.f64 (neg.f64 (acosh.f64 x))))) (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (sinh.f64 (acosh.f64 x)) (exp.f64 (acosh.f64 x)) (*.f64 x x)) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(fma.f64 (pow.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64))) (pow.f64 (neg.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (/.f64 #s(literal -1 binary64) (exp.f64 (acosh.f64 x))) (/.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (acosh.f64 x))) (exp.f64 (neg.f64 (acosh.f64 x)))) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (/.f64 #s(literal -1 binary64) (exp.f64 (acosh.f64 x))) (*.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (acosh.f64 x))) (exp.f64 (acosh.f64 x))) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 (acosh.f64 x))) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) x)
(fma.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (exp.f64 (acosh.f64 x)) (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) (*.f64 (exp.f64 (acosh.f64 x)) (pow.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (-.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 x (exp.f64 (neg.f64 (acosh.f64 x))) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 (exp.f64 (acosh.f64 x)) #s(literal 1 binary64) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 #s(literal 1 binary64) (exp.f64 (acosh.f64 x)) (exp.f64 (neg.f64 (acosh.f64 x))))
(fma.f64 #s(literal 1 binary64) x x)
(fma.f64 x #s(literal 1 binary64) x)
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 (exp.f64 (acosh.f64 x)) (exp.f64 (neg.f64 (acosh.f64 x))))
(+.f64 x x)

eval14.0ms (0.3%)

Memory: -15.0MiB live, 21.8MiB allocated
Compiler: Compiled 2 848 to 481 computations (83.1% saved)

prune2.0ms (0%)

Memory

6.8MiB live, 6.8MiB allocated

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	112	2	114

Accuracy

100.0%

Counts

114 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.3%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
✓	99.7%	(acosh.f64 x)

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify158.0ms (3.5%)

Memory

-13.5MiB live, 148.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-128	(+.f64 x x)
cost-diff	0	#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
0	11	29
1	27	29
2	56	29
3	170	29
4	609	29
5	1278	29
6	2640	29
7	4682	29
8	5733	29
9	6795	29
10	7606	29
0	8018	27

Stop Event

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

Calls

Call 1

Inputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(+.f64 x x)
x

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

localize21.0ms (0.5%)

Memory

24.3MiB live, 24.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x x)
accuracy	0.2460418520454816	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
accuracy	0.9633915082111679	#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))

Samples

15.0ms

256×

valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-log: 3.0ms (29.7% of total)

ival-add: 2.0ms (19.8% of total)

ival-mult: 2.0ms (19.8% of total)

ival-sqrt: 2.0ms (19.8% of total)

ival-sub: 1.0ms (9.9% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

3 → 24

Calls

Call 1

Inputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(+.f64 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))

simplify23.0ms (0.5%)

Memory

-17.6MiB live, 21.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	339
0	397	328

Stop Event

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

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.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (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.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) (*.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ (log 2) (* -1 (log (/ 1 x))))
(fma.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (log.f64 x)) (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x x))) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (fma.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (log.f64 x)) (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal -1 binary64) #s(literal 2 binary64)) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64))) (+.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(neg.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1 binary64) #s(literal -1/2 binary64)) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x))

rewrite109.0ms (2.4%)

Memory

-15.7MiB live, 69.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
0	11	22
1	63	22
0	504	22

Stop Event

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

Counts

3 → 14

Calls

Call 1

Inputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(+.f64 x x)

Outputs
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 x x)

eval6.0ms (0.1%)

Memory: 5.1MiB live, 5.1MiB allocated
Compiler: Compiled 814 to 195 computations (76% saved)

prune2.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	38	2	40

Accuracy

100.0%

Counts

40 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.3%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
✓	99.7%	(acosh.f64 x)

Compiler

Compiled 52 to 31 computations (40.4% saved)

regimes6.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Accuracy

Total -32.9b remaining (-17554.9%)

Threshold costs -32.9b (-17554.9%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(acosh.f64 x)

Calls

3 calls:

2.0ms	x
2.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
2.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.7%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify45.0ms (1%)

Memory

-8.2MiB live, 31.0MiB allocated

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.f64 x)

Outputs
(acosh.f64 x)

soundness146.0ms (3.2%)

Memory

-0.2MiB live, 36.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
0	12	15
1	57	15
2	408	13
3	5453	13
0	8310	12

Stop Event

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

Compiler

Compiled 13 to 10 computations (23.1% saved)

preprocess17.0ms (0.4%)

Memory: 34.2MiB live, 34.2MiB allocated
Compiler: Compiled 22 to 18 computations (18.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze68.0ms (1.5%)

sample2.5s (54.4%)

explain162.0ms (3.6%)

preprocess310.0ms (6.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify133.0ms (2.9%)

localize22.0ms (0.5%)

series5.0ms (0.1%)

simplify66.0ms (1.4%)

rewrite241.0ms (5.3%)

eval74.0ms (1.6%)

prune14.0ms (0.3%)

simplify155.0ms (3.4%)

localize69.0ms (1.5%)

series3.0ms (0.1%)

simplify28.0ms (0.6%)

rewrite169.0ms (3.7%)

eval14.0ms (0.3%)

prune2.0ms (0%)

simplify158.0ms (3.5%)

localize21.0ms (0.5%)

series2.0ms (0%)

simplify23.0ms (0.5%)

rewrite109.0ms (2.4%)

eval6.0ms (0.1%)

prune2.0ms (0%)

regimes6.0ms (0.1%)

simplify45.0ms (1%)

soundness146.0ms (3.2%)

preprocess17.0ms (0.4%)

end0.0ms (0%)

Profiling