Details

analyze2.2s (24.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
12.5%	87.3%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
23.4%	76.4%	0.2%	11
31.6%	68.2%	0.2%	12
34.5%	64.9%	0.6%	13
40.3%	59.2%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample2.8s (31.3%)

Results

1.9s	8256×	body	128	valid
722.0ms	3158×	body	128	invalid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify141.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

871×	`distribute-rgt-in_binary64`
685×	`div-sub_binary64`
652×	`distribute-lft-in_binary64`
409×	`distribute-neg-frac_binary64`
395×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	58	22
3	109	22
4	223	20
5	437	16
6	876	14
7	2098	14
8	2320	14
9	2451	14
10	3042	14
11	3226	14
12	3327	14
13	4913	14

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.2b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	4.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
✓	0.2b	(.f64 (.f64 z 3) y)
✓	0.2b	(/.f64 y (*.f64 z 3))
✓	6.8b	(/.f64 t (.f64 (.f64 z 3) y))

series83.0ms (0.9%)

Counts

4 → 120

Calls

4 calls:

39.0ms	(/.f64 t (.f64 (.f64 z 3) y))
16.0ms	(.f64 (.f64 z 3) y)
15.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
12.0ms	(/.f64 y (*.f64 z 3))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`

Counts

4 → 114

Calls

4 calls:

9.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
7.0ms	(/.f64 y (*.f64 z 3))
7.0ms	(/.f64 t (.f64 (.f64 z 3) y))
6.0ms	(.f64 (.f64 z 3) y)

simplify203.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-def_binary64`
515×	`associate-*l/_binary64`
392×	`associate-*r/_binary64`
308×	`associate-/l/_binary64`
175×	`exp-prod_binary64`

Counts

234 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2758
1	498	2435
2	1639	2122
3	4282	2122
4	4997	2122
5	4827	2122

prune332.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	164	7	171

Error

0.0b

Counts

171 → 7

Alt Table

Status	Error	Program
	20.2b	(+.f64 (-.f64 x (cbrt.f64 (pow.f64 (.f64 1/3 (/.f64 y z)) 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.2b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	1.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	4.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 1 (*.f64 z 3)) (/.f64 t y)))
	4.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
	4.2b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
	4.2b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 4258 to 2528 computations (40.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
	0.2b	(/.f64 y (*.f64 z 3))
✓	0.2b	(/.f64 t (*.f64 z 3))
✓	4.7b	(/.f64 (/.f64 t (*.f64 z 3)) y)

series50.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

37.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
12.0ms	(/.f64 t (*.f64 z 3))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

9.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
6.0ms	(/.f64 t (*.f64 z 3))

simplify216.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

570×	`times-frac_binary64`
474×	`associate-/l*_binary64`
444×	`associate-/l/_binary64`
414×	`associate-/r*_binary64`
266×	`fma-def_binary64`

Counts

133 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1704
1	295	1560
2	869	1559
3	3386	1559
4	3767	1559
5	4426	1559
6	5033	1559

prune432.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	219	7	226

Error

Counts

226 → 7

Alt Table

Status	Error	Program
	20.2b	(+.f64 (-.f64 x (cbrt.f64 (pow.f64 (.f64 1/3 (/.f64 y z)) 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.2b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
✓	1.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	4.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 (/.f64 1 z) 1) (/.f64 (/.f64 t 3) y)))
▶	4.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
	4.2b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
	4.2b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 5432 to 3155 computations (41.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
✓	0.2b	(.f64 z (.f64 3 y))
	0.2b	(/.f64 y (*.f64 z 3))
✓	6.8b	(/.f64 t (.f64 z (.f64 3 y)))

series43.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

35.0ms	(/.f64 t (.f64 z (.f64 3 y)))
8.0ms	(.f64 z (.f64 3 y))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`cbrt-unprod_binary64`
6×	`prod-exp_binary64`

Counts

2 → 45

Calls

2 calls:

11.0ms	(/.f64 t (.f64 z (.f64 3 y)))
7.0ms	(.f64 z (.f64 3 y))

simplify161.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

896×	`times-frac_binary64`
581×	`associate-/r*_binary64`
497×	`associate-l_binary64`
455×	`associate-/l*_binary64`
340×	`associate-r_binary64`

Counts

105 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1136
1	187	1011
2	728	1010
3	3684	1010
4	4035	1010
5	4588	1010
6	4971	1010
7	4994	1010

prune338.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Error

Counts

178 → 7

Alt Table

Status	Error	Program
▶	1.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 3 y)))
	20.2b	(+.f64 (-.f64 x (cbrt.f64 (pow.f64 (.f64 1/3 (/.f64 y z)) 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.2b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
✓	1.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
✓	4.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
	4.2b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
	4.2b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 4269 to 2524 computations (40.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 3 y)))
	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
	0.2b	(/.f64 y (*.f64 z 3))
✓	4.7b	(/.f64 (/.f64 t z) (*.f64 3 y))

series83.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

50.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 3 y)))
33.0ms	(/.f64 (/.f64 t z) (*.f64 3 y))

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`times-frac_binary64`
39×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
29×	`associate-+l+_binary64`

Counts

2 → 101

Calls

2 calls:

24.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 3 y)))
13.0ms	(/.f64 (/.f64 t z) (*.f64 3 y))

simplify210.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
537×	`fma-def_binary64`
291×	`fma-neg_binary64`
246×	`distribute-rgt-in_binary64`
234×	`distribute-lft-in_binary64`

Counts

185 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	3755
1	644	2921
2	1880	2585
3	4892	2585
4	4914	2585

prune482.0ms (5.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	273	7	280

Error

Counts

280 → 7

Alt Table

Status	Error	Program
✓	1.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t z) (.f64 3 y)))
	20.2b	(+.f64 (-.f64 x (cbrt.f64 (pow.f64 (.f64 1/3 (/.f64 y z)) 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	4.2b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
✓	1.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
✓	4.2b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 z (*.f64 3 y))))
	4.2b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
	4.2b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 7219 to 3807 computations (47.3% saved)

regimes783.0ms (8.8%)

Accuracy

Total 1.6b remaining (98.7%)

Threshold costs 0b (0%)

Counts

73 → 1

Compiler

Compiled 8672 to 6028 computations (30.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	20	34
2	27	34
3	31	34
4	34	34
5	35	34
6	35	34

end206.0ms (2.3%)

Compiler: Compiled 185 to 124 computations (33% saved)

Details

analyze2.2s (24.3%)

sample2.8s (31.3%)

simplify141.0ms (1.6%)

prune7.0ms (0.1%)

localize16.0ms (0.2%)

series83.0ms (0.9%)

rewrite40.0ms (0.5%)

simplify203.0ms (2.3%)

prune332.0ms (3.7%)

localize16.0ms (0.2%)

series50.0ms (0.6%)

rewrite23.0ms (0.3%)

simplify216.0ms (2.4%)

prune432.0ms (4.8%)

localize18.0ms (0.2%)

series43.0ms (0.5%)

rewrite21.0ms (0.2%)

simplify161.0ms (1.8%)

prune338.0ms (3.8%)

localize17.0ms (0.2%)

series83.0ms (0.9%)

rewrite53.0ms (0.6%)

simplify210.0ms (2.3%)

prune482.0ms (5.4%)

regimes783.0ms (8.8%)

simplify6.0ms (0.1%)

end206.0ms (2.3%)

Profiling