Details

analyze1.4s (24.9%)

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)

sample1.7s (29.8%)

Results

1.2s	8256×	body	128	valid
412.0ms	3123×	body	128	invalid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify90.0ms (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

prune4.0ms (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
	4.4b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	2.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize10.0ms (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)
✓	4.9b	(/.f64 t (.f64 (.f64 z 3) y))

series38.0ms (0.7%)

Counts

4 → 120

Calls

4 calls:

18.0ms	(/.f64 t (.f64 (.f64 z 3) y))
9.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
7.0ms	(/.f64 y (*.f64 z 3))
5.0ms	(.f64 (.f64 z 3) y)

rewrite25.0ms (0.4%)

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:

8.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
5.0ms	(/.f64 t (.f64 (.f64 z 3) y))
4.0ms	(.f64 (.f64 z 3) y)
3.0ms	(/.f64 y (*.f64 z 3))

simplify112.0ms (2%)

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

prune166.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	164	7	171

Error

0.0b

Counts

171 → 7

Alt Table

Status	Error	Program
	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (.f64 z 3)) (/.f64 (cbrt.f64 t) y)))
	2.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 1/3 (/.f64 t (*.f64 y z))))
	2.4b	(+.f64 (-.f64 x (/.f64 1 (/.f64 z (/.f64 y 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	2.4b	(+.f64 (-.f64 x (.f64 y (/.f64 1/3 z))) (/.f64 t (.f64 (*.f64 z 3) y)))
▶	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	4.4b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 1 (*.f64 z 3)) (/.f64 t y)))
	2.4b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))

Compiler

Compiled 4276 to 2536 computations (40.7% saved)

localize10.0ms (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))
✓	0.3b	(/.f64 t (*.f64 z 3))
✓	4.6b	(/.f64 (/.f64 t (*.f64 z 3)) y)

series27.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

20.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
6.0ms	(/.f64 t (*.f64 z 3))

rewrite14.0ms (0.2%)

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:

6.0ms	(/.f64 (/.f64 t (*.f64 z 3)) y)
3.0ms	(/.f64 t (*.f64 z 3))

simplify100.0ms (1.8%)

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

prune212.0ms (3.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	220	6	226

Error

Counts

226 → 6

Alt Table

Status	Error	Program
	2.4b	(+.f64 (-.f64 x (/.f64 1 (/.f64 z (/.f64 y 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	3.9b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 (/.f64 1 z) (/.f64 y (/.f64 t 3))))
	2.4b	(+.f64 (-.f64 x (.f64 y (/.f64 1/3 z))) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
	2.4b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
▶	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 t (*.f64 z 3)) (/.f64 1 y)))

Compiler

Compiled 5398 to 3131 computations (42% saved)

localize9.0ms (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))
	0.3b	(/.f64 t (*.f64 z 3))
✓	4.6b	(.f64 (/.f64 t (.f64 z 3)) (/.f64 1 y))

series19.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

19.0ms

(*.f64 (/.f64 t (*.f64 z 3)) (/.f64 1 y))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`prod-exp_binary64`
14×	`times-frac_binary64`

Counts

1 → 56

Calls

1 calls:

9.0ms

(*.f64 (/.f64 t (*.f64 z 3)) (/.f64 1 y))

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-/l*_binary64`
581×	`associate-*r/_binary64`
536×	`*-commutative_binary64`
371×	`associate-/r*_binary64`
289×	`associate-/l/_binary64`

Counts

92 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1227
1	260	1050
2	963	1049
3	3219	1049
4	4083	1049
5	4765	1049
6	4904	1049
7	4986	1049

prune206.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	218	6	224

Error

Counts

224 → 6

Alt Table

Status	Error	Program
	2.4b	(+.f64 (-.f64 x (/.f64 1 (/.f64 z (/.f64 y 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	3.9b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 (/.f64 1 z) (/.f64 y (/.f64 t 3))))
	2.4b	(+.f64 (-.f64 x (.f64 y (/.f64 1/3 z))) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
▶	2.4b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
✓	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 t (*.f64 z 3)) (/.f64 1 y)))

Compiler

Compiled 5695 to 3543 computations (37.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (/.f64 y z) 3))
✓	0.2b	(/.f64 (/.f64 y z) 3)
	0.2b	(.f64 (.f64 z 3) y)
	4.9b	(/.f64 t (.f64 (.f64 z 3) y))

series17.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

10.0ms	(-.f64 x (/.f64 (/.f64 y z) 3))
7.0ms	(/.f64 (/.f64 y z) 3)

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

342×	`times-frac_binary64`
237×	`add-sqr-sqrt_binary64`
230×	`*-un-lft-identity_binary64`
228×	`add-cube-cbrt_binary64`
129×	`prod-diff_binary64`

Counts

2 → 264

Calls

2 calls:

18.0ms	(-.f64 x (/.f64 (/.f64 y z) 3))
4.0ms	(/.f64 (/.f64 y z) 3)

simplify316.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

544×	`associate-*r/_binary64`
407×	`associate-*l/_binary64`
299×	`*-commutative_binary64`
222×	`distribute-neg-frac_binary64`
201×	`associate-/l*_binary64`

Counts

324 → 348

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	535	15082
1	1493	8282
2	4301	8100
3	4823	8100
4	4995	8100
5	4967	8100

prune421.0ms (7.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	416	0	416
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	416	6	422

Error

Counts

422 → 6

Alt Table

Status	Error	Program
	2.4b	(+.f64 (-.f64 x (/.f64 1 (/.f64 z (/.f64 y 3)))) (/.f64 t (.f64 (.f64 z 3) y)))
	3.9b	(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 (/.f64 1 z) (/.f64 y (/.f64 t 3))))
	2.4b	(+.f64 (-.f64 x (.f64 y (/.f64 1/3 z))) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))
✓	2.4b	(+.f64 (-.f64 x (/.f64 (/.f64 y z) 3)) (/.f64 t (.f64 (.f64 z 3) y)))
✓	1.7b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (/.f64 t (*.f64 z 3)) (/.f64 1 y)))

Compiler

Compiled 15722 to 8311 computations (47.1% saved)

regimes433.0ms (7.7%)

Accuracy

Total 0.4b remaining (90.9%)

Threshold costs 0.4b (90.9%)

Counts

47 → 3

Compiler

Compiled 5939 to 4115 computations (30.7% saved)

bsearch38.0ms (0.7%)

Steps

Iters	Range		Point
2	108822426278385260.0	987968444660967600.0	551368187064176000.0
8	-1.6949839072643712e+36	-8.419539076778492e+32	-6.382969987282973e+34

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
11×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	81
1	52	81
2	68	81
3	81	81
4	90	81
5	94	81
6	95	81
7	93	81

end108.0ms (1.9%)

Compiler: Compiled 238 to 160 computations (32.8% saved)

Details

analyze1.4s (24.9%)

sample1.7s (29.8%)

simplify90.0ms (1.6%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series38.0ms (0.7%)

rewrite25.0ms (0.4%)

simplify112.0ms (2%)

prune166.0ms (2.9%)

localize10.0ms (0.2%)

series27.0ms (0.5%)

rewrite14.0ms (0.2%)

simplify100.0ms (1.8%)

prune212.0ms (3.7%)

localize9.0ms (0.2%)

series19.0ms (0.3%)

rewrite13.0ms (0.2%)

simplify100.0ms (1.8%)

prune206.0ms (3.6%)

localize10.0ms (0.2%)

series17.0ms (0.3%)

rewrite57.0ms (1%)

simplify316.0ms (5.6%)

prune421.0ms (7.4%)

regimes433.0ms (7.7%)

bsearch38.0ms (0.7%)

simplify5.0ms (0.1%)

end108.0ms (1.9%)

Profiling