Metrics for Rust f64::acosh

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample1.4s (37.5%)

Memory

-14.3MiB live, 849.9MiB allocated; 1.3s collecting garbage

Samples

1.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 869.0ms

ival-acosh: 831.0ms (95.7% of total)

ival->=: 24.0ms (2.8% of total)

exact: 7.0ms (0.8% of total)

ival-assert: 4.0ms (0.5% of total)

adjust: 3.0ms (0.3% of total)

Bogosity

explain227.0ms (6.3%)

Memory

7.4MiB live, 246.2MiB allocated; 35ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
121	-	-	`(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	-	-	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #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	121	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	121
↳	`(*.f64 x x)`	overflow	121

Confusion

	Predicted +	Predicted -
+	121	0
-	0	135

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	121	0	0
-	0	0	135

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	135
1	121

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

48.0ms

512×

valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-add: 13.0ms (35.9% of total)

ival-log: 12.0ms (33.1% of total)

ival-mult: 4.0ms (11% of total)

ival-sub: 3.0ms (8.3% of total)

ival-sqrt: 3.0ms (8.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess228.0ms (6.3%)

Memory

-22.4MiB live, 165.9MiB allocated; 19ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

Inputs
(log.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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.2%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify176.0ms (4.9%)

Memory

3.6MiB live, 148.0MiB allocated; 22ms collecting garbage

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

Inputs
(log.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)

localize25.0ms (0.7%)

Memory

0.5MiB live, 45.0MiB allocated; 7ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	0.0078125	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	28.138364931096433	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

19.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

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

ival-log: 3.0ms (31.9% of total)

ival-mult: 2.0ms (21.3% of total)

ival-sqrt: 2.0ms (21.3% of total)

ival-add: 1.0ms (10.6% of total)

ival-sub: 1.0ms (10.6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Counts

5 → 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)))
(*.f64 x x)

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)) (* x x))
1.0ms	x	@	-inf	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (* x x))
1.0ms	x	@	inf	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (* x x))

Time

Variable

Point

Expression

2.0ms

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

1.0ms

-inf

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

1.0ms

inf

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

simplify239.0ms (6.6%)

Memory

-30.6MiB live, 264.9MiB allocated; 38ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

39 → 38

Calls

Call 1

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

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

rewrite71.0ms (2%)

Memory

16.5MiB live, 104.8MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	31
0	12	18
1	53	18
0	400	17

Stop Event

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

Counts

5 → 86

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)))
(*.f64 x x)

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

eval40.0ms (1.1%)

Memory: -13.4MiB live, 41.9MiB allocated; 11ms collecting garbage
Compiler: Compiled 1 956 to 593 computations (69.7% saved)

prune2.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	2	125

Accuracy

100.0%

Counts

125 → 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)

simplify200.0ms (5.5%)

Memory

11.6MiB live, 189.6MiB allocated; 63ms collecting garbage

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	27	33
2	59	33
3	149	33
4	562	33
5	3969	33
0	8175	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

localize34.0ms (0.9%)

Memory

8.8MiB live, 53.8MiB allocated; 12ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.0	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	0.37960138091334755	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
accuracy	0.2109375	(acosh.f64 x)

Samples

20.0ms

256×

valid

Compiler

Compiled 27 to 12 computations (55.6% saved)

Precisions

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

ival-acosh: 4.0ms (28.1% of total)

ival-mult: 3.0ms (21.1% of total)

ival-log: 2.0ms (14.1% of total)

ival-sqrt: 2.0ms (14.1% of total)

ival-add: 1.0ms (7% of total)

ival-sub: 1.0ms (7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

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))

simplify232.0ms (6.4%)

Memory

-16.1MiB live, 233.7MiB allocated; 112ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

24 → 24

Calls

Call 1

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

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

rewrite62.0ms (1.7%)

Memory

-14.7MiB live, 89.4MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
0	14	24
1	57	24
0	421	24

Stop Event

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

Counts

4 → 15

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

eval4.0ms (0.1%)

Memory: 14.7MiB live, 14.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 689 to 194 computations (71.8% saved)

prune1.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	39	2	41

Accuracy

100.0%

Counts

41 → 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)

simplify137.0ms (3.8%)

Memory

13.4MiB live, 98.9MiB allocated; 18ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.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	23	29
2	52	29
3	130	29
4	431	29
5	2677	29
6	6902	29
0	8193	27

Stop Event

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

Calls

Call 1

Inputs
(log.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

localize25.0ms (0.7%)

Memory

-6.8MiB live, 35.9MiB allocated; 9ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x x)
accuracy	0.0	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
accuracy	0.37960138091334755	#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))

Samples

19.0ms

256×

valid

Compiler

Compiled 23 to 10 computations (56.5% saved)

Precisions

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

ival-log: 3.0ms (29.2% of total)

ival-add: 2.0ms (19.5% of total)

ival-mult: 2.0ms (19.5% of total)

ival-sqrt: 2.0ms (19.5% of total)

ival-sub: 1.0ms (9.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

4.3MiB live, 4.2MiB allocated; 0ms collecting garbage

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))

simplify280.0ms (7.7%)

Memory

-3.9MiB live, 286.5MiB allocated; 73ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

24 → 24

Calls

Call 1

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

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

rewrite43.0ms (1.2%)

Memory

7.6MiB live, 53.6MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 10

Calls

Call 1

Inputs
(log.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 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 (*.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 (/.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: 11.0MiB live, 11.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 713 to 174 computations (75.6% saved)

prune5.0ms (0.1%)

Memory

-38.0MiB live, 8.4MiB allocated; 2ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	34	2	36

Accuracy

100.0%

Counts

36 → 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)

regimes6.0ms (0.2%)

Memory

19.2MiB live, 19.2MiB allocated; 0ms collecting garbage

Accuracy

Total -29.5b remaining (-13976%)

Threshold costs -29.5b (-13976%)

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

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify21.0ms (0.6%)

Memory

-34.4MiB live, 25.7MiB allocated; 23ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2

Stop Event

1×

saturated

Calls

Call 1

Inputs
(acosh.f64 x)

Outputs
(acosh.f64 x)

derivations102.0ms (2.8%)

Memory

12.1MiB live, 103.8MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	31
0	12	18
1	53	18
0	400	17

Stop Event

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

Compiler

Compiled 2 to 2 computations (0% saved)

preprocess85.0ms (2.3%)

Memory: 8.7MiB live, 52.8MiB allocated; 10ms collecting garbage
Compiler: Compiled 46 to 36 computations (21.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.4s (37.5%)

explain227.0ms (6.3%)

preprocess228.0ms (6.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify176.0ms (4.9%)

localize25.0ms (0.7%)

series5.0ms (0.1%)

simplify239.0ms (6.6%)

rewrite71.0ms (2%)

eval40.0ms (1.1%)

prune2.0ms (0.1%)

simplify200.0ms (5.5%)

localize34.0ms (0.9%)

series2.0ms (0.1%)

simplify232.0ms (6.4%)

rewrite62.0ms (1.7%)

eval4.0ms (0.1%)

prune1.0ms (0%)

simplify137.0ms (3.8%)

localize25.0ms (0.7%)

series2.0ms (0%)

simplify280.0ms (7.7%)

rewrite43.0ms (1.2%)

eval4.0ms (0.1%)

prune5.0ms (0.1%)

regimes6.0ms (0.2%)

simplify21.0ms (0.6%)

derivations102.0ms (2.8%)

preprocess85.0ms (2.3%)

end0.0ms (0%)

Profiling