Details

analyze1.1s (13.1%)

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
15.6%	84.2%	0.2%	8
15.6%	84.2%	0.2%	9
20.3%	79.5%	0.2%	10
25.3%	74.5%	0.2%	11
34.2%	65.6%	0.2%	12
37.4%	62%	0.6%	13
41.7%	57.7%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample109.0ms (1.4%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
5.0ms	87×	body	128	invalid

Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify257.0ms (3.2%)

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
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	3.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 95 to 62 computations (34.7% 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 y (*.f64 z 3))
✓	0.2b	(.f64 (.f64 z 3) y)
✓	6.3b	(/.f64 t (.f64 (.f64 z 3) y))

series88.0ms (1.1%)

Counts

4 → 120

Calls

4 calls:

43.0ms	(/.f64 t (.f64 (.f64 z 3) y))
20.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
15.0ms	(/.f64 y (*.f64 z 3))
10.0ms	(.f64 (.f64 z 3) y)

rewrite47.0ms (0.6%)

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:

11.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
9.0ms	(/.f64 t (.f64 (.f64 z 3) y))
8.0ms	(.f64 (.f64 z 3) y)
6.0ms	(/.f64 y (*.f64 z 3))

simplify204.0ms (2.5%)

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

prune330.0ms (4.1%)

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
▶	2.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 3 (*.f64 y z))))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	4.0b	(+.f64 (-.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) z) (/.f64 (cbrt.f64 y) 3))) (/.f64 t (.f64 (.f64 z 3) y)))
	34.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 (sqrt.f64 t) (*.f64 z 3)) (/.f64 (sqrt.f64 t) y)))
	3.7b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	3.9b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 4270 to 2528 computations (40.8% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series60.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

44.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
16.0ms	(/.f64 t (*.f64 z 3))

rewrite33.0ms (0.4%)

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:

14.0ms	(/.f64 t (*.f64 z 3))
11.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)

simplify161.0ms (2%)

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

prune489.0ms (6.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	219	7	226

Error

Counts

226 → 7

Alt Table

Status	Error	Program
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 3 (*.f64 y z))))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	4.0b	(+.f64 (-.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) z) (/.f64 (cbrt.f64 y) 3))) (/.f64 t (.f64 (.f64 z 3) y)))
	34.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 (sqrt.f64 t) (*.f64 z 3)) (/.f64 (sqrt.f64 t) y)))
	2.7b	(+.f64 (fma.f64 (/.f64 y z) -1/3 x) (/.f64 (/.f64 t (*.f64 z 3)) y))
	3.7b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
▶	2.4b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 (/.f64 (/.f64 t z) 3) y))

Compiler

Compiled 5457 to 3162 computations (42.1% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series51.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

38.0ms	(/.f64 (/.f64 (/.f64 t z) 3) y)
13.0ms	(/.f64 (/.f64 t z) 3)

rewrite86.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

468×	`times-frac_binary64`
228×	`*-un-lft-identity_binary64`
228×	`add-sqr-sqrt_binary64`
228×	`add-cube-cbrt_binary64`
56×	`associate-/l*_binary64`

Counts

2 → 266

Calls

2 calls:

19.0ms	(/.f64 (/.f64 (/.f64 t z) 3) y)
8.0ms	(/.f64 (/.f64 t z) 3)

simplify435.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

637×	`times-frac_binary64`
548×	`associate-/l*_binary64`
340×	`associate-/r/_binary64`
330×	`associate-*l/_binary64`
297×	`associate-/r*_binary64`

Counts

326 → 393

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	453	6813
1	997	6669
2	1789	6660
3	3959	6660
4	4233	6660
5	4764	6660
6	4975	6660

prune927.0ms (11.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	493	1	494
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	494	7	501

Error

Counts

501 → 7

Alt Table

Status	Error	Program
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 3 (*.f64 y z))))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	2.7b	(+.f64 (fma.f64 (/.f64 y z) -1/3 x) (/.f64 (/.f64 t (*.f64 z 3)) y))
	3.7b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
▶	2.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 t z) (/.f64 1/3 y)))
	4.0b	(+.f64 (-.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) z) (/.f64 (cbrt.f64 y) 3))) (/.f64 t (.f64 (.f64 z 3) y)))
✓	2.4b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 (/.f64 (/.f64 t z) 3) y))

Compiler

Compiled 13355 to 6938 computations (48% saved)

localize22.0ms (0.3%)

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))
✓	0.3b	(/.f64 1/3 y)
✓	6.9b	(*.f64 (/.f64 t z) (/.f64 1/3 y))

series48.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

45.0ms	(*.f64 (/.f64 t z) (/.f64 1/3 y))
3.0ms	(/.f64 1/3 y)

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 81

Calls

2 calls:

19.0ms	(*.f64 (/.f64 t z) (/.f64 1/3 y))
4.0ms	(/.f64 1/3 y)

simplify190.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

547×	`associate-*l/_binary64`
489×	`associate-*r/_binary64`
440×	`associate-/l*_binary64`
438×	`fma-def_binary64`
395×	`associate-l_binary64`

Counts

117 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	1456
1	326	1330
2	956	1330
3	3175	1329
4	3445	1329
5	4039	1329
6	4648	1329
7	4971	1329
8	5002	1329

prune398.0ms (5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	216	7	223

Error

Counts

223 → 7

Alt Table

Status	Error	Program
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 3 (*.f64 y z))))
	4.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	2.7b	(+.f64 (fma.f64 (/.f64 y z) -1/3 x) (/.f64 (/.f64 t (*.f64 z 3)) y))
	3.7b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	2.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 t z) (/.f64 1/3 y)))
	4.0b	(+.f64 (-.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) z) (/.f64 (cbrt.f64 y) 3))) (/.f64 t (.f64 (.f64 z 3) y)))
✓	2.4b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 (/.f64 (/.f64 t z) 3) y))

Compiler

Compiled 5253 to 2867 computations (45.4% saved)

regimes713.0ms (8.9%)

Accuracy

Total 0.5b remaining (96.8%)

Threshold costs 0.5b (96.8%)

Counts

49 → 3

Compiler

Compiled 5906 to 4078 computations (31% saved)

bsearch3.0ms (0%)

Compiler: Compiled 19 to 13 computations (31.6% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	112
1	42	112
2	54	112
3	62	112
4	68	112
5	70	112
6	70	112

end2.0ms (0%)

Compiler: Compiled 80 to 51 computations (36.3% saved)

sample2.2s (27.5%)

Algorithm

1×

intervals

Results

924.0ms	8000×	body	128	valid
358.0ms	3187×	body	128	invalid

Compiler

Compiled 240 to 160 computations (33.3% saved)

Details

analyze1.1s (13.1%)

sample109.0ms (1.4%)

simplify257.0ms (3.2%)

prune7.0ms (0.1%)

localize18.0ms (0.2%)

series88.0ms (1.1%)

rewrite47.0ms (0.6%)

simplify204.0ms (2.5%)

prune330.0ms (4.1%)

localize21.0ms (0.3%)

series60.0ms (0.7%)

rewrite33.0ms (0.4%)

simplify161.0ms (2%)

prune489.0ms (6.1%)

localize21.0ms (0.3%)

series51.0ms (0.6%)

rewrite86.0ms (1.1%)

simplify435.0ms (5.4%)

prune927.0ms (11.5%)

localize22.0ms (0.3%)

series48.0ms (0.6%)

rewrite34.0ms (0.4%)

simplify190.0ms (2.4%)

prune398.0ms (5%)

regimes713.0ms (8.9%)

bsearch3.0ms (0%)

simplify13.0ms (0.2%)

end2.0ms (0%)

sample2.2s (27.5%)

Profiling