Metrics for Hyperbolic arc-cosine

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze83.0ms (2.2%)

Memory

9.4MiB live, 163.5MiB 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)

sample2.4s (62.2%)

Memory

58.9MiB live, 2 653.9MiB allocated

Samples

1.1s	7 023×	1	invalid
631.0ms	8 256×	0	valid
61.0ms	1 100×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-sqrt: 252.0ms (21.6% of total)

ival-log: 230.0ms (19.7% of total)

ival-sub: 222.0ms (19% of total)

ival-mult: 173.0ms (14.8% of total)

adjust: 145.0ms (12.4% of total)

ival-add: 117.0ms (10% of total)

ival-true: 13.0ms (1.1% of total)

exact: 10.0ms (0.9% of total)

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

Bogosity

explain100.0ms (2.6%)

Memory

-5.2MiB live, 115.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
136	-	-	`(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	136	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	136
↳	`(*.f64 x x)`	overflow	136
`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	136
↳	`(*.f64 x x)`	overflow	136

Confusion

	Predicted +	Predicted -
+	136	0
-	0	120

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	0	0
-	0	0	120

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	120
1	135
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms

512×

valid

Compiler

Compiled 112 to 32 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-log: 6.0ms (29.1% of total)

ival-sqrt: 5.0ms (24.2% of total)

ival-mult: 4.0ms (19.4% of total)

ival-sub: 3.0ms (14.5% of total)

ival-add: 2.0ms (9.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess226.0ms (6%)

Memory

-0.6MiB live, 124.1MiB 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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.5%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize24.0ms (0.6%)

Memory

-13.3MiB live, 25.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.2421356003831183	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	31.70572215018939	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

17.0ms

256×

valid

Compiler

Compiled 68 to 16 computations (76.5% saved)

Precisions

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

ival-log: 4.0ms (36.5% of total)

ival-mult: 2.0ms (18.2% of total)

ival-sqrt: 2.0ms (18.2% of total)

ival-sub: 1.0ms (9.1% of total)

ival-add: 1.0ms (9.1% 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

6.7MiB live, 6.7MiB allocated

Counts

4 → 36

Calls

Call 1

Inputs
(sqrt.f64 (-.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))))
(*.f64 x x)

Outputs
(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))))))
(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)))))
(+ 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))))))))
(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 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)))))
(* -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))))))
(+ (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
2.0ms	x	@	0	((sqrt (- (* x x) 1)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* x x))
2.0ms	x	@	inf	((sqrt (- (* x x) 1)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* x x))
2.0ms	x	@	-inf	((sqrt (- (* x x) 1)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* x x))

Time

Variable

Point

Expression

2.0ms

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

2.0ms

inf

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

2.0ms

-inf

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

simplify28.0ms (0.7%)

Memory

-11.7MiB live, 26.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	508
0	481	492

Stop Event

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

Counts

36 → 35

Calls

Call 1

Inputs
(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))))))
(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)))))
(+ 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))))))))
(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 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)))))
(* -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))))))
(+ (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
(sqrt -1)
(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 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) #s(literal -1/8 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)))
(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 #s(literal -1/6 binary64) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 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))))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 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 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) #s(literal -1/8 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)))
(pow x 2)
(*.f64 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 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)
(* -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))))
(+ (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))

rewrite182.0ms (4.8%)

Memory

10.4MiB live, 158.7MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	26
0	12	13
1	57	13
2	408	11
3	5453	11
0	8310	11

Stop Event

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

Counts

4 → 267

Calls

Call 1

Inputs
(sqrt.f64 (-.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))))
(*.f64 x x)

Outputs
(*.f64 (neg.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64))))
(*.f64 (fabs.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64))) (fabs.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64))))
(*.f64 (fabs.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (fabs.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (sinh.f64 (neg.f64 (acosh.f64 x)))) (sqrt.f64 (sinh.f64 (neg.f64 (acosh.f64 x)))))
(*.f64 (sqrt.f64 (sinh.f64 (acosh.f64 x))) (sqrt.f64 (sinh.f64 (acosh.f64 x))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (sinh.f64 (neg.f64 (acosh.f64 x))) #s(literal 1/2 binary64)) (pow.f64 (sinh.f64 (neg.f64 (acosh.f64 x))) #s(literal 1/2 binary64)))
(*.f64 (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 (sinh.f64 (acosh.f64 (.f64 x x))) (cos.f64 (atan.f64 x)))
(.f64 (sinh.f64 (acosh.f64 (.f64 x x))) (sqrt.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))))
(.f64 (sinh.f64 (acosh.f64 (.f64 x x))) (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)))
(*.f64 (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.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 (pow.f64 x #s(literal 3 binary64)))) (exp.f64 (.f64 (neg.f64 (log1p.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (acosh.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (cosh.f64 (asinh.f64 x)) (sinh.f64 (acosh.f64 (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.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))))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 (acosh.f64 x)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 1 binary64))
(pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sinh.f64 (acosh.f64 (*.f64 x x)))) (neg.f64 (cosh.f64 (asinh.f64 x))))
(/.f64 (neg.f64 (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (acosh.f64 x)))) #s(literal -2 binary64))
(/.f64 (fabs.f64 (sinh.f64 (acosh.f64 (*.f64 x x)))) (fabs.f64 (cosh.f64 (asinh.f64 x))))
(/.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))))))))
(*.f64 #s(literal -1 binary64) (neg.f64 (acosh.f64 x)))
(/.f64 (-.f64 (.f64 (-.f64 (acosh.f64 x) (acosh.f64 x)) (-.f64 (acosh.f64 x) (acosh.f64 x))) (.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 (pow.f64 (-.f64 (acosh.f64 x) (acosh.f64 x)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (acosh.f64 x)) #s(literal 3 binary64))) (fma.f64 (-.f64 (acosh.f64 x) (acosh.f64 x)) (-.f64 (acosh.f64 x) (acosh.f64 x)) (fma.f64 (neg.f64 (acosh.f64 x)) (neg.f64 (acosh.f64 x)) (*.f64 (-.f64 (acosh.f64 x) (acosh.f64 x)) (neg.f64 (acosh.f64 x))))))
(/.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 (/.f64 (exp.f64 (neg.f64 (acosh.f64 x))) #s(literal 1 binary64))))
(neg.f64 (neg.f64 (acosh.f64 x)))
(fma.f64 #s(literal -1 binary64) (neg.f64 (acosh.f64 x)) (-.f64 (acosh.f64 x) (acosh.f64 x)))
(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 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 4 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 (cosh.f64 (-.f64 (acosh.f64 x) (acosh.f64 x))) #s(literal 1 binary64))) (neg.f64 (acosh.f64 x)))
(-.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)))))
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(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (exp.f64 (acosh.f64 x))) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (exp.f64 (neg.f64 (acosh.f64 x)))))
(fma.f64 #s(literal 1 binary64) x (sinh.f64 (acosh.f64 x)))
(fma.f64 (*.f64 x x) (/.f64 x (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)))))
(fma.f64 (.f64 x x) (exp.f64 (acosh.f64 x)) (neg.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x)))))
(fma.f64 (*.f64 x x) (exp.f64 (acosh.f64 x)) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (exp.f64 (neg.f64 (acosh.f64 x)))))
(fma.f64 x (/.f64 x (exp.f64 (neg.f64 (acosh.f64 x)))) (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (exp.f64 (acosh.f64 x)))))
(fma.f64 x (/.f64 x (exp.f64 (neg.f64 (acosh.f64 x)))) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (exp.f64 (neg.f64 (acosh.f64 x)))))
(fma.f64 x (/.f64 (*.f64 x x) (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)))))
(fma.f64 x #s(literal 1 binary64) (sinh.f64 (acosh.f64 x)))
(-.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (sinh.f64 (acosh.f64 x)) x)) (/.f64 (*.f64 x x) (-.f64 (sinh.f64 (acosh.f64 x)) 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 x (sinh.f64 (neg.f64 (acosh.f64 x))))
(exp.f64 (*.f64 (neg.f64 (acosh.f64 x)) #s(literal -1 binary64)))
(exp.f64 (acosh.f64 x))
(+.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 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 (.f64 (.f64 x x) (exp.f64 (acosh.f64 x))) (neg.f64 (*.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 (neg.f64 x) x #s(literal 1 binary64)) (exp.f64 (neg.f64 (acosh.f64 x)))))
(+.f64 (sinh.f64 (acosh.f64 x)) x)
(+.f64 x (sinh.f64 (acosh.f64 x)))
(.f64 (.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(.f64 (sqrt.f64 (.f64 (neg.f64 x) x)) (sqrt.f64 (*.f64 (neg.f64 x) x)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval42.0ms (1.1%)

Memory: 25.7MiB live, 61.8MiB allocated
Compiler: Compiled 6 608 to 1 159 computations (82.5% saved)

prune35.0ms (0.9%)

Memory

-20.0MiB live, 29.5MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	2	303

Accuracy

100.0%

Counts

303 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(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)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize34.0ms (0.9%)

Memory

7.7MiB live, 45.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.13910742150364347	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
accuracy	0.2421356003831183	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	0.1875	(acosh.f64 x)

Samples

27.0ms

256×

valid

Compiler

Compiled 60 to 23 computations (61.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-add: 7.0ms (34.2% of total)

ival-acosh: 4.0ms (19.6% of total)

ival-mult: 3.0ms (14.7% of total)

ival-log: 3.0ms (14.7% of total)

ival-sqrt: 2.0ms (9.8% of total)

ival-sub: 1.0ms (4.9% 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

4.0MiB live, 4.0MiB 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))

simplify32.0ms (0.9%)

Memory

-12.0MiB live, 26.1MiB 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))

rewrite279.0ms (7.4%)

Memory

17.2MiB live, 172.8MiB 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))))
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(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 (0.4%)

Memory: -16.3MiB live, 21.9MiB allocated
Compiler: Compiled 2 848 to 481 computations (83.1% saved)

prune2.0ms (0.1%)

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
▶	99.5%	(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)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize39.0ms (1%)

Memory

-19.9MiB live, 40.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x x)
accuracy	0.13910742150364347	#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
accuracy	0.2421356003831183	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))

Samples

29.0ms

256×

valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

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

ival-assert: 12.0ms (52.2% of total)

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

ival-add: 2.0ms (8.7% of total)

ival-mult: 2.0ms (8.7% of total)

ival-sqrt: 2.0ms (8.7% of total)

ival-sub: 1.0ms (4.4% of total)

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

1.9MiB live, 1.9MiB 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))

simplify21.0ms (0.6%)

Memory

14.6MiB live, 14.6MiB 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))

rewrite64.0ms (1.7%)

Memory

-8.1MiB live, 30.5MiB 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)

eval4.0ms (0.1%)

Memory: 5.0MiB live, 5.0MiB 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
✓	99.5%	(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)

regimes32.0ms (0.8%)

Memory

-25.4MiB live, 13.1MiB allocated

Accuracy

Total -32.9b remaining (-17545%)

Threshold costs -32.9b (-17545%)

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:

28.0ms	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)

simplify39.0ms (1%)

Memory

6.5MiB live, 44.0MiB 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)

soundness127.0ms (3.3%)

Memory

-9.4MiB live, 72.4MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	26
0	12	13
1	57	13
2	408	11
3	5453	11
0	8310	11

Stop Event

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

Compiler

Compiled 13 to 10 computations (23.1% saved)

preprocess13.0ms (0.3%)

Memory: 27.2MiB live, 27.2MiB allocated
Compiler: Compiled 22 to 18 computations (18.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze83.0ms (2.2%)

sample2.4s (62.2%)

explain100.0ms (2.6%)

preprocess226.0ms (6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

localize24.0ms (0.6%)

series5.0ms (0.1%)

simplify28.0ms (0.7%)

rewrite182.0ms (4.8%)

eval42.0ms (1.1%)

prune35.0ms (0.9%)

simplify0.0ms (0%)

localize34.0ms (0.9%)

series3.0ms (0.1%)

simplify32.0ms (0.9%)

rewrite279.0ms (7.4%)

eval14.0ms (0.4%)

prune2.0ms (0.1%)

simplify0.0ms (0%)

localize39.0ms (1%)

series2.0ms (0%)

simplify21.0ms (0.6%)

rewrite64.0ms (1.7%)

eval4.0ms (0.1%)

prune2.0ms (0%)

regimes32.0ms (0.8%)

simplify39.0ms (1%)

soundness127.0ms (3.3%)

preprocess13.0ms (0.3%)

end0.0ms (0%)

Profiling