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)

sample551.0ms (37.4%)

Results

345.0ms	5527×	body	256	valid
196.0ms	2729×	body	256	infinite

Bogosity

preprocess98.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

2828×	`fma-def`
1928×	`unswap-sqr`
704×	`distribute-lft-neg-in`
690×	`neg-sub0`
674×	`distribute-lft-neg-out`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	21	18
2	61	18
3	119	18
4	185	18
5	338	18
6	632	18
7	1518	18
8	2769	18
9	5938	18
10	7054	18
11	7946	18

Stop Event

1×	node limit

Calls

Call 1

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

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify247.0ms (16.7%)

Algorithm

1×	egg-herbie

Rules

3406×	`sqr-pow`
1566×	`cube-prod`
1330×	`pow-sqr`
852×	`unpow3`
736×	`cube-mult`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	6	7
2	8	7
3	13	7
4	18	7
5	27	7
6	48	7
7	132	7
8	495	7
9	1155	7
10	1242	7
11	1375	7
12	1533	7
13	1766	7
14	2077	7
15	2484	7
16	2965	7
17	3532	7
18	4212	7
19	4483	7
20	4723	7
21	4903	7
22	5033	7
23	5103	7
24	6017	7
25	6984	7
26	7368	7
27	7672	7
28	7880	7
29	7900	7
30	7900	7

Stop Event

1×	node limit

Counts

1 → 3

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 14 to 6 computations (57.1% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1	2	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	3	4

Accurracy

100.0%

Counts

4 → 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)
▶	100.0%	(pow.f64 x 3)
▶	99.9%	(.f64 (.f64 x x) x)

Compiler

Compiled 20 to 12 computations (40% saved)

localize26.0ms (1.8%)

Local Accuracy

Found 2 expressions with local accuracy:

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

Compiler

Compiled 16 to 7 computations (56.3% saved)

series3.0ms (0.2%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (.f64 x x) x)
1.0ms	x	@	-inf	(pow.f64 x 3)
0.0ms	x	@	-inf	(.f64 (.f64 x x) x)
0.0ms	x	@	inf	(pow.f64 x 3)
0.0ms	x	@	inf	(.f64 (.f64 x x) x)

rewrite56.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

978×	`pow1`
948×	`add-sqr-sqrt`
912×	`add-exp-log`
912×	`log1p-expm1-u`
912×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	146	14
2	1382	14

Stop Event

1×	node limit

Counts

2 → 31

Calls

Call 1

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

Outputs
(-.f64 (+.f64 1 (pow.f64 x 3)) 1)
(pow.f64 x 3)
(pow.f64 (*.f64 x x) 3/2)
(pow.f64 (pow.f64 x 3) 1)
(pow.f64 (pow.f64 (pow.f64 x 3) 3) 1/3)
(pow.f64 (pow.f64 x 3/2) 2)
(sqrt.f64 (pow.f64 x 6))
(log.f64 (exp.f64 (pow.f64 x 3)))
(cbrt.f64 (pow.f64 (pow.f64 x 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(exp.f64 (*.f64 3 (log.f64 x)))
(log1p.f64 (expm1.f64 (pow.f64 x 3)))
(-.f64 (+.f64 1 (pow.f64 x 3)) 1)
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x 3) 1)
(*.f64 1 (pow.f64 x 3))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x x)))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (pow.f64 (cbrt.f64 x) 2) x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x x)))
(*.f64 (pow.f64 x 3/2) (pow.f64 x 3/2))
(*.f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (sqrt.f64 x) 3))
(.f64 (.f64 x (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 (*.f64 x x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 (*.f64 x x) (sqrt.f64 x)) (sqrt.f64 x))
(sqrt.f64 (pow.f64 x 6))
(log.f64 (exp.f64 (pow.f64 x 3)))
(cbrt.f64 (pow.f64 (pow.f64 x 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(exp.f64 (*.f64 3 (log.f64 x)))
(log1p.f64 (expm1.f64 (pow.f64 x 3)))

simplify58.0ms (4%)

Algorithm

1×	egg-herbie

Rules

864×	`associate-r`
854×	`exp-prod`
786×	`associate-+r+`
742×	`cube-prod`
712×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	301
1	132	301
2	383	301
3	2480	301
4	5193	301

Stop Event

1×	node limit

Counts

43 → 24

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 1 (pow.f64 x 3)) 1)
(pow.f64 x 3)
(pow.f64 (*.f64 x x) 3/2)
(pow.f64 (pow.f64 x 3) 1)
(pow.f64 (pow.f64 (pow.f64 x 3) 3) 1/3)
(pow.f64 (pow.f64 x 3/2) 2)
(sqrt.f64 (pow.f64 x 6))
(log.f64 (exp.f64 (pow.f64 x 3)))
(cbrt.f64 (pow.f64 (pow.f64 x 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(exp.f64 (*.f64 3 (log.f64 x)))
(log1p.f64 (expm1.f64 (pow.f64 x 3)))
(-.f64 (+.f64 1 (pow.f64 x 3)) 1)
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x 3) 1)
(*.f64 1 (pow.f64 x 3))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x x)))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (pow.f64 (cbrt.f64 x) 2) x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x x)))
(*.f64 (pow.f64 x 3/2) (pow.f64 x 3/2))
(*.f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (sqrt.f64 x) 3))
(.f64 (.f64 x (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 (*.f64 x x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 (*.f64 x x) (sqrt.f64 x)) (sqrt.f64 x))
(sqrt.f64 (pow.f64 x 6))
(log.f64 (exp.f64 (pow.f64 x 3)))
(cbrt.f64 (pow.f64 (pow.f64 x 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(exp.f64 (*.f64 3 (log.f64 x)))
(log1p.f64 (expm1.f64 (pow.f64 x 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 1 (pow.f64 x 3)) 1)
(pow.f64 x 3)
(pow.f64 x 3)
(pow.f64 (*.f64 x x) 3/2)
(pow.f64 x 3)
(pow.f64 (pow.f64 x 3) 1)
(pow.f64 x 3)
(pow.f64 (pow.f64 (pow.f64 x 3) 3) 1/3)
(pow.f64 x 3)
(pow.f64 (pow.f64 x 3/2) 2)
(pow.f64 x 3)
(sqrt.f64 (pow.f64 x 6))
(pow.f64 x 3)
(log.f64 (exp.f64 (pow.f64 x 3)))
(pow.f64 x 3)
(cbrt.f64 (pow.f64 (pow.f64 x 3) 3))
(pow.f64 x 3)
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(pow.f64 x 3)
(exp.f64 (*.f64 3 (log.f64 x)))
(pow.f64 x 3)
(log1p.f64 (expm1.f64 (pow.f64 x 3)))
(pow.f64 x 3)
(-.f64 (+.f64 1 (pow.f64 x 3)) 1)
(pow.f64 x 3)
(.f64 x (.f64 x x))
(pow.f64 x 3)
(.f64 (.f64 x x) x)
(pow.f64 x 3)
(*.f64 (pow.f64 x 3) 1)
(pow.f64 x 3)
(*.f64 1 (pow.f64 x 3))
(pow.f64 x 3)
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x x)))
(pow.f64 x 3)
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (pow.f64 (cbrt.f64 x) 2) x))
(pow.f64 x 3)
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x x)))
(pow.f64 x 3)
(*.f64 (pow.f64 x 3/2) (pow.f64 x 3/2))
(pow.f64 x 3)
(*.f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (sqrt.f64 x) 3))
(pow.f64 x 3)
(.f64 (.f64 x (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(pow.f64 x 3)
(.f64 (.f64 (*.f64 x x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(pow.f64 x 3)
(.f64 (.f64 (*.f64 x x) (sqrt.f64 x)) (sqrt.f64 x))
(pow.f64 x 3)
(sqrt.f64 (pow.f64 x 6))
(pow.f64 x 3)
(log.f64 (exp.f64 (pow.f64 x 3)))
(pow.f64 x 3)
(cbrt.f64 (pow.f64 (pow.f64 x 3) 3))
(pow.f64 x 3)
(expm1.f64 (log1p.f64 (pow.f64 x 3)))
(pow.f64 x 3)
(exp.f64 (*.f64 3 (log.f64 x)))
(pow.f64 x 3)
(log1p.f64 (expm1.f64 (pow.f64 x 3)))
(pow.f64 x 3)

eval4.0ms (0.3%)

Compiler: Compiled 161 to 98 computations (39.1% saved)

prune4.0ms (0.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	24	2	26

Accurracy

100.0%

Counts

26 → 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)

regimes6.0ms (0.4%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(pow.f64 x 3)

Calls

2 calls:

3.0ms	x
2.0ms	(.f64 (.f64 x x) x)

Results

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

Compiler

Compiled 17 to 9 computations (47.1% saved)

regimes5.0ms (0.3%)

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 14 to 7 computations (50% saved)

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	8	20

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)

soundness329.0ms (22.3%)

Rules

3406×	`sqr-pow`
1566×	`cube-prod`
1330×	`pow-sqr`
852×	`unpow3`
736×	`cube-mult`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	6	7
2	8	7
3	13	7
4	18	7
5	27	7
6	48	7
7	132	7
8	495	7
9	1155	7
10	1242	7
11	1375	7
12	1533	7
13	1766	7
14	2077	7
15	2484	7
16	2965	7
17	3532	7
18	4212	7
19	4483	7
20	4723	7
21	4903	7
22	5033	7
23	5103	7
24	6017	7
25	6984	7
26	7368	7
27	7672	7
28	7880	7
29	7900	7
30	7900	7

Stop Event

1×	node limit

Compiler

Compiled 9 to 5 computations (44.4% saved)

end0.0ms (0%)

preprocess80.0ms (5.4%)

Compiler: Compiled 38 to 22 computations (42.1% saved)

analyze0.0ms (0%)

sample551.0ms (37.4%)

preprocess98.0ms (6.7%)

simplify247.0ms (16.7%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize26.0ms (1.8%)

series3.0ms (0.2%)

rewrite56.0ms (3.8%)

simplify58.0ms (4%)

eval4.0ms (0.3%)

prune4.0ms (0.3%)

regimes6.0ms (0.4%)

regimes5.0ms (0.3%)

simplify4.0ms (0.3%)

soundness329.0ms (22.3%)

end0.0ms (0%)

preprocess80.0ms (5.4%)

Profiling