Metrics for math.cube on real

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.1s (52.5%)

Results

503.0ms	5511×	256	valid
565.0ms	2744×	256	infinite
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 212.0ms

Operation ival-mult, time spent: 204.0ms, 96.0% of total-time

Operation const, time spent: 8.0ms, 4.0% of total-time

Bogosity

preprocess228.0ms (10.8%)

Algorithm

1×	egg-herbie

Rules

1810×	`fma-neg`
1022×	`distribute-lft-neg-in`
968×	`unswap-sqr`
846×	`distribute-rgt-neg-in`
816×	`fma-define`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`(.f64 (.f64 x x) x)`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	92
1	30	44
2	66	44
3	150	44
4	219	44
5	361	44
6	650	44
7	1003	44
8	1511	44
9	3040	44
10	5152	44
11	6372	44
12	7328	44

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)
(.f64 (.f64 x x) x)
(.f64 (.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 x))
(neg.f64 (.f64 (.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 x)))

Outputs
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(pow.f64 x 3)
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(pow.f64 x 3)
(.f64 (.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 x))
(.f64 (neg.f64 x) (.f64 x x))
(pow.f64 (neg.f64 x) 3)
(neg.f64 (.f64 (.f64 (neg.f64 x) (neg.f64 x)) (neg.f64 x)))
(.f64 x (.f64 x x))
(pow.f64 x 3)

Symmetry

(negabs x)

Compiler

Compiled 28 to 11 computations (60.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

Operation ival-mult, time spent: 7.0ms, 97.0% of total-time

Operation const, time spent: 1.0ms, 14.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 x 3)
▶	99.9%	(.f64 (.f64 x x) x)

Compiler

Compiled 10 to 6 computations (40% saved)

localize52.0ms (2.5%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.9%	(.f64 (.f64 x x) x)

Compiler

Compiled 16 to 7 computations (56.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

Operation ival-mult, time spent: 4.0ms, 62.0% of total-time

Operation ival-pow, time spent: 2.0ms, 31.0% of total-time

Operation const, time spent: 1.0ms, 15.0% of total-time

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (.f64 x x) x)
1.0ms	x	@	-inf	(.f64 (.f64 x x) x)
1.0ms	x	@	inf	(.f64 (.f64 x x) x)

rewrite303.0ms (14.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1115×	`log1p-expm1-u`
616×	`associate-r`
446×	`associate-l`
418×	`unpow-prod-down`
252×	`prod-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	66	10
2	623	10
3	6377	10

Stop Event

1×	node limit

Counts

1 → 28

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)

Outputs
(+.f64 (+.f64 (pow.f64 x 3) 1) -1)
(+.f64 0 (pow.f64 x 3))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 2))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 3)))))
(-.f64 (+.f64 (pow.f64 x 3) 1) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 x 3) 1) 3) 1) (+.f64 (*.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 1)) (+.f64 1 (+.f64 (pow.f64 x 3) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 1)) 1) (+.f64 (+.f64 (pow.f64 x 3) 1) 1))
(pow.f64 x 3)
(pow.f64 (pow.f64 x 2) 3/2)
(pow.f64 (pow.f64 x 3) 1)
(pow.f64 (cbrt.f64 x) 9)
(pow.f64 (pow.f64 x 6) 1/2)
(pow.f64 (pow.f64 x 3/2) 2)
(pow.f64 (sqrt.f64 x) 6)
(pow.f64 (pow.f64 x 9) 1/3)
(pow.f64 (E.f64) (*.f64 3 (log.f64 x)))
(pow.f64 (exp.f64 3) (log.f64 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (.f64 3 (log.f64 x))) 2)) (cbrt.f64 (.f64 3 (log.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (.f64 3 (log.f64 x)))) (sqrt.f64 (.f64 3 (log.f64 x))))
(sqrt.f64 (pow.f64 x 6))
(fabs.f64 (pow.f64 x 3))
(log.f64 (exp.f64 (pow.f64 x 3)))
(cbrt.f64 (pow.f64 x 9))
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(log1p.f64 (expm1.f64 (pow.f64 x 3)))
(exp.f64 (*.f64 3 (log.f64 x)))
(exp.f64 (.f64 (.f64 3/2 (log.f64 x)) 2))
(exp.f64 (*.f64 (log.f64 (pow.f64 x 9)) 1/3))

simplify53.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-neg`
740×	`distribute-lft-out`
630×	`associate-+l-`
620×	`*-commutative`
568×	`associate-+r-`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	614
1	199	614
2	560	603
3	2962	599

Stop Event

1×	node limit

Counts

40 → 32

Calls

Call 1

Inputs
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(+.f64 (+.f64 (pow.f64 x 3) 1) -1)
(+.f64 0 (pow.f64 x 3))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 2))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 3)))))
(-.f64 (+.f64 (pow.f64 x 3) 1) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 x 3) 1) 3) 1) (+.f64 (*.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 1)) (+.f64 1 (+.f64 (pow.f64 x 3) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 1)) 1) (+.f64 (+.f64 (pow.f64 x 3) 1) 1))
(pow.f64 x 3)
(pow.f64 (pow.f64 x 2) 3/2)
(pow.f64 (pow.f64 x 3) 1)
(pow.f64 (cbrt.f64 x) 9)
(pow.f64 (pow.f64 x 6) 1/2)
(pow.f64 (pow.f64 x 3/2) 2)
(pow.f64 (sqrt.f64 x) 6)
(pow.f64 (pow.f64 x 9) 1/3)
(pow.f64 (E.f64) (*.f64 3 (log.f64 x)))
(pow.f64 (exp.f64 3) (log.f64 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (.f64 3 (log.f64 x))) 2)) (cbrt.f64 (.f64 3 (log.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (.f64 3 (log.f64 x)))) (sqrt.f64 (.f64 3 (log.f64 x))))
(sqrt.f64 (pow.f64 x 6))
(fabs.f64 (pow.f64 x 3))
(log.f64 (exp.f64 (pow.f64 x 3)))
(cbrt.f64 (pow.f64 x 9))
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(log1p.f64 (expm1.f64 (pow.f64 x 3)))
(exp.f64 (*.f64 3 (log.f64 x)))
(exp.f64 (.f64 (.f64 3/2 (log.f64 x)) 2))
(exp.f64 (*.f64 (log.f64 (pow.f64 x 9)) 1/3))

Outputs
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 x 3)
(+.f64 (+.f64 (pow.f64 x 3) 1) -1)
(pow.f64 x 3)
(+.f64 0 (pow.f64 x 3))
(pow.f64 x 3)
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) 2))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x 3)))))
(pow.f64 x 3)
(-.f64 (+.f64 (pow.f64 x 3) 1) 1)
(pow.f64 x 3)
(/.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 x 3) 1) 3) 1) (+.f64 (*.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 1)) (+.f64 1 (+.f64 (pow.f64 x 3) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 (pow.f64 x 3) 1) 3) -1) (fma.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (pow.f64 x 3) 1) 3)) (fma.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (pow.f64 x 3) 1) 3)) (+.f64 1 (*.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (pow.f64 x 3) 1) 3)) (fma.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 2) 1))
(/.f64 (-.f64 (*.f64 (+.f64 (pow.f64 x 3) 1) (+.f64 (pow.f64 x 3) 1)) 1) (+.f64 (+.f64 (pow.f64 x 3) 1) 1))
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 (pow.f64 x 2) 3/2)
(pow.f64 x 3)
(pow.f64 (pow.f64 x 3) 1)
(pow.f64 x 3)
(pow.f64 (cbrt.f64 x) 9)
(pow.f64 (pow.f64 x 6) 1/2)
(pow.f64 x 3)
(pow.f64 (pow.f64 x 3/2) 2)
(pow.f64 x 3)
(pow.f64 (sqrt.f64 x) 6)
(pow.f64 x 3)
(pow.f64 (pow.f64 x 9) 1/3)
(pow.f64 x 3)
(pow.f64 (E.f64) (*.f64 3 (log.f64 x)))
(pow.f64 (exp.f64 3) (log.f64 x))
(pow.f64 x 3)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (.f64 3 (log.f64 x))) 2)) (cbrt.f64 (.f64 3 (log.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (.f64 3 (log.f64 x)))) (sqrt.f64 (.f64 3 (log.f64 x))))
(sqrt.f64 (pow.f64 x 6))
(pow.f64 x 3)
(fabs.f64 (pow.f64 x 3))
(pow.f64 x 3)
(log.f64 (exp.f64 (pow.f64 x 3)))
(pow.f64 x 3)
(cbrt.f64 (pow.f64 x 9))
(pow.f64 x 3)
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(pow.f64 x 3)
(log1p.f64 (expm1.f64 (pow.f64 x 3)))
(pow.f64 x 3)
(exp.f64 (*.f64 3 (log.f64 x)))
(pow.f64 x 3)
(exp.f64 (.f64 (.f64 3/2 (log.f64 x)) 2))
(pow.f64 x 3)
(exp.f64 (*.f64 (log.f64 (pow.f64 x 9)) 1/3))
(pow.f64 x 3)

eval8.0ms (0.4%)

Compiler: Compiled 314 to 256 computations (18.5% saved)

prune5.0ms (0.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	32	2	34

Accuracy

100.0%

Counts

34 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x 3)
✓	99.9%	(.f64 (.f64 x x) x)

Compiler

Compiled 19 to 11 computations (42.1% saved)

regimes13.0ms (0.6%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)
(pow.f64 x 3)

Outputs
(pow.f64 x 3)

Calls

2 calls:

10.0ms	(.f64 (.f64 x x) x)
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 8 to 4 computations (50% saved)

regimes5.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)

Outputs
(.f64 (.f64 x x) x)

Calls

2 calls:

2.0ms	x
2.0ms	(.f64 (.f64 x x) x)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 8 to 4 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	10	32

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(pow.f64 x 3)
(.f64 (.f64 x x) x)

Outputs
(pow.f64 x 3)
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))

Compiler

Compiled 10 to 6 computations (40% saved)

soundness241.0ms (11.5%)

Rules

1810×	`fma-neg`
1022×	`distribute-lft-neg-in`
968×	`unswap-sqr`
846×	`distribute-rgt-neg-in`
816×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	92
1	30	44
2	66	44
3	150	44
4	219	44
5	361	44
6	650	44
7	1003	44
8	1511	44
9	3040	44
10	5152	44
11	6372	44
12	7328	44

Stop Event

1×	node limit

Compiler

Compiled 9 to 5 computations (44.4% saved)

end0.0ms (0%)

preprocess86.0ms (4.1%)

Remove: (negabs x)
Compiler: Compiled 62 to 40 computations (35.5% saved)

analyze0.0ms (0%)

sample1.1s (52.5%)

preprocess228.0ms (10.8%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize52.0ms (2.5%)

series3.0ms (0.1%)

rewrite303.0ms (14.4%)

simplify53.0ms (2.5%)

eval8.0ms (0.4%)

prune5.0ms (0.2%)

regimes13.0ms (0.6%)

regimes5.0ms (0.2%)

simplify3.0ms (0.1%)

soundness241.0ms (11.5%)

end0.0ms (0%)

preprocess86.0ms (4.1%)

Profiling