Details

analyze1.2s (16.8%)

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
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
26.2%	73.5%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample72.0ms (1%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify120.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1627×	`fma-def_binary64`
927×	`div-sub_binary64`
619×	`times-frac_binary64`
541×	`fma-neg_binary64`
386×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	40	14
3	78	14
4	161	14
5	302	14
6	659	14
7	1591	14
8	3045	14
9	3070	14
10	3380	14
11	3469	14
12	3480	14
13	4892	14
14	5124	14

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series61.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

40.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
20.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify115.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune101.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	4	139

Error

0.0b

Counts

139 → 4

Alt Table

Status	Error	Program
	12.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	11.3b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 a t)) (/.f64 (-.f64 z t) (-.f64 a t))) (/.f64 (-.f64 z t) (-.f64 a t)))) x)
▶	3.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 3355 to 1108 computations (67% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	11.0b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series106.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

49.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
36.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
21.0ms	(/.f64 y (-.f64 a t))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

12.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
5.0ms	(/.f64 y (-.f64 a t))
5.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

simplify253.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

422×	`sub-neg_binary64`
404×	`fma-neg_binary64`
222×	`associate--l+_binary64`
218×	`+-commutative_binary64`
182×	`associate-l_binary64`

Counts

287 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	443	6869
1	1078	6148
2	3977	6052
3	4707	6051
4	4994	6051
5	4942	6051

prune204.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	305	3	308
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	307	5	312

Error

Counts

312 → 5

Alt Table

Status	Error	Program
▶	0.9b	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t))))
	12.9b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	4.4b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t)))) (*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t))))
✓	3.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 8063 to 2078 computations (74.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	0.7b	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t)))
✓	4.3b	(*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t))

series268.0ms (3.9%)

Counts

4 → 120

Calls

4 calls:

151.0ms	(*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t))
49.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t)))
37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
30.0ms	(cbrt.f64 y)

rewrite65.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
75×	`add-cube-cbrt_binary64`
68×	`add-exp-log_binary64`
65×	`distribute-lft-in_binary64`

Counts

4 → 252

Calls

4 calls:

17.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t)))
13.0ms	(*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify149.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

699×	`associate-l_binary64`
373×	`times-frac_binary64`
369×	`associate-/l*_binary64`
280×	`associate-*l/_binary64`
235×	`associate-/r*_binary64`

Counts

372 → 420

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	586	8526
1	1321	7780
2	4998	7780

prune323.0ms (4.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	450	0	450
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	450	5	455

Error

Counts

455 → 5

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t))))
	12.9b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	4.4b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t)))) (*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t))))
✓	3.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 15183 to 4463 computations (70.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t))))
✓	2.7b	(.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t)))) (*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t)))
✓	14.0b	(cbrt.f64 (/.f64 y (-.f64 a t)))

series1.3s (19%)

Counts

4 → 168

Calls

4 calls:

520.0ms	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t))))
401.0ms	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t))
310.0ms	(cbrt.f64 (/.f64 y (-.f64 a t)))
79.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t)))) (*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t)))

rewrite103.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`add-sqr-sqrt_binary64`
166×	`*-un-lft-identity_binary64`
152×	`cbrt-prod_binary64`
110×	`add-cube-cbrt_binary64`
109×	`times-frac_binary64`

Counts

4 → 317

Calls

4 calls:

22.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t)))) (*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t)))
20.0ms	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t))))
13.0ms	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t))
3.0ms	(cbrt.f64 (/.f64 y (-.f64 a t)))

simplify335.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

614×	`times-frac_binary64`
564×	`fma-def_binary64`
417×	`*-commutative_binary64`
186×	`associate-r_binary64`
163×	`+-commutative_binary64`

Counts

485 → 597

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1034	16334
1	2606	15504
2	4899	15144
3	5028	15144

prune581.0ms (8.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	769	0	769
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	769	5	774

Error

Counts

774 → 5

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (/.f64 (cbrt.f64 y) (-.f64 a t)) (-.f64 z t))))
	12.9b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	0.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	4.4b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t)))) (*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t))))
✓	3.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 34671 to 10529 computations (69.6% saved)

regimes647.0ms (9.4%)

Accuracy

Total 1.3b remaining (98.8%)

Threshold costs 0b (0%)

Counts

87 → 1

Compiler

Compiled 13672 to 7994 computations (41.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	19	14
3	21	14
4	22	14
5	22	14

end0.0ms (0%)

Compiler: Compiled 15 to 9 computations (40% saved)

sample845.0ms (12.2%)

Algorithm

1×

intervals

Results

409.0ms	8000×	body	128	valid
36.0ms	731×	body	128	invalid

Compiler

Compiled 140 to 82 computations (41.4% saved)

Details

analyze1.2s (16.8%)

sample72.0ms (1%)

simplify120.0ms (1.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series61.0ms (0.9%)

rewrite11.0ms (0.2%)

simplify115.0ms (1.7%)

prune101.0ms (1.5%)

localize8.0ms (0.1%)

series106.0ms (1.5%)

rewrite35.0ms (0.5%)

simplify253.0ms (3.7%)

prune204.0ms (3%)

localize12.0ms (0.2%)

series268.0ms (3.9%)

rewrite65.0ms (0.9%)

simplify149.0ms (2.2%)

prune323.0ms (4.7%)

localize12.0ms (0.2%)

series1.3s (19%)

rewrite103.0ms (1.5%)

simplify335.0ms (4.9%)

prune581.0ms (8.4%)

regimes647.0ms (9.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample845.0ms (12.2%)

Profiling