Metrics for Hyperbolic arcsine

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze71.0ms (2.1%)

Memory

-9.1MiB live, 123.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
62.5%	62.5%	37.5%	0%	0%	0%	0%	5
68.8%	68.7%	31.2%	0%	0%	0%	0%	6
71.9%	71.8%	28.1%	0%	0%	0%	0%	7
73.4%	73.4%	26.5%	0%	0%	0%	0%	8
74.2%	74.2%	25.8%	0%	0%	0%	0%	9
74.6%	74.6%	25.4%	0%	0%	0%	0%	10
74.8%	74.8%	25.2%	0%	0%	0%	0%	11
74.9%	74.9%	25.1%	0%	0%	0%	0%	12

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.8s (51.9%)

Memory

33.3MiB live, 988.7MiB allocated

Samples

668.0ms	4 398×	1	valid
645.0ms	1 565×	2	valid
123.0ms	2 293×	0	valid

Precisions

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

ival-log: 636.0ms (52.1% of total)

ival-hypot: 362.0ms (29.7% of total)

adjust: 130.0ms (10.6% of total)

ival-add: 76.0ms (6.2% of total)

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

exact: 5.0ms (0.4% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

explain177.0ms (5.3%)

Memory

2.8MiB live, 91.8MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	sensitivity	120	0
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	66	0
↳	`(*.f64 x x)`	overflow	66
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	66
`+.f64`	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`	cancellation	64	0

Confusion

	Predicted +	Predicted -
+	216	0
-	0	40

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	216	0	0
-	0	0	40

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	40
1	182
2	34

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

50.0ms	278×	1	valid
39.0ms	88×	2	valid
10.0ms	146×	0	valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-log: 37.0ms (46.2% of total)

ival-hypot: 20.0ms (25% of total)

adjust: 8.0ms (10% of total)

ival-add: 7.0ms (8.7% of total)

ival-mult: 7.0ms (8.7% of total)

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

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

exact: 0.0ms (0% of total)

preprocess17.0ms (0.5%)

Memory

-39.3MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	22	21
2	47	21
3	58	21
4	73	21
0	7	9
0	12	9
1	20	9
2	39	9
3	66	9
4	81	9
0	81	8

Stop Event

1×	iter limit
1×	saturated
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: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	19.5%	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify4.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
cost-diff	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	20	33
2	39	33
3	66	33
4	81	33
0	81	29

Stop Event

1×	iter limit
1×	saturated
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)

localize59.0ms (1.8%)

Memory

13.0MiB live, 42.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	15.145670469026992	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	15.420460032954175	(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))
accuracy	28.03151539346399	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Samples

25.0ms	139×	1	valid
22.0ms	44×	2	valid
5.0ms	73×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-log: 19.0ms (44.2% of total)

ival-hypot: 11.0ms (25.6% of total)

ival-add: 7.0ms (16.3% of total)

adjust: 4.0ms (9.3% of total)

ival-mult: 2.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated

Counts

4 → 37

Calls

Call 1

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

Outputs
1
(+ 1 (pow x 2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+ (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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

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

1.0ms

-inf

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

simplify152.0ms (4.5%)

Memory

16.3MiB live, 137.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	448
1	384	440
2	1149	432
3	4065	428
0	8153	409

Stop Event

1×	iter limit
1×	node limit

Counts

37 → 36

Calls

Call 1

Inputs
1
(+ 1 (pow x 2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+ (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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))

Outputs
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/112 binary64) (-.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) #s(literal 1/6 binary64))) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(+ (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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 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 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(-.f64 (-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x)
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(.f64 (-.f64 (-.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x)
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) x x)
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x x)
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(fma.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) 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 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (/.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))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (+.f64 (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (-.f64 (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(.f64 x (-.f64 #s(literal -1 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(.f64 x (-.f64 #s(literal -1 binary64) (-.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))))))

rewrite149.0ms (4.4%)

Memory

-29.1MiB live, 134.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
0	12	15
1	51	15
2	360	13
3	4421	13
0	8160	12

Stop Event

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

Counts

4 → 349

Calls

Call 1

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

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

eval53.0ms (1.6%)

Memory: 10.6MiB live, 40.4MiB allocated
Compiler: Compiled 8 369 to 1 703 computations (79.7% saved)

prune5.0ms (0.1%)

Memory

13.9MiB live, 13.9MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	381	3	384
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	382	3	385

Accuracy

100.0%

Counts

385 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	25.5%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
▶	28.2%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	99.8%	(asinh.f64 x)

Compiler

Compiled 28 to 22 computations (21.4% saved)

simplify5.0ms (0.2%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	63
0	20	63
1	31	63
2	50	63
3	77	63
4	100	63
5	109	63
6	115	63
0	115	59

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize106.0ms (3.1%)

Memory

-21.5MiB live, 15.4MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal -1/2 binary64) x)
accuracy	28.03151539346399	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
accuracy	46.88152338993326	#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	28.03151539346399	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	44.886604497136844	#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
accuracy	0.10546875	(asinh.f64 x)

Samples

66.0ms	44×	2	valid
26.0ms	139×	1	valid
7.0ms	73×	0	valid

Compiler

Compiled 49 to 12 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-mult: 38.0ms (49.4% of total)

ival-log: 18.0ms (23.4% of total)

ival-hypot: 10.0ms (13% of total)

adjust: 3.0ms (3.9% of total)

ival-div: 2.0ms (2.6% of total)

ival-asinh: 2.0ms (2.6% of total)

ival-add: 2.0ms (2.6% 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

1.8MiB live, 1.8MiB allocated

Counts

7 → 24

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(* 2 x)
(/ -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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+ (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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x))
1.0ms	x	@	0	((asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x))
1.0ms	x	@	inf	((asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x))

Time

Variable

Point

Expression

1.0ms

-inf

((asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x))

1.0ms

((asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x))

1.0ms

inf

((asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x))

simplify172.0ms (5.1%)

Memory

-0.5MiB live, 29.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	301
1	303	293
2	863	286
3	3083	278
0	8422	267

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 23

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(* 2 x)
(/ -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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+ (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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))

Outputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 3/40 binary64) x) x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/112 binary64)) #s(literal 1/6 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 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 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(-.f64 (-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))))
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(fma.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) x (fma.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x (/.f64 #s(literal 1/2 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)) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (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))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (-.f64 (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))))
(* -1 (/ (- 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 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) x) (-.f64 (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))))

rewrite169.0ms (5%)

Memory

19.9MiB live, 49.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	58
0	20	46
1	63	46
2	381	38
3	4641	38
0	8245	38

Stop Event

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

Counts

7 → 55

Calls

Call 1

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

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

eval9.0ms (0.3%)

Memory: 6.2MiB live, 6.2MiB allocated
Compiler: Compiled 1 807 to 381 computations (78.9% saved)

prune22.0ms (0.7%)

Memory

-27.4MiB live, 3.6MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	78	3	81

Accuracy

100.0%

Counts

81 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	25.5%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
▶	28.2%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
✓	99.8%	(asinh.f64 x)

Compiler

Compiled 28 to 21 computations (25% saved)

simplify5.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated

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	21	29
2	42	29
3	69	29
4	90	29
5	95	29
6	98	29
0	98	27

Stop Event

1×	iter limit
1×	saturated
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

localize50.0ms (1.5%)

Memory

11.2MiB live, 11.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x x)
accuracy	28.03151539346399	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
accuracy	44.886604497136844	#s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x))

Samples

21.0ms	139×	1	valid
18.0ms	44×	2	valid
4.0ms	73×	0	valid

Compiler

Compiled 23 to 8 computations (65.2% saved)

Precisions

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

ival-log: 18.0ms (49.8% of total)

ival-hypot: 10.0ms (27.7% of total)

adjust: 4.0ms (11.1% of total)

ival-add: 3.0ms (8.3% 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

1.0MiB live, 1.0MiB 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
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(* 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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+ (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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

0.0ms

-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))

simplify137.0ms (4.1%)

Memory

-5.4MiB live, 29.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	301
1	303	293
2	863	286
3	3086	278
0	8433	267

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 23

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(* 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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+ (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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))

Outputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 3/40 binary64) x) x (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/112 binary64)) #s(literal 1/6 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 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 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(-.f64 (-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))))
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(fma.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) x (fma.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x (/.f64 #s(literal 1/2 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)) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (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))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (-.f64 (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 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 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) x) (-.f64 (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))))

rewrite48.0ms (1.4%)

Memory

3.6MiB live, 3.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
0	11	22
1	57	22
0	444	22

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
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 #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 (/.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)

eval3.0ms (0.1%)

Memory: 2.6MiB live, 2.6MiB allocated
Compiler: Compiled 668 to 159 computations (76.2% saved)

prune2.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	33	3	36

Accuracy

100.0%

Counts

36 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	25.5%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
✓	28.2%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
✓	99.8%	(asinh.f64 x)

Compiler

Compiled 78 to 45 computations (42.3% saved)

regimes5.0ms (0.2%)

Memory

4.6MiB live, 4.6MiB allocated

Accuracy

Total -63.9b remaining (-60581.5%)

Threshold costs -63.9b (-60581.5%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(asinh.f64 x)

Calls

3 calls:

2.0ms	x
1.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
1.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.8%	1	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
99.8%	1	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.8%	1	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify58.0ms (1.7%)

Memory

-25.7MiB live, 5.7MiB 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
(asinh.f64 x)

Outputs
(asinh.f64 x)

soundness114.0ms (3.4%)

Memory

1.4MiB live, 1.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
0	12	15
1	51	15
2	360	13
3	4421	13
0	8160	12

Stop Event

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

Compiler

Compiled 13 to 10 computations (23.1% saved)

preprocess22.0ms (0.7%)

Memory: 14.0MiB live, 14.0MiB allocated
Compiler: Compiled 70 to 46 computations (34.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze71.0ms (2.1%)

sample1.8s (51.9%)

explain177.0ms (5.3%)

preprocess17.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize59.0ms (1.8%)

series4.0ms (0.1%)

simplify152.0ms (4.5%)

rewrite149.0ms (4.4%)

eval53.0ms (1.6%)

prune5.0ms (0.1%)

simplify5.0ms (0.2%)

localize106.0ms (3.1%)

series3.0ms (0.1%)

simplify172.0ms (5.1%)

rewrite169.0ms (5%)

eval9.0ms (0.3%)

prune22.0ms (0.7%)

simplify5.0ms (0.1%)

localize50.0ms (1.5%)

series2.0ms (0.1%)

simplify137.0ms (4.1%)

rewrite48.0ms (1.4%)

eval3.0ms (0.1%)

prune2.0ms (0.1%)

regimes5.0ms (0.2%)

simplify58.0ms (1.7%)

soundness114.0ms (3.4%)

preprocess22.0ms (0.7%)

end0.0ms (0%)

Profiling