Details

analyze1.4s (21.1%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (17.9%)

Results

1.0s	8255×	body	128	valid
96.0ms	750×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify123.0ms (1.9%)

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

1.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.2b	(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))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series52.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

34.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
17.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite12.0ms (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:

7.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify114.0ms (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

prune105.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	5	139

Error

0.0b

Counts

139 → 5

Alt Table

Status	Error	Program
▶	3.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	31.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
	32.6b	(+.f64 (.f64 (/.f64 y t) (+.f64 a (/.f64 (.f64 a a) t))) (-.f64 (+.f64 x y) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z a) t)))))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 3411 to 1140 computations (66.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 a t))
✓	10.3b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series99.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

44.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
40.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
15.0ms	(/.f64 y (-.f64 a t))

rewrite32.0ms (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:

10.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
6.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
4.0ms	(/.f64 y (-.f64 a t))

simplify205.0ms (3.1%)

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

prune268.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	308	5	313

Error

Counts

313 → 5

Alt Table

Status	Error	Program
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	10.4b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))))
✓	3.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
▶	4.0b	(+.f64 x (*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t)))

Compiler

Compiled 8057 to 2080 computations (74.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t)))
✓	0.0b	(/.f64 (-.f64 a t) y)
✓	1.1b	(/.f64 1 (/.f64 (-.f64 a t) y))
✓	10.3b	(*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t))

series93.0ms (1.4%)

Counts

4 → 172

Calls

4 calls:

40.0ms	(+.f64 x (*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t)))
29.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t))
15.0ms	(/.f64 1 (/.f64 (-.f64 a t) y))
9.0ms	(/.f64 (-.f64 a t) y)

rewrite68.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64`
213×	`add-sqr-sqrt_binary64`
201×	`*-un-lft-identity_binary64`
147×	`add-cube-cbrt_binary64`
62×	`associate-l_binary64`

Counts

4 → 308

Calls

4 calls:

18.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t))
6.0ms	(/.f64 1 (/.f64 (-.f64 a t) y))
5.0ms	(+.f64 x (*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t)))
4.0ms	(/.f64 (-.f64 a t) y)

simplify215.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

328×	`fma-neg_binary64`
281×	`associate-l_binary64`
261×	`associate-/l*_binary64`
260×	`associate-r_binary64`
223×	`associate--l+_binary64`

Counts

480 → 524

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	503	9961
1	1206	8866
2	4734	8866
3	5023	8866

prune365.0ms (5.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	524	0	524
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	524	5	529

Error

Counts

529 → 5

Alt Table

Status	Error	Program
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	10.4b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))))
✓	3.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	4.0b	(+.f64 x (*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t)))

Compiler

Compiled 13738 to 4452 computations (67.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
✓	0.5b	(cbrt.f64 (-.f64 a t))
✓	2.7b	(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))
✓	9.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t)))

series414.0ms (6.3%)

Counts

4 → 144

Calls

4 calls:

321.0ms	(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))
38.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
32.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t)))
23.0ms	(cbrt.f64 (-.f64 a t))

rewrite88.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
89×	`add-exp-log_binary64`
73×	`add-cube-cbrt_binary64`
65×	`distribute-lft-in_binary64`

Counts

4 → 280

Calls

4 calls:

23.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t)))
12.0ms	(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))
8.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
4.0ms	(cbrt.f64 (-.f64 a t))

simplify238.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

471×	`times-frac_binary64`
452×	`fma-def_binary64`
317×	`*-commutative_binary64`
286×	`associate-/l*_binary64`
181×	`associate-r_binary64`

Counts

424 → 516

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	850	13521
1	2205	11564
2	5029	11564

prune529.0ms (8.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	620	0	620
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	620	5	625

Error

Counts

625 → 5

Alt Table

Status	Error	Program
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	10.4b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))))
✓	3.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	4.0b	(+.f64 x (*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t)))

Compiler

Compiled 25902 to 9030 computations (65.1% saved)

regimes846.0ms (13%)

Accuracy

Total 1.4b remaining (99.2%)

Threshold costs 0b (0%)

Counts

114 → 1

Compiler

Compiled 18552 to 11538 computations (37.8% 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

end68.0ms (1%)

Compiler: Compiled 130 to 76 computations (41.5% saved)

Details

analyze1.4s (21.1%)

sample1.2s (17.9%)

simplify123.0ms (1.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series52.0ms (0.8%)

rewrite12.0ms (0.2%)

simplify114.0ms (1.7%)

prune105.0ms (1.6%)

localize8.0ms (0.1%)

series99.0ms (1.5%)

rewrite32.0ms (0.5%)

simplify205.0ms (3.1%)

prune268.0ms (4.1%)

localize9.0ms (0.1%)

series93.0ms (1.4%)

rewrite68.0ms (1%)

simplify215.0ms (3.3%)

prune365.0ms (5.6%)

localize12.0ms (0.2%)

series414.0ms (6.3%)

rewrite88.0ms (1.4%)

simplify238.0ms (3.7%)

prune529.0ms (8.1%)

regimes846.0ms (13%)

simplify2.0ms (0%)

end68.0ms (1%)

Profiling