Details

analyze1.3s (6.8%)

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
12.5%	87.3%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
43.7%	56.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample52.0ms (0.3%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
2.0ms	21×	body	128	invalid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify138.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1226×	`div-sub_binary64`
778×	`fma-def_binary64`
701×	`unsub-neg_binary64`
456×	`sub-neg_binary64`
437×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	16
2	50	16
3	121	16
4	299	16
5	674	16
6	1361	16
7	2742	16
8	3706	16
9	3871	16
10	4083	16
11	4304	16
12	4387	16
13	5424	16

prune3.0ms (0%)

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

1.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.1b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	6.2b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

rewrite80.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cube-cbrt_binary64`
20×	`flip3--_binary64`
15×	`pow1_binary64`
14×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

2 → 100

Calls

2 calls:

35.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
34.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

series290.0ms (1.5%)

Counts

2 → 84

Calls

2 calls:

249.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
40.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

simplify198.0ms (1%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
622×	`associate-/l*_binary64`
514×	`associate-/r*_binary64`
208×	`fma-def_binary64`
107×	`*-commutative_binary64`

Counts

184 → 319

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	403	6031
1	1393	5560
2	5382	5560

prune332.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	314	5	319
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	315	5	320

Error

0.0b

Counts

320 → 5

Alt Table

Status	Error	Program
	1.8b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z)))
	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
▶	1.1b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
	6.6b	(-.f64 1 (/.f64 x (.f64 (cbrt.f64 (.f64 (.f64 (-.f64 y z) (-.f64 y t)) (.f64 (-.f64 y z) (-.f64 y t)))) (cbrt.f64 (*.f64 (-.f64 y z) (-.f64 y t))))))

Compiler

Compiled 6722 to 2689 computations (60% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.5b	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
✓	6.0b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))

rewrite73.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
15×	`add-cube-cbrt_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`

Counts

2 → 97

Calls

2 calls:

32.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
31.0ms	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))

series402.0ms (2.1%)

Counts

2 → 84

Calls

2 calls:

267.0ms	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))
133.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))

simplify289.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

828×	`associate-/l*_binary64`
808×	`associate-/r*_binary64`
241×	`fma-def_binary64`
164×	`+-commutative_binary64`
123×	`*-commutative_binary64`

Counts

181 → 311

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	540	8190
1	1880	7815
2	5282	7815

prune687.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	466	1	467
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	467	5	472

Error

Counts

472 → 5

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	1.4b	(-.f64 1 (.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))))
	1.8b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z)))
▶	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))

Compiler

Compiled 11028 to 5121 computations (53.6% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))

rewrite126.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
8×	`times-frac_binary64`
8×	`pow1_binary64`

Counts

2 → 96

Calls

2 calls:

91.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
27.0ms	(/.f64 x (-.f64 y z))

series310.0ms (1.6%)

Counts

2 → 72

Calls

2 calls:

265.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
44.0ms	(/.f64 x (-.f64 y z))

simplify167.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

912×	`times-frac_binary64`
652×	`associate-/l*_binary64`
541×	`associate-/r*_binary64`
165×	`fma-def_binary64`
102×	`*-commutative_binary64`

Counts

168 → 268

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	400	5664
1	1357	5395
2	5107	5395

prune310.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	268	5	273

Error

Counts

273 → 5

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
▶	1.4b	(-.f64 1 (.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))))
	1.8b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z)))
✓	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))

Compiler

Compiled 5849 to 2474 computations (57.7% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.3b	(.f64 x (.f64 (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))))
	19.9b	(cbrt.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))))
	19.9b	(cbrt.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))))
✓	19.9b	(cbrt.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))))

rewrite53.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-div_binary64`
11×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`associate-*r/_binary64`

Counts

2 → 77

Calls

2 calls:

23.0ms	(cbrt.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))))
23.0ms	(.f64 x (.f64 (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))))

series10.4s (53.2%)

Counts

2 → 84

Calls

2 calls:

9.3s	(.f64 x (.f64 (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))))
1.1s	(cbrt.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))))

simplify641.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
429×	`times-frac_binary64`
181×	`unpow1/3_binary64`
11×	`log-div_binary64`
9×	`exp-prod_binary64`

Counts

161 → 262

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3574	44747
1	5431	44747

prune1.8s (9.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	604	0	604
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	604	5	609

Error

Counts

609 → 5

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
✓	1.4b	(-.f64 1 (.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))) (cbrt.f64 (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))))
	1.8b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y t)) (-.f64 y z)))
✓	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))

Compiler

Compiled 102020 to 64601 computations (36.7% saved)

regimes765.0ms (3.9%)

Accuracy

Total 0.8b remaining (99.1%)

Threshold costs 0.8b (99.1%)

Compiler

Compiled 15363 to 9720 computations (36.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	26	28
2	43	28
3	59	28
4	69	28
5	73	28
6	74	28
7	73	28

end7.0ms (0%)

Compiler: Compiled 66 to 39 computations (40.9% saved)

sample1.1s (5.4%)

Algorithm

1×

intervals

Results

399.0ms	8000×	body	128	valid
25.0ms	392×	body	128	invalid

Compiler

Compiled 149 to 93 computations (37.6% saved)

Details

analyze1.3s (6.8%)

sample52.0ms (0.3%)

simplify138.0ms (0.7%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite80.0ms (0.4%)

series290.0ms (1.5%)

simplify198.0ms (1%)

prune332.0ms (1.7%)

localize17.0ms (0.1%)

rewrite73.0ms (0.4%)

series402.0ms (2.1%)

simplify289.0ms (1.5%)

prune687.0ms (3.5%)

localize14.0ms (0.1%)

rewrite126.0ms (0.6%)

series310.0ms (1.6%)

simplify167.0ms (0.8%)

prune310.0ms (1.6%)

localize28.0ms (0.1%)

rewrite53.0ms (0.3%)

series10.4s (53.2%)

simplify641.0ms (3.3%)

prune1.8s (9.1%)

regimes765.0ms (3.9%)

simplify5.0ms (0%)

end7.0ms (0%)

sample1.1s (5.4%)

Profiling