Metrics for Hyperbolic arc-cosine

analyze88.0ms (4.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-log: 13.0ms (29% of total)

ival-sqrt: 11.0ms (24.5% of total)

ival-mult: 9.0ms (20.1% of total)

ival-sub: 6.0ms (13.4% of total)

ival-add: 5.0ms (11.2% of total)

const: 1.0ms (2.2% of total)

sample1.4s (75.3%)

Results

577.0ms	8256×	256	valid
486.0ms	8411×	256	invalid

Precisions

Click to see histograms. Total time spent on operations: 694.0ms

ival-log: 189.0ms (27.3% of total)

ival-mult: 146.0ms (21.1% of total)

ival-sqrt: 137.0ms (19.8% of total)

ival-sub: 113.0ms (16.3% of total)

ival-add: 88.0ms (12.7% of total)

const: 21.0ms (3% of total)

Bogosity

preprocess259.0ms (13.7%)

Algorithm

1×	egg-herbie

Rules

653×	`distribute-lft-out`
621×	`distribute-rgt-out--`
518×	`unsub-neg`
473×	`sub-neg`
450×	`distribute-rgt-out`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	140
1	48	132
2	83	132
3	179	132
4	416	132
5	923	132
6	1685	132
7	3206	132
8	4236	132
9	4890	132
10	5182	132
11	5490	132
12	5640	132
13	5713	132
14	5924	132
15	6691	132
16	6872	132

Stop Event

1×	node limit

Calls

Call 1

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

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) #s(literal 1 binary64)))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
(neg.f64 (log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) #s(literal 1 binary64))))))
(neg.f64 (log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))
(neg.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)))

explain85.0ms (4.5%)

FPErrors

Click to see full error table

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

Results

46.0ms

512×

256

valid

Compiler

Compiled 80 to 23 computations (71.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-log: 8.0ms (29.2% of total)

ival-sqrt: 8.0ms (29.2% of total)

ival-mult: 4.0ms (14.6% of total)

ival-sub: 3.0ms (11% of total)

ival-add: 3.0ms (11% of total)

const: 1.0ms (3.7% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.8%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 20 to 14 computations (30% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
3×	`+-commutative`
2×	`unsub-neg`
2×	`sub-neg`
2×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	20	36
2	24	36
3	27	36
4	30	36
5	33	36

Stop Event

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

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 10 to 7 computations (30% saved)

preprocess25.0ms (1.3%)

Compiler: Compiled 40 to 28 computations (30% saved)

Hyperbolic arc-cosine

analyze88.0ms (4.7%)

sample1.4s (75.3%)

preprocess259.0ms (13.7%)

explain85.0ms (4.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.4%)

soundness0.0ms (0%)

preprocess25.0ms (1.3%)

end0.0ms (0%)

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