Metrics for Hyperbolic arcsine

start0.0ms (0%)

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

analyze63.0ms (1.1%)

Memory

40.7MiB live, 87.7MiB allocated; 4ms collecting garbage

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)

sample2.6s (45.2%)

Memory

21.9MiB live, 3 142.2MiB allocated; 703ms collecting garbage

Samples

1.1s	1 656×	2	valid
1.0s	4 429×	1	valid
136.0ms	2 171×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-log: 1.0s (52.6% of total)

ival-hypot: 531.0ms (27.2% of total)

adjust: 246.0ms (12.6% of total)

ival-add: 132.0ms (6.8% of total)

ival-true: 6.0ms (0.3% of total)

exact: 5.0ms (0.3% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain358.0ms (6.2%)

Memory

13.0MiB live, 490.3MiB allocated; 47ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
132	-	-	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
65	-	-	`(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	132	0
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	65	0
↳	`(*.f64 x x)`	overflow	65
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	65
`+.f64`	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`	cancellation	64	0

Confusion

	Predicted +	Predicted -
+	229	0
-	0	27

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	229	0	0
-	0	0	27

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	27
1	197
2	32

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

180.0ms	274×	1	valid
78.0ms	116×	2	valid
9.0ms	122×	0	valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 182.0ms

ival-log: 95.0ms (52.2% of total)

adjust: 46.0ms (25.3% of total)

ival-hypot: 23.0ms (12.6% of total)

ival-mult: 9.0ms (4.9% of total)

ival-add: 8.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess18.0ms (0.3%)

Memory

-2.6MiB live, 44.5MiB allocated; 2ms collecting garbage

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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	15.2%	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify0.0ms (0%)

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

series5.0ms (0.1%)

Memory

11.3MiB live, 11.3MiB allocated; 0ms collecting garbage

Counts

7 → 37

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
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)))))))
(+ 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)))))
(+ 1 (pow x 2))
(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))))
(* (pow x 2) (+ 1 (/ 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 (/ (- 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
2.0ms	x	@	inf	((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) x (sqrt (+ (* x x) 1)) (+ (* x x) 1) (* x x) 1)
2.0ms	x	@	-inf	((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) x (sqrt (+ (* x x) 1)) (+ (* x x) 1) (* x x) 1)
1.0ms	x	@	0	((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) x (sqrt (+ (* x x) 1)) (+ (* x x) 1) (* x x) 1)

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify246.0ms (4.2%)

Memory

-16.4MiB live, 268.8MiB allocated; 34ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	448
1	384	440
2	1149	432
3	4056	428
0	8148	409

Stop Event

1×	iter limit
1×	node limit

Counts

37 → 36

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)))))))
(+ 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)))))
(+ 1 (pow x 2))
(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))))
(* (pow x 2) (+ 1 (/ 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 (/ (- 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
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
#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 (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))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 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))) (* 1/4 (/ 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)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(+ (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)))) x) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 7 binary64))))
(* -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))))))

rewrite168.0ms (2.9%)

Memory

25.5MiB live, 255.9MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	20
1	51	20
2	360	18
3	4421	18
0	8160	17

Stop Event

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

Counts

7 → 406

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
(asinh.f64 x)
(/.f64 (-.f64 (pow.f64 (+.f64 (log.f64 (-.f64 x (cosh.f64 (asinh.f64 x)))) (asinh.f64 x)) #s(literal 2 binary64)) (pow.f64 (log.f64 (-.f64 x (cosh.f64 (asinh.f64 x)))) #s(literal 2 binary64))) (log.f64 (.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) (-.f64 x (cosh.f64 (asinh.f64 x))))))
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(hypot.f64 (cosh.f64 (asinh.f64 x)) (*.f64 (neg.f64 x) (cosh.f64 (asinh.f64 x))))
(hypot.f64 (cosh.f64 (asinh.f64 x)) (*.f64 (cosh.f64 (asinh.f64 x)) x))
(exp.f64 (.f64 (.f64 (log.f64 (cosh.f64 (asinh.f64 x))) #s(literal 2 binary64)) #s(literal 1 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 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (cosh.f64 (asinh.f64 x)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.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 1/2 binary64)))
(exp.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal 1 binary64)))
(exp.f64 (log1p.f64 (*.f64 x x)))
(+.f64 (cosh.f64 (.f64 (log.f64 (cosh.f64 (asinh.f64 x))) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (cosh.f64 (asinh.f64 x))) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 4 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 4 binary64))) #s(literal 1/2 binary64))))
(+.f64 (cosh.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal 1 binary64))) (sinh.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal 1 binary64))))
(+.f64 (cosh.f64 (log1p.f64 (.f64 x x))) (sinh.f64 (log1p.f64 (.f64 x x))))
(+.f64 (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 x #s(literal 6 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 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 #s(literal 1 binary64) (*.f64 x x))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)

eval139.0ms (2.4%)

Memory: -29.1MiB live, 220.4MiB allocated; 112ms collecting garbage
Compiler: Compiled 10 526 to 2 263 computations (78.5% saved)

prune12.0ms (0.2%)

Memory

-8.5MiB live, 44.8MiB allocated; 5ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	503	4	507
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	504	4	508

Accuracy

100.0%

Counts

508 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	25.3%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
▶	23.7%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	99.9%	(asinh.f64 x)
▶	52.0%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))

Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

series6.0ms (0.1%)

Memory

25.5MiB live, 25.5MiB allocated; 0ms collecting garbage

Counts

15 → 28

Calls

Call 1

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

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))))
(pow x 3)
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)))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* 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 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -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
3.0ms	x	@	-inf	((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3) x 3 -1/6 (asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) 2 (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x) -1/2)
2.0ms	x	@	inf	((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3) x 3 -1/6 (asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) 2 (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x) -1/2)
1.0ms	x	@	0	((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3) x 3 -1/6 (asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) 2 (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x) -1/2)

Time

Variable

Point

Expression

3.0ms

-inf

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3) x 3 -1/6 (asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) 2 (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x) -1/2)

2.0ms

inf

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3) x 3 -1/6 (asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) 2 (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x) -1/2)

1.0ms

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3) x 3 -1/6 (asinh x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) 2 (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (/ -1/2 x) -1/2)

simplify123.0ms (2.1%)

Memory

36.0MiB live, 306.2MiB allocated; 31ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	332
1	320	318
2	909	317
3	3247	309
0	8365	298

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 27

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))))
(pow x 3)
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)))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* 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 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -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)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
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 (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))
(* 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))))
(* -1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(*.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 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 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/6 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) 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 -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 7 binary64)))))

rewrite248.0ms (4.3%)

Memory

-6.4MiB live, 337.6MiB allocated; 87ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	88
0	29	69
1	90	69
2	558	61
3	7268	61
0	8418	61

Stop Event

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

Counts

15 → 276

Calls

Call 1

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

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(.f64 (/.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (.f64 #s(literal 1/1296 binary64) (pow.f64 x #s(literal 12 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) x)))
(.f64 (/.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/46656 binary64) (pow.f64 x #s(literal 18 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) x) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/1296 binary64) (pow.f64 x #s(literal 12 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) x) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) x)))))
(.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))
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(.f64 (neg.f64 x) (.f64 (neg.f64 x) x))
(.f64 (neg.f64 x) (.f64 x x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))
(.f64 (.f64 x x) (neg.f64 x))
(.f64 (.f64 x x) x)
(.f64 x (.f64 (neg.f64 x) x))
(.f64 x (.f64 x x))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(pow.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 x #s(literal 3 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64)))) (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64)))))))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))))
(neg.f64 (pow.f64 x #s(literal 3 binary64)))
(fabs.f64 (pow.f64 x #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(+.f64 (cosh.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64))) (sinh.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 3/2 binary64))) (sinh.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 3/2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 3 binary64))))
(+.f64 (neg.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64)))) (sinh.f64 (neg.f64 (.f64 (log.f64 x) #s(literal 3 binary64)))))
(+.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))
(sinh.f64 (asinh.f64 x))
(neg.f64 (neg.f64 x))
(sqrt.f64 (*.f64 x x))
(-.f64 (.f64 (sinh.f64 (log.f64 (neg.f64 (-.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (cosh.f64 (log.f64 (neg.f64 (fma.f64 x (/.f64 #s(literal -1 binary64) (exp.f64 (asinh.f64 x))) (fma.f64 x x #s(literal 1 binary64))))))) (.f64 (cosh.f64 (log.f64 (neg.f64 (-.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))) (sinh.f64 (log.f64 (neg.f64 (fma.f64 x (/.f64 #s(literal -1 binary64) (exp.f64 (asinh.f64 x))) (fma.f64 x x #s(literal 1 binary64))))))))
(-.f64 (*.f64 #s(literal 0 binary64) (cosh.f64 (asinh.f64 x))) (neg.f64 x))
(-.f64 (.f64 (sinh.f64 (log.f64 #s(literal -1 binary64))) (cosh.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (asinh.f64 x)))) (.f64 (cosh.f64 (log.f64 #s(literal -1 binary64))) (sinh.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (asinh.f64 x)))))
(-.f64 (.f64 (sinh.f64 (log.f64 (-.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (cosh.f64 (log1p.f64 (fma.f64 x x (.f64 x (/.f64 #s(literal -1 binary64) (exp.f64 (asinh.f64 x)))))))) (.f64 (cosh.f64 (log.f64 (-.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sinh.f64 (log1p.f64 (fma.f64 x x (.f64 x (/.f64 #s(literal -1 binary64) (exp.f64 (asinh.f64 x)))))))))
(fabs.f64 (neg.f64 x))
(fabs.f64 x)
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(exp.f64 (log.f64 x))
(+.f64 (cosh.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))) (sinh.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 1 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 1 binary64))))
(+.f64 (cosh.f64 (log.f64 x)) (sinh.f64 (log.f64 x)))
x
#s(literal 3 binary64)
#s(literal -1/6 binary64)
(asinh.f64 x)
(/.f64 (-.f64 (.f64 (log.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (asinh.f64 x)) (-.f64 (log.f64 #s(literal -1 binary64)) (asinh.f64 x)))) (+.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (log.f64 #s(literal -1 binary64)) (asinh.f64 x))))
(/.f64 (-.f64 (.f64 (log.f64 (-.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (-.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (.f64 (log1p.f64 (fma.f64 x x (.f64 x (/.f64 #s(literal -1 binary64) (exp.f64 (asinh.f64 x)))))) (log1p.f64 (fma.f64 x x (.f64 x (/.f64 #s(literal -1 binary64) (exp.f64 (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 (-.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)) (fma.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (asinh.f64 x)) (-.f64 (log.f64 #s(literal -1 binary64)) (asinh.f64 x)) (*.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))) (fma.f64 (log.f64 (-.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (-.f64 (pow.f64 (cosh.f64 (asinh.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (log1p.f64 (fma.f64 x x (.f64 x (/.f64 #s(literal -1 binary64) (exp.f64 (asinh.f64 x)))))) (log1p.f64 (fma.f64 x x (.f64 x (/.f64 #s(literal -1 binary64) (exp.f64 (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))))))))))
(neg.f64 (asinh.f64 (neg.f64 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 x (/.f64 #s(literal -1 binary64) (exp.f64 (asinh.f64 x))) (fma.f64 x x #s(literal 1 binary64))))))
(-.f64 #s(literal 0 binary64) (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 x (/.f64 #s(literal -1 binary64) (exp.f64 (asinh.f64 x))) (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (asinh.f64 (neg.f64 x)) (log.f64 (/.f64 (-.f64 (neg.f64 x) (cosh.f64 (asinh.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 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(fma.f64 #s(literal 1 binary64) x x)
(fma.f64 x #s(literal 1 binary64) x)
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(-.f64 (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)
#s(literal 2 binary64)
(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))
#s(literal -1/2 binary64)

eval46.0ms (0.8%)

Memory: -2.8MiB live, 89.1MiB allocated; 7ms collecting garbage
Compiler: Compiled 9 735 to 1 261 computations (87% saved)

prune17.0ms (0.3%)

Memory

-21.5MiB live, 30.6MiB allocated; 5ms collecting garbage

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	396	7	403
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	398	9	407

Accuracy

100.0%

Counts

407 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	25.3%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
	23.7%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
✓	99.9%	(asinh.f64 x)
	53.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (neg.f64 x) x) x) #s(literal -1/6 binary64) x))
▶	52.0%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))
▶	53.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) x) x) (neg.f64 x) x))
▶	3.9%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x (neg.f64 x)))
▶	53.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x x))
▶	53.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 x x) x))

Compiler

Compiled 263 to 180 computations (31.6% saved)

simplify0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

series7.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

20 → 28

Calls

Call 1

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 x) (* x x)) x) (* 1/6 x) 1/6 x (* x x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) x) (* 1/6 (* x x)) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* x x) x) -1/6) x) (* (* x x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* -1/6 x) x) (neg x)) x) (* (* -1/6 x) x) (* -1/6 x))
2.0ms	x	@	inf	((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 x) (* x x)) x) (* 1/6 x) 1/6 x (* x x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) x) (* 1/6 (* x x)) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* x x) x) -1/6) x) (* (* x x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* -1/6 x) x) (neg x)) x) (* (* -1/6 x) x) (* -1/6 x))
2.0ms	x	@	0	((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 x) (* x x)) x) (* 1/6 x) 1/6 x (* x x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) x) (* 1/6 (* x x)) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* x x) x) -1/6) x) (* (* x x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* -1/6 x) x) (neg x)) x) (* (* -1/6 x) x) (* -1/6 x))

Time

Variable

Point

Expression

2.0ms

-inf

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 x) (* x x)) x) (* 1/6 x) 1/6 x (* x x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) x) (* 1/6 (* x x)) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* x x) x) -1/6) x) (* (* x x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* -1/6 x) x) (neg x)) x) (* (* -1/6 x) x) (* -1/6 x))

2.0ms

inf

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 x) (* x x)) x) (* 1/6 x) 1/6 x (* x x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) x) (* 1/6 (* x x)) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* x x) x) -1/6) x) (* (* x x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* -1/6 x) x) (neg x)) x) (* (* -1/6 x) x) (* -1/6 x))

2.0ms

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 x) (* x x)) x) (* 1/6 x) 1/6 x (* x x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) x) (* 1/6 (* x x)) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* x x) x) -1/6) x) (* (* x x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* -1/6 x) x) (neg x)) x) (* (* -1/6 x) x) (* -1/6 x))

simplify116.0ms (2%)

Memory

-1.5MiB live, 86.0MiB allocated; 16ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	275
1	206	253
2	555	253
3	1999	247
0	8789	237

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 27

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))))
(* x (+ 1 (* 1/6 (pow x 2))))
(* 1/6 x)
(pow x 2)
(* 1/6 (pow x 2))
(pow x 3)
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* -1/6 (pow x 2))
(* -1/6 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)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (/ 1 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- 1/6 (/ 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 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))

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 (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)
(* x (+ 1 (* 1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (* 1/6 (pow x 2)) 1))
(.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(* -1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 #s(literal -1/6 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))))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (/ 1 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) x)
(* -1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 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 (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 #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)))) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))

rewrite169.0ms (2.9%)

Memory

9.0MiB live, 202.4MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	163
0	42	112
1	158	112
2	1072	102
0	9104	102

Stop Event

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

Counts

20 → 637

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 x x) x))
(fma.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 x x) x)
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1/6 binary64)
x
(*.f64 x x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x x))
(fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x x)
(.f64 #s(literal 1/6 binary64) (.f64 x x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x)
(.f64 (.f64 x x) x)
#s(literal -1/6 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x (neg.f64 x)))
(fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x (neg.f64 x))
(neg.f64 x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) x) x) (neg.f64 x) x))
(fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) x) x) (neg.f64 x) x)
(.f64 (.f64 #s(literal -1/6 binary64) x) x)
(*.f64 #s(literal -1/6 binary64) x)

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(.f64 (/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/1296 binary64) (pow.f64 x #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 8 binary64)))))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(.f64 (/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/46656 binary64) (pow.f64 x #s(literal 18 binary64)) (pow.f64 (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/1296 binary64) (pow.f64 x #s(literal 12 binary64)) (.f64 (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))))))
(.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (neg.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) x)
(.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64))) (/.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) x))
(.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) x) (/.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) x)
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)))
(/.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64))) x)
(/.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x x)) x) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) x) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) x) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(/.f64 (.f64 x (-.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))) (.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))))) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (fma.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))))) (.f64 (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)) (.f64 (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x) (.f64 x x))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)))
(/.f64 (fma.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))) (.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/1296 binary64) (pow.f64 x #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 8 binary64))))))
(/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)) (fma.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x))
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eval87.0ms (1.5%)

Memory: 11.2MiB live, 106.0MiB allocated; 10ms collecting garbage
Compiler: Compiled 13 048 to 1 564 computations (88% saved)

prune82.0ms (1.4%)

Memory

-28.5MiB live, 60.1MiB allocated; 14ms collecting garbage

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	574	7	581
Fresh	0	2	2
Picked	3	2	5
Done	0	2	2
Total	577	13	590

Accuracy

100.0%

Counts

590 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	25.3%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
	23.7%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
✓	99.9%	(asinh.f64 x)
▶	26.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x) #s(literal -1/6 binary64) x))
▶	53.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (neg.f64 x) x) x) #s(literal -1/6 binary64) x))
	26.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))) #s(literal -1/6 binary64) x))
✓	52.0%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))
	53.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) x x))
▶	27.0%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x)) x x))
	27.0%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (*.f64 x x) x))
✓	3.9%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x (neg.f64 x)))
▶	53.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) x))
▶	2.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) (neg.f64 x)))

Compiler

Compiled 418 to 277 computations (33.7% saved)

simplify0.0ms (0%)

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

series11.0ms (0.2%)

Memory

15.1MiB live, 15.1MiB allocated; 0ms collecting garbage

Counts

27 → 40

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal 1 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) (neg.f64 x)))
#s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) (neg.f64 x))
(neg.f64 x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (neg.f64 x) x) x) #s(literal -1/6 binary64) x))
(fma.f64 (.f64 (.f64 (neg.f64 x) x) x) #s(literal -1/6 binary64) x)
(.f64 (.f64 (neg.f64 x) x) x)
(*.f64 (neg.f64 x) x)
#s(literal -1/6 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x)) x x))
(fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x)) x x)
(.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x))
(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) x)
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x) #s(literal -1/6 binary64) x))
(fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x) #s(literal -1/6 binary64) x)
(.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x)
(.f64 (.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x)
(*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))
(sqrt.f64 (neg.f64 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))))
(* x (+ 1 (* 1/6 (pow x 2))))
1
(+ 1 (* 1/6 (pow x 2)))
(pow x 2)
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* -1 (pow x 3))
(* -1 (pow x 2))
(* 1/6 (pow x 2))
(sqrt x)
(* x (+ 1 (* -1/6 (* (pow x 2) (pow (sqrt -1) 2)))))
(* (pow x 3) (pow (sqrt -1) 2))
(* (pow x 2) (pow (sqrt -1) 2))
(* x (pow (sqrt -1) 2))
(* (sqrt x) (sqrt -1))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 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)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* -1/6 (* (pow x 3) (pow (sqrt -1) 2)))
(* (pow x 3) (+ (* -1/6 (pow (sqrt -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 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (* 1/6 (pow (sqrt -1) 2)) (/ 1 (pow x 2)))))
(* -1/6 (* (pow x 2) (pow (sqrt -1) 2)))
(* -1 (* (pow x 2) (pow (sqrt -1) 2)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (sqrt -1)))

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

((log (+ x (sqrt (+ (* x x) 1)))) (* (+ (* (* x x) 1/6) 1) x) (+ (* (* x x) 1/6) 1) (* x x) x 1/6 1 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* (neg x) x) x) -1/6) x) (* (* (neg x) x) x) (* (neg x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* (* (sqrt x) (sqrt x)) x)) x) x) (* 1/6 (* (* (sqrt x) (sqrt x)) x)) (* (* (sqrt x) (sqrt x)) x) (* (sqrt x) (sqrt x)) (sqrt x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* (* (sqrt (neg x)) (sqrt (neg x))) x) x) -1/6) x) (* (* (* (sqrt (neg x)) (sqrt (neg x))) x) x) (* (* (sqrt (neg x)) (sqrt (neg x))) x) (* (sqrt (neg x)) (sqrt (neg x))) (sqrt (neg x)))

4.0ms

inf

((log (+ x (sqrt (+ (* x x) 1)))) (* (+ (* (* x x) 1/6) 1) x) (+ (* (* x x) 1/6) 1) (* x x) x 1/6 1 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* (neg x) x) x) -1/6) x) (* (* (neg x) x) x) (* (neg x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* (* (sqrt x) (sqrt x)) x)) x) x) (* 1/6 (* (* (sqrt x) (sqrt x)) x)) (* (* (sqrt x) (sqrt x)) x) (* (sqrt x) (sqrt x)) (sqrt x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* (* (sqrt (neg x)) (sqrt (neg x))) x) x) -1/6) x) (* (* (* (sqrt (neg x)) (sqrt (neg x))) x) x) (* (* (sqrt (neg x)) (sqrt (neg x))) x) (* (sqrt (neg x)) (sqrt (neg x))) (sqrt (neg x)))

3.0ms

((log (+ x (sqrt (+ (* x x) 1)))) (* (+ (* (* x x) 1/6) 1) x) (+ (* (* x x) 1/6) 1) (* x x) x 1/6 1 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* x x)) x) (neg x)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* (neg x) x) x) -1/6) x) (* (* (neg x) x) x) (* (neg x) x) -1/6 (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* 1/6 (* (* (sqrt x) (sqrt x)) x)) x) x) (* 1/6 (* (* (sqrt x) (sqrt x)) x)) (* (* (sqrt x) (sqrt x)) x) (* (sqrt x) (sqrt x)) (sqrt x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (* (* (* (sqrt (neg x)) (sqrt (neg x))) x) x) -1/6) x) (* (* (* (sqrt (neg x)) (sqrt (neg x))) x) x) (* (* (sqrt (neg x)) (sqrt (neg x))) x) (* (sqrt (neg x)) (sqrt (neg x))) (sqrt (neg x)))

simplify154.0ms (2.7%)

Memory

14.3MiB live, 112.2MiB allocated; 40ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	328
1	274	304
2	792	304
0	4126	293

Stop Event

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

Counts

40 → 39

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))))
(* x (+ 1 (* 1/6 (pow x 2))))
1
(+ 1 (* 1/6 (pow x 2)))
(pow x 2)
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* -1 (pow x 3))
(* -1 (pow x 2))
(* 1/6 (pow x 2))
(sqrt x)
(* x (+ 1 (* -1/6 (* (pow x 2) (pow (sqrt -1) 2)))))
(* (pow x 3) (pow (sqrt -1) 2))
(* (pow x 2) (pow (sqrt -1) 2))
(* x (pow (sqrt -1) 2))
(* (sqrt x) (sqrt -1))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 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)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* -1/6 (* (pow x 3) (pow (sqrt -1) 2)))
(* (pow x 3) (+ (* -1/6 (pow (sqrt -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 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (* 1/6 (pow (sqrt -1) 2)) (/ 1 (pow x 2)))))
(* -1/6 (* (pow x 2) (pow (sqrt -1) 2)))
(* -1 (* (pow x 2) (pow (sqrt -1) 2)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (sqrt -1)))

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

rewrite211.0ms (3.6%)

Memory

-0.7MiB live, 134.6MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	240
0	57	143
1	213	119
2	1088	119
0	8434	119

Stop Event

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

Counts

27 → 1 234

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal 1 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) (neg.f64 x)))
#s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) (neg.f64 x))
(neg.f64 x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (neg.f64 x) x) x) #s(literal -1/6 binary64) x))
(fma.f64 (.f64 (.f64 (neg.f64 x) x) x) #s(literal -1/6 binary64) x)
(.f64 (.f64 (neg.f64 x) x) x)
(*.f64 (neg.f64 x) x)
#s(literal -1/6 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x)) x x))
(fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x)) x x)
(.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x))
(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) x)
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x) #s(literal -1/6 binary64) x))
(fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x) #s(literal -1/6 binary64) x)
(.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x)
(.f64 (.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x)
(*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))
(sqrt.f64 (neg.f64 x))

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) x) (-.f64 (.f64 #s(literal 1/1296 binary64) (pow.f64 x #s(literal 8 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (-.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1/6 binary64) (*.f64 x x))) #s(literal 1 binary64)))
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(*.f64 x #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1 binary64))
(neg.f64 x)
(sqrt.f64 (*.f64 x x))
(fabs.f64 x)
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(exp.f64 (log.f64 x))
(+.f64 (cosh.f64 (log.f64 x)) (sinh.f64 (log.f64 x)))
x
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))

eval149.0ms (2.6%)

Memory: -10.9MiB live, 132.9MiB allocated; 24ms collecting garbage
Compiler: Compiled 25 450 to 3 250 computations (87.2% saved)

prune39.0ms (0.7%)

Memory

-0.6MiB live, 46.2MiB allocated; 2ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	881	1	882
Fresh	3	1	4
Picked	5	0	5
Done	1	3	4
Total	890	5	895

Accuracy

100.0%

Counts

895 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	25.3%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
	23.7%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (+.f64 x x)))
✓	99.9%	(asinh.f64 x)
✓	52.0%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))
	54.2%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) x))

Compiler

Compiled 418 to 131 computations (68.7% saved)

regimes15.0ms (0.3%)

Memory

19.8MiB live, 19.8MiB allocated; 0ms collecting garbage

Counts

20 → 1

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) (neg.f64 x)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 x x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) x x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x (neg.f64 x)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) x) x) (neg.f64 x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (neg.f64 x) x) x) #s(literal -1/6 binary64) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (*.f64 x x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x)) x x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))) #s(literal -1/6 binary64) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x) #s(literal -1/6 binary64) x))
(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)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 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:

5.0ms	x
4.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
4.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.9%	1	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
99.9%	1	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.9%	1	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes17.0ms (0.3%)

Memory

-42.9MiB live, 15.1MiB allocated; 3ms collecting garbage

Accuracy

Total -34.7b remaining (-118.5%)

Threshold costs -34.7b (-118.5%)

Counts

14 → 1

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) (neg.f64 x)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 x x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) x x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) x (neg.f64 x)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) x) x) (neg.f64 x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (neg.f64 x) x) x) #s(literal -1/6 binary64) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (*.f64 x x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) x)) x x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))) #s(literal -1/6 binary64) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))) x) x) #s(literal -1/6 binary64) x))

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) x))

Calls

3 calls:

9.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
4.0ms	x
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
54.2%	1	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
54.2%	1	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
54.2%	1	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify29.0ms (0.5%)

Memory

25.9MiB live, 25.9MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	29	24
2	77	22
3	235	22
4	449	22
5	511	22
6	523	22
7	550	21
8	706	21
9	903	21
10	935	21
11	935	21
12	1019	21
13	1135	21
14	1135	21

Stop Event

1×

saturated

Calls

Call 1

Inputs
(asinh.f64 x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) x))

Outputs
(asinh.f64 x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) #s(approx (+ (* (* 1/6 (* x x)) x) (neg x)) x))

derivations616.0ms (10.6%)

Memory

5.4MiB live, 385.6MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	20
1	51	20
2	360	18
3	4421	18
0	8160	17
0	78	275
1	206	253
2	555	253
3	1999	247
0	8789	237
0	125	448
1	384	440
2	1149	432
3	4056	428
0	8148	409
0	36	240
0	57	143
1	213	119
2	1088	119
0	8434	119
0	21	88
0	29	69
1	90	69
2	558	61
3	7268	61
0	8418	61

Stop Event

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

Compiler

Compiled 24 to 15 computations (37.5% saved)

preprocess27.0ms (0.5%)

Memory: 7.6MiB live, 53.7MiB allocated; 3ms collecting garbage
Compiler: Compiled 114 to 72 computations (36.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze63.0ms (1.1%)

sample2.6s (45.2%)

explain358.0ms (6.2%)

preprocess18.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

series5.0ms (0.1%)

simplify246.0ms (4.2%)

rewrite168.0ms (2.9%)

eval139.0ms (2.4%)

prune12.0ms (0.2%)

simplify0.0ms (0%)

series6.0ms (0.1%)

simplify123.0ms (2.1%)

rewrite248.0ms (4.3%)

eval46.0ms (0.8%)

prune17.0ms (0.3%)

simplify0.0ms (0%)

series7.0ms (0.1%)

simplify116.0ms (2%)

rewrite169.0ms (2.9%)

eval87.0ms (1.5%)

prune82.0ms (1.4%)

simplify0.0ms (0%)

series11.0ms (0.2%)

simplify154.0ms (2.7%)

rewrite211.0ms (3.6%)

eval149.0ms (2.6%)

prune39.0ms (0.7%)

regimes15.0ms (0.3%)

regimes17.0ms (0.3%)

simplify29.0ms (0.5%)

derivations616.0ms (10.6%)

preprocess27.0ms (0.5%)

end0.0ms (0%)

Profiling