Metrics for Falkner and Boettcher, Appendix B, 1

analyze422.0ms (8.1%)

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
0%	0%	100%	0%	0%	0%	0%	4
0%	0%	100%	0%	0%	0%	0%	5
0%	0%	100%	0%	0%	0%	0%	6
0%	0%	100%	0%	0%	0%	0%	7
0%	0%	100%	0%	0%	0%	0%	8
0%	0%	100%	0%	0%	0%	0%	9
0%	0%	100%	0%	0%	0%	0%	10
0%	0%	100%	0%	0%	0%	0%	11
0%	0%	100%	0%	0%	0%	0%	12

Compiler

Compiled 16 to 10 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-mult: 72.0ms (30.8% of total)

ival-acos: 68.0ms (29.1% of total)

ival-sub: 47.0ms (20.1% of total)

ival-div: 41.0ms (17.6% of total)

const: 6.0ms (2.6% of total)

sample4.3s (82.8%)

Results

1.7s	4108×	2048	valid
973.0ms	2093×	1024	valid
621.0ms	8463×	256	invalid
225.0ms	1006×	512	valid
89.0ms	1047×	256	valid
6.0ms	2×	4096	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

ival-acos: 1.2s (39.1% of total)

ival-mult: 1.0s (34.5% of total)

ival-sub: 393.0ms (13.4% of total)

ival-div: 333.0ms (11.3% of total)

const: 51.0ms (1.7% of total)

Bogosity

preprocess147.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-neg`
504×	`sub-neg`
432×	`fma-define`
359×	`unsub-neg`
342×	`distribute-lft-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	200
1	69	200
2	188	184
3	652	184
4	2521	184
5	5095	184
6	6375	184
7	7330	184

Stop Event

1×	node limit

Calls

Call 1

Inputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 (neg.f64 v) (neg.f64 v)))) (-.f64 (*.f64 (neg.f64 v) (neg.f64 v)) #s(literal 1 binary64))))
(neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 (neg.f64 v) (neg.f64 v)))) (-.f64 (*.f64 (neg.f64 v) (neg.f64 v)) #s(literal 1 binary64)))))

Outputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -5 binary64) (.f64 v v))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5 binary64))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -5 binary64) (.f64 v v))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5 binary64))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 (neg.f64 v) (neg.f64 v)))) (-.f64 (*.f64 (neg.f64 v) (neg.f64 v)) #s(literal 1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -5 binary64) (.f64 v v))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5 binary64))) (fma.f64 v v #s(literal -1 binary64))))
(acos.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (fma.f64 v v #s(literal -1 binary64))))
(neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 (neg.f64 v) (neg.f64 v)))) (-.f64 (*.f64 (neg.f64 v) (neg.f64 v)) #s(literal 1 binary64)))))
(neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -5 binary64) (.f64 v v))) (fma.f64 v v #s(literal -1 binary64)))))
(neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5 binary64))) (fma.f64 v v #s(literal -1 binary64)))))
(neg.f64 (acos.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (fma.f64 v v #s(literal -1 binary64)))))

Symmetry

(abs v)

explain304.0ms (5.8%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
7	247	(6.208939175953316e-184)	-	`(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v)))`
0	0	-	-	`(-.f64 (*.f64 v v) #s(literal 1 binary64))`
0	0	-	-	`v`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))`
0	0	-	-	`(*.f64 v v)`
0	0	-	-	`#s(literal 5 binary64)`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 #s(literal 5 binary64) (.f64 v v))`

Results

133.0ms	270×	2048	valid
39.0ms	130×	1024	valid
12.0ms	66×	512	valid
4.0ms	46×	256	valid

Compiler

Compiled 119 to 29 computations (75.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

ival-acos: 45.0ms (39.8% of total)

ival-mult: 29.0ms (25.7% of total)

ival-sub: 22.0ms (19.5% of total)

ival-div: 14.0ms (12.4% of total)

const: 3.0ms (2.7% 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
	99.5%	(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))

Compiler

Compiled 30 to 18 computations (40% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`neg-mul-1`
10×	`unsub-neg`
8×	`*-commutative`
8×	`+-commutative`
7×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	27	53
2	41	53
3	55	53
4	74	53
5	101	53
6	109	53
7	111	53

Stop Event

1×

saturated

Calls

Call 1

Inputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 5 binary64) (.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))

Outputs

(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))

(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 15 to 10 computations (33.3% saved)

preprocess20.0ms (0.4%)

Remove: (abs v)
Compiler: Compiled 120 to 78 computations (35% saved)

Falkner and Boettcher, Appendix B, 1

analyze422.0ms (8.1%)

sample4.3s (82.8%)

preprocess147.0ms (2.8%)

explain304.0ms (5.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

soundness0.0ms (0%)

preprocess20.0ms (0.4%)

end0.0ms (0%)

Profiling