Metrics for Hyperbolic arc-cosine

analyze103.0ms (2.8%)

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
33.3%	25%	50%	0%	0%	25%	0%	4
40%	25%	37.5%	0%	0%	37.5%	0%	5
44.4%	25%	31.2%	0%	0%	43.7%	0%	6
47.1%	25%	28.1%	0%	0%	46.9%	0%	7
48.5%	25%	26.5%	0%	0%	48.4%	0%	8
49.2%	25%	25.8%	0%	0%	49.2%	0%	9
49.6%	25%	25.4%	0%	0%	49.6%	0%	10
49.8%	25%	25.2%	0%	0%	49.8%	0%	11
49.9%	25%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.8s (77.3%)

Results

1.2s	8256×	body	256	valid
916.0ms	4146×	body	2048	invalid
392.0ms	2100×	body	1024	invalid
213.0ms	1039×	body	512	invalid
73.0ms	1015×	body	256	invalid
3.0ms	14×	body	4096	invalid

Bogosity

preprocess257.0ms (7%)

Algorithm

1×	egg-herbie

Rules

1460×	`fma-def`
1306×	`distribute-lft-out`
1242×	`distribute-rgt-out--`
1038×	`unsub-neg`
938×	`sub-neg`

Problems

144×	No Errors
112×	`(sqrt.f64 (-.f64 (*.f64 x x) 1))`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	100
1	42	96
2	75	96
3	170	96
4	402	96
5	916	96
6	1692	96
7	3215	96
8	4263	96
9	4910	96
10	5201	96
11	5509	96
12	5657	96
13	5730	96
14	5941	96
15	6708	96
16	6889	96

Stop Event

1×	node limit

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 1))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x -1))))
(log.f64 (-.f64 (sqrt.f64 (fma.f64 x x -1)) x))

Compiler

Compiled 45 to 25 computations (44.4% saved)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	57.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

localize46.0ms (1.3%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	59.2%	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 35 to 18 computations (48.6% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0ms	x	@	inf	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0ms	x	@	-inf	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite94.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`unpow-prod-down`
396×	`log1p-expm1-u`
396×	`expm1-log1p-u`
390×	`log-prod`
382×	`prod-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	106	19
2	1231	19

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (*.f64 x x) 1))

Outputs
(+.f64 0 (sqrt.f64 (fma.f64 x x -1)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) 2))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))
(-.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)
(*.f64 1 (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (pow.f64 (fma.f64 x x -1) 1/6))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/6) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 2) (pow.f64 (pow.f64 (fma.f64 x x -1) 5/6) 1/3))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 5/6)))
(.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (.f64 (+.f64 x -1) (sqrt.f64 (fma.f64 x x -1))) 1/3))
(.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (.f64 (+.f64 x -1) (sqrt.f64 (fma.f64 x x -1)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 4)) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 (+.f64 x 1)))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)) (pow.f64 (pow.f64 (fma.f64 x x -1) 3/4) 1/2))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (pow.f64 (/.f64 1 (fma.f64 x x 1)) 1/2))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (pow.f64 (/.f64 1 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))) 1/2))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 3/4) 1/2) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 5/6) 1/2) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3))
(*.f64 (pow.f64 1 1/3) (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 4) 1/3) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 5/4) 1/3) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x -1) 5/4)) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (hypot.f64 1 x))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (hypot.f64 (pow.f64 x 2) (hypot.f64 1 x)))
(/.f64 (cbrt.f64 (*.f64 (+.f64 (pow.f64 x 6) -1) (sqrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (cbrt.f64 (*.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x 1)))
(pow.f64 (fma.f64 x x -1) 1/2)
(pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(pow.f64 (cbrt.f64 (fma.f64 x x -1)) 3/2)
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/6) 3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 2) 1/4)
(pow.f64 (pow.f64 (fma.f64 x x -1) 3) 1/6)
(pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 1/2) (log.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))) (sqrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))
(fabs.f64 (sqrt.f64 (fma.f64 x x -1)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (fma.f64 x x -1))) 1/3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x -1) 1/4)) 2))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))

simplify70.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

800×	`associate-r`
716×	`associate-l`
706×	`fma-def`
480×	`distribute-lft-out`
466×	`log-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2268
1	425	2250
2	1074	2218
3	4757	2218

Stop Event

1×	node limit

Counts

63 → 104

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x))))
(-.f64 x (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 -1 x) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (.f64 -1 x) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))))
(+.f64 0 (sqrt.f64 (fma.f64 x x -1)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) 2))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))
(-.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)
(*.f64 1 (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (pow.f64 (fma.f64 x x -1) 1/6))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/6) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 2) (pow.f64 (pow.f64 (fma.f64 x x -1) 5/6) 1/3))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 5/6)))
(.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (.f64 (+.f64 x -1) (sqrt.f64 (fma.f64 x x -1))) 1/3))
(.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (.f64 (+.f64 x -1) (sqrt.f64 (fma.f64 x x -1)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 4)) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 (+.f64 x 1)))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)) (pow.f64 (pow.f64 (fma.f64 x x -1) 3/4) 1/2))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (pow.f64 (/.f64 1 (fma.f64 x x 1)) 1/2))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (pow.f64 (/.f64 1 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))) 1/2))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 3/4) 1/2) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 5/6) 1/2) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3))
(*.f64 (pow.f64 1 1/3) (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 4) 1/3) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 5/4) 1/3) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x -1) 5/4)) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (hypot.f64 1 x))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (hypot.f64 (pow.f64 x 2) (hypot.f64 1 x)))
(/.f64 (cbrt.f64 (*.f64 (+.f64 (pow.f64 x 6) -1) (sqrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (cbrt.f64 (*.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x 1)))
(pow.f64 (fma.f64 x x -1) 1/2)
(pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(pow.f64 (cbrt.f64 (fma.f64 x x -1)) 3/2)
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/6) 3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 2) 1/4)
(pow.f64 (pow.f64 (fma.f64 x x -1) 3) 1/6)
(pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 1/2) (log.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))) (sqrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))
(fabs.f64 (sqrt.f64 (fma.f64 x x -1)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (fma.f64 x x -1))) 1/3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x -1) 1/4)) 2))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(fma.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(fma.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (+.f64 (fma.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))) (/.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 6)))))
(+.f64 (sqrt.f64 -1) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (fma.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (*.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 -1) 5)) (pow.f64 x 6)))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (sqrt.f64 -1)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (/.f64 1/2 x))
(+.f64 x (/.f64 -1/2 x))
(-.f64 x (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (-.f64 x (/.f64 1/8 (pow.f64 x 3))) (/.f64 -1/2 x))
(+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (/.f64 -1/2 x) (+.f64 x (/.f64 -1/8 (pow.f64 x 3))))
(-.f64 x (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))))
(-.f64 x (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 5))))
(-.f64 (+.f64 (-.f64 x (/.f64 1/8 (pow.f64 x 3))) (/.f64 -1/2 x)) (/.f64 1/16 (pow.f64 x 5)))
(+.f64 x (+.f64 (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/8 (pow.f64 x 3)) (/.f64 -1/16 (pow.f64 x 5))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(fma.f64 -1 x (/.f64 1/2 x))
(-.f64 (/.f64 1/2 x) x)
(+.f64 (.f64 -1 x) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
(fma.f64 -1 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 1/2 x) x))
(+.f64 (.f64 -1 x) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))))
(fma.f64 -1 x (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 1/2 x) x)))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 1/16 (pow.f64 x 5)) x)))
(+.f64 0 (sqrt.f64 (fma.f64 x x -1)))
(sqrt.f64 (fma.f64 x x -1))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) 2))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))
(sqrt.f64 (fma.f64 x x -1))
(-.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 1 (sqrt.f64 (fma.f64 x x -1)))
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (pow.f64 (fma.f64 x x -1) 1/6))
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/6) (cbrt.f64 (fma.f64 x x -1)))
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 2) (pow.f64 (pow.f64 (fma.f64 x x -1) 5/6) 1/3))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 5/6)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 5/6)))
(.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (.f64 (+.f64 x -1) (sqrt.f64 (fma.f64 x x -1))) 1/3))
(.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (.f64 (sqrt.f64 (fma.f64 x x -1)) (+.f64 -1 x))))
(.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (.f64 (+.f64 x -1) (sqrt.f64 (fma.f64 x x -1)))))
(.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (.f64 (sqrt.f64 (fma.f64 x x -1)) (+.f64 -1 x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 4)) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 4)))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
(*.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 -1 x)))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 (+.f64 x 1)))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
(*.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 -1 x)))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)) (pow.f64 (pow.f64 (fma.f64 x x -1) 3/4) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 3/4)))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/8) (pow.f64 (fma.f64 x x -1) 3/8))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (pow.f64 (/.f64 1 (fma.f64 x x 1)) 1/2))
(*.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 4))) (sqrt.f64 (/.f64 1 (fma.f64 x x 1))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (pow.f64 (/.f64 1 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))) 1/2))
(*.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 6))) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 x 4) (fma.f64 x x 1)))))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 3/4) 1/2) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 3/4)))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/8) (pow.f64 (fma.f64 x x -1) 3/8))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 5/6) 1/2) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 5/6)) (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/12) (pow.f64 (fma.f64 x x -1) 5/12))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3))
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 1 1/3) (sqrt.f64 (fma.f64 x x -1)))
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 4) 1/3) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 4)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x -1) 5/4) 1/3) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x -1) 5/4)) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x -1) 5/4)) (cbrt.f64 (pow.f64 (fma.f64 x x -1) 1/4)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (hypot.f64 1 x))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 4))) (hypot.f64 1 x))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (hypot.f64 (pow.f64 x 2) (hypot.f64 1 x)))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 6))) (hypot.f64 (pow.f64 x 2) (hypot.f64 1 x)))
(/.f64 (cbrt.f64 (*.f64 (+.f64 (pow.f64 x 6) -1) (sqrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (cbrt.f64 (*.f64 (sqrt.f64 (fma.f64 x x -1)) (+.f64 -1 (pow.f64 x 6)))) (cbrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (cbrt.f64 (*.f64 (+.f64 (pow.f64 x 4) -1) (sqrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x 1)))
(/.f64 (cbrt.f64 (*.f64 (sqrt.f64 (fma.f64 x x -1)) (+.f64 -1 (pow.f64 x 4)))) (cbrt.f64 (fma.f64 x x 1)))
(pow.f64 (fma.f64 x x -1) 1/2)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (cbrt.f64 (fma.f64 x x -1)) 3/2)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/6) 3)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (fma.f64 x x -1) 2) 1/4)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (fma.f64 x x -1) 3) 1/6)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 1/2) (log.f64 (fma.f64 x x -1)))
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))) (sqrt.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))
(fabs.f64 (sqrt.f64 (fma.f64 x x -1)))
(sqrt.f64 (fma.f64 x x -1))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))
(sqrt.f64 (fma.f64 x x -1))
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(sqrt.f64 (fma.f64 x x -1))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
(sqrt.f64 (fma.f64 x x -1))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(sqrt.f64 (fma.f64 x x -1))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3))
(sqrt.f64 (fma.f64 x x -1))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (fma.f64 x x -1))) 1/3))
(sqrt.f64 (fma.f64 x x -1))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x -1) 1/4)) 2))
(sqrt.f64 (fma.f64 x x -1))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))
(sqrt.f64 (fma.f64 x x -1))

eval41.0ms (1.1%)

Compiler: Compiled 1688 to 1280 computations (24.2% saved)

prune15.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	3	105

Accuracy

100.0%

Counts

105 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	57.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	99.2%	(log.f64 (+.f64 x x))
▶	99.4%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	57.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	99.2%	(log.f64 (+.f64 x x))

Compiler

Compiled 48 to 32 computations (33.3% saved)

localize53.0ms (1.4%)

Compiler: Compiled 35 to 19 computations (45.7% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	1	1
Total	3	3

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	57.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	99.2%	(log.f64 (+.f64 x x))

Compiler

Compiled 46 to 30 computations (34.8% saved)

regimes13.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

Inputs
(log.f64 (+.f64 x x))
(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))

Calls

3 calls:

5.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
3.0ms	x
3.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
99.4%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 43 to 28 computations (34.9% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(log.f64 (+.f64 x x))

Outputs
(log.f64 (+.f64 x x))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.2%	1	`x`

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
6×	`sub-neg`
4×	`neg-mul-1`
4×	`*-commutative`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	16	49
2	23	49
3	27	49
4	30	49
5	31	49

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
(log.f64 (+.f64 x x))

Outputs
(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
(log.f64 (+.f64 x x))

Compiler

Compiled 14 to 9 computations (35.7% saved)

soundness103.0ms (2.8%)

Rules

800×	`associate-r`
716×	`associate-l`
706×	`fma-def`
480×	`distribute-lft-out`
466×	`log-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2268
1	425	2250
2	1074	2218
3	4757	2218

Stop Event

1×	node limit

Compiler

Compiled 29 to 20 computations (31% saved)

end0.0ms (0%)

preprocess28.0ms (0.8%)

Compiler: Compiled 46 to 30 computations (34.8% saved)

analyze103.0ms (2.8%)

sample2.8s (77.3%)

preprocess257.0ms (7%)

eval0.0ms (0%)

prune1.0ms (0%)

localize46.0ms (1.3%)

series1.0ms (0%)

rewrite94.0ms (2.6%)

simplify70.0ms (1.9%)

eval41.0ms (1.1%)

prune15.0ms (0.4%)

localize53.0ms (1.4%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes13.0ms (0.3%)

regimes3.0ms (0.1%)

simplify3.0ms (0.1%)

soundness103.0ms (2.8%)

end0.0ms (0%)

preprocess28.0ms (0.8%)

Profiling