Details

analyze291.0ms (9.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
31.2%	50%	18.8%	7
34.3%	43.7%	22%	8
45.3%	26.5%	28.2%	9
46.8%	23.4%	29.8%	10
48.8%	14%	37.2%	11
49.8%	12.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	6.1%	40.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	26×	body	128	invalid

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify158.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

952×	`unsub-neg_binary64`
743×	`sub-neg_binary64`
539×	`distribute-rgt-out_binary64`
467×	`+-commutative_binary64`
464×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	25	33
2	55	33
3	116	20
4	263	20
5	631	20
6	1195	20
7	2783	20
8	3808	20
9	4029	20
10	4107	20
11	4146	20
12	4222	20
13	4648	20
14	4915	20

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
	7.9b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 81 to 49 computations (39.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
0.1b	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))
0.3b	(.f64 (.f64 x.re x.im) 3)

rewrite100.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`cancel-sign-sub-inv_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
8×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 62

Calls

3 calls:

9.0ms	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
8.0ms	(.f64 (.f64 x.re x.im) 3)
6.0ms	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))

Compiler

Compiled 1004 to 586 computations (41.6% saved)

series75.0ms (2.4%)

Error

0.1b

Counts

3 → 24

Calls

3 calls:

36.0ms	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
18.0ms	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))
16.0ms	(.f64 (.f64 x.re x.im) 3)

Compiler

Compiled 552 to 413 computations (25.2% saved)

simplify128.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

558×	`*-commutative_binary64`
513×	`exp-prod_binary64`
272×	`cancel-sign-sub-inv_binary64`
267×	`cube-prod_binary64`
237×	`associate-l_binary64` `associate-r_binary64`

Counts

86 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	120	1271
1	275	1187
2	1158	1169
3	2473	1159
4	4477	1156
5	4951	1156
6	4888	1156

prune54.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	51	7	58

Error

0.0b

Counts

58 → 7

Alt Table

Status	Error	Program
	36.7b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (*.f64 3 x.im) (pow.f64 x.re 3/2))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
	24.5b	(-.f64 (.f64 x.re (.f64 (sqrt.f64 (.f64 3 (.f64 x.im x.re))) (sqrt.f64 (.f64 3 (.f64 x.im x.re))))) (pow.f64 x.im 3))
	7.9b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	8.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2)))) (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))))) (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))))) (pow.f64 x.im 3))
	0.3b	(-.f64 (.f64 x.re (.f64 (.f64 (.f64 x.im x.re) (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))

Compiler

Compiled 753 to 532 computations (29.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))
0.1b	(.f64 x.re (.f64 x.re (*.f64 3 x.im)))
0.2b	(.f64 x.re (.f64 3 x.im))

rewrite103.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`cancel-sign-sub-inv_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
8×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
6×	`associate-l_binary64`

Counts

3 → 62

Calls

3 calls:

10.0ms	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))
7.0ms	(.f64 x.re (.f64 x.re (*.f64 3 x.im)))
5.0ms	(.f64 x.re (.f64 3 x.im))

Compiler

Compiled 991 to 639 computations (35.5% saved)

series73.0ms (2.4%)

Error

0.0b

Counts

3 → 24

Calls

3 calls:

33.0ms	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))
20.0ms	(.f64 x.re (.f64 x.re (*.f64 3 x.im)))
15.0ms	(.f64 x.re (.f64 3 x.im))

Compiler

Compiled 552 to 413 computations (25.2% saved)

simplify134.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

540×	`*-commutative_binary64`
468×	`exp-prod_binary64`
288×	`cancel-sign-sub-inv_binary64`
249×	`associate-r_binary64`
230×	`cube-prod_binary64`

Counts

86 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	115	1265
1	270	1175
2	1096	1163
3	2298	1157
4	4494	1156
5	4948	1156
6	4894	1156

prune51.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	55	8	63

Error

0.0b

Counts

63 → 8

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 3 x.re) x.im)) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
	24.5b	(-.f64 (.f64 x.re (.f64 (sqrt.f64 (.f64 3 (.f64 x.im x.re))) (sqrt.f64 (.f64 3 (.f64 x.im x.re))))) (pow.f64 x.im 3))
	7.9b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	8.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2)))) (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))))) (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))))) (pow.f64 x.im 3))
	49.8b	(/.f64 (-.f64 (pow.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))) 3) (pow.f64 x.im 9)) (+.f64 (pow.f64 x.im 6) (.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))) (+.f64 (.f64 3 (*.f64 x.im (pow.f64 x.re 2))) (pow.f64 x.im 3)))))
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 x.re (.f64 (*.f64 3 x.im) (cbrt.f64 x.re)))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))

Compiler

Compiled 816 to 568 computations (30.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x.re (.f64 (*.f64 3 x.re) x.im)) (pow.f64 x.im 3))
0.1b	(.f64 x.re (.f64 (*.f64 3 x.re) x.im))
0.2b	(.f64 (.f64 3 x.re) x.im)

rewrite112.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`cancel-sign-sub-inv_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
8×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 62

Calls

3 calls:

10.0ms	(-.f64 (.f64 x.re (.f64 (*.f64 3 x.re) x.im)) (pow.f64 x.im 3))
6.0ms	(.f64 x.re (.f64 (*.f64 3 x.re) x.im))
5.0ms	(.f64 (.f64 3 x.re) x.im)

Compiler

Compiled 1004 to 649 computations (35.4% saved)

series73.0ms (2.4%)

Error

0.0b

Counts

3 → 24

Calls

3 calls:

36.0ms	(-.f64 (.f64 x.re (.f64 (*.f64 3 x.re) x.im)) (pow.f64 x.im 3))
18.0ms	(.f64 x.re (.f64 (*.f64 3 x.re) x.im))
15.0ms	(.f64 (.f64 3 x.re) x.im)

Compiler

Compiled 552 to 413 computations (25.2% saved)

simplify111.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

609×	`*-commutative_binary64`
463×	`exp-prod_binary64`
414×	`times-frac_binary64`
399×	`cancel-sign-sub-inv_binary64`
292×	`cube-prod_binary64`

Counts

86 → 55

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	1300
1	279	1187
2	1223	1173
3	2585	1163
4	4388	1158
5	5462	1158

prune41.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	55	8	63

Error

0.0b

Counts

63 → 8

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 3 x.re) x.im)) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
	24.5b	(-.f64 (.f64 x.re (.f64 (sqrt.f64 (.f64 3 (.f64 x.im x.re))) (sqrt.f64 (.f64 3 (.f64 x.im x.re))))) (pow.f64 x.im 3))
▶	7.9b	(-.f64 (.f64 (.f64 3 (pow.f64 x.re 2)) x.im) (pow.f64 x.im 3))
	7.9b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	8.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2)))) (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))))) (cbrt.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))))) (pow.f64 x.im 3))
	49.8b	(/.f64 (-.f64 (pow.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))) 3) (pow.f64 x.im 9)) (+.f64 (pow.f64 x.im 6) (.f64 (.f64 3 (.f64 x.im (pow.f64 x.re 2))) (+.f64 (.f64 3 (*.f64 x.im (pow.f64 x.re 2))) (pow.f64 x.im 3)))))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))

Compiler

Compiled 771 to 548 computations (28.9% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 3 (pow.f64 x.re 2)) x.im) (pow.f64 x.im 3))
0.2b	(*.f64 3 (pow.f64 x.re 2))
8.2b	(.f64 (.f64 3 (pow.f64 x.re 2)) x.im)

rewrite121.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`cancel-sign-sub-inv_binary64`
11×	`associate-r_binary64`
10×	`prod-exp_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

3 → 70

Calls

3 calls:

8.0ms	(.f64 (.f64 3 (pow.f64 x.re 2)) x.im)
8.0ms	(-.f64 (.f64 (.f64 3 (pow.f64 x.re 2)) x.im) (pow.f64 x.im 3))
5.0ms	(*.f64 3 (pow.f64 x.re 2))

Compiler

Compiled 1164 to 871 computations (25.2% saved)

series64.0ms (2.1%)

Error

0.0b

Counts

3 → 21

Calls

3 calls:

35.0ms	(-.f64 (.f64 (.f64 3 (pow.f64 x.re 2)) x.im) (pow.f64 x.im 3))
18.0ms	(.f64 (.f64 3 (pow.f64 x.re 2)) x.im)
8.0ms	(*.f64 3 (pow.f64 x.re 2))

Compiler

Compiled 474 to 366 computations (22.8% saved)

simplify114.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

498×	`times-frac_binary64`
472×	`exp-prod_binary64`
435×	`*-commutative_binary64`
405×	`cancel-sign-sub-inv_binary64`
302×	`cube-prod_binary64`

Counts

91 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1319
1	275	1206
2	1016	1197
3	2365	1184
4	4219	1177
5	5485	1177

prune43.0ms (1.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	2	2	4
Picked	0	1	1
Done	1	2	3
Total	59	6	65

Error

0.0b

Counts

65 → 6

Alt Table

Status	Error	Program
	7.9b	(-.f64 (.f64 (.f64 (*.f64 3 x.re) (pow.f64 x.re (/.f64 2 2))) x.im) (pow.f64 x.im 3))
	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
	24.5b	(-.f64 (.f64 x.re (.f64 (sqrt.f64 (.f64 3 (.f64 x.im x.re))) (sqrt.f64 (.f64 3 (.f64 x.im x.re))))) (pow.f64 x.im 3))
	7.9b	(-.f64 (.f64 (.f64 3 (pow.f64 x.re 2)) x.im) (pow.f64 x.im 3))
	7.9b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.2b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))

Compiler

Compiled 580 to 428 computations (26.2% saved)

regimes394.0ms (12.8%)

Accuracy

Total 0.1b remaining (79.7%)

Threshold costs 0.1b (79.7%)

Compiler

Compiled 5685 to 3975 computations (30.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	16	20
2	21	20
3	23	20
4	24	20
5	24	20

end1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample772.0ms (25.1%)

Algorithm

1×

intervals

Results

369.0ms	8000×	body	128	valid
25.0ms	578×	body	128	invalid

Compiler

Compiled 135 to 89 computations (34.1% saved)

Details

analyze291.0ms (9.5%)

sample22.0ms (0.7%)

simplify158.0ms (5.1%)

prune5.0ms (0.2%)

localize7.0ms (0.2%)

rewrite100.0ms (3.2%)

series75.0ms (2.4%)

simplify128.0ms (4.2%)

prune54.0ms (1.8%)

localize7.0ms (0.2%)

rewrite103.0ms (3.3%)

series73.0ms (2.4%)

simplify134.0ms (4.4%)

prune51.0ms (1.6%)

localize7.0ms (0.2%)

rewrite112.0ms (3.6%)

series73.0ms (2.4%)

simplify111.0ms (3.6%)

prune41.0ms (1.3%)

localize8.0ms (0.3%)

rewrite121.0ms (4%)

series64.0ms (2.1%)

simplify114.0ms (3.7%)

prune43.0ms (1.4%)

regimes394.0ms (12.8%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample772.0ms (25.1%)

Profiling