Details

analyze1.2s (4.6%)

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
16.5%	83.2%	0.2%	13
25.9%	73.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (4.2%)

Results

971.0ms	8255×	body	128	valid
89.0ms	761×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify116.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1893×	`fma-neg_binary64`
867×	`div-sub_binary64`
749×	`fma-def_binary64`
696×	`distribute-rgt-in_binary64`
535×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	81	14
4	160	14
5	302	14
6	620	14
7	1528	14
8	2624	14
9	2858	14
10	3205	14
11	3392	14
12	3498	14
13	3533	14
14	5398	14

prune4.0ms (0%)

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
▶	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series55.0ms (0.2%)

Counts

2 → 84

Calls

2 calls:

40.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
15.0ms	(/.f64 t (-.f64 a z))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

3.0ms	(/.f64 t (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary64`
633×	`fma-def_binary64`
620×	`associate-/l*_binary64`
272×	`cancel-sign-sub-inv_binary64`
175×	`associate-/l/_binary64`

Counts

133 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3215
1	492	3156
2	1711	2520
3	5110	2520

prune78.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	104	6	110

Error

0.0b

Counts

110 → 6

Alt Table

Status	Error	Program
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	47.3b	(fma.f64 (-.f64 y z) (*.f64 (/.f64 1 (+.f64 (sqrt.f64 a) (sqrt.f64 z))) (/.f64 t (-.f64 (sqrt.f64 a) (sqrt.f64 z)))) x)
	27.3b	(+.f64 t (+.f64 x (*.f64 t (-.f64 (/.f64 a z) (/.f64 y z)))))
	2.9b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
▶	2.1b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)

Compiler

Compiled 2453 to 791 computations (67.8% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (-.f64 a z))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	0.0b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	3.4b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series111.0ms (0.4%)

Counts

4 → 144

Calls

4 calls:

44.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
41.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
18.0ms	(/.f64 y (-.f64 a z))
8.0ms	(/.f64 z (-.f64 a z))

rewrite856.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

2650×	`*-un-lft-identity_binary64`
2642×	`add-sqr-sqrt_binary64`
2628×	`times-frac_binary64`
1764×	`prod-diff_binary64`
1576×	`add-cube-cbrt_binary64`

Counts

4 → 1983

Calls

4 calls:

100.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
52.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
3.0ms	(/.f64 y (-.f64 a z))
3.0ms	(/.f64 z (-.f64 a z))

simplify2.6s (9.6%)

Algorithm

1×	egg-herbie

Rules

579×	`times-frac_binary64`
426×	`*-commutative_binary64`
373×	`distribute-rgt-in_binary64`
308×	`fma-udef_binary64`
265×	`unsub-neg_binary64`

Counts

2127 → 2371

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1502	111893
1	2630	82196
2	4521	72767
3	4467	72767
4	4900	72767
5	5040	72767

prune1.6s (6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	2370	1	2371
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	2372	5	2377

Error

0.0b

Counts

2377 → 5

Alt Table

Status	Error	Program
▶	2.1b	(+.f64 (*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z)))) x)
	27.3b	(+.f64 t (+.f64 x (*.f64 t (-.f64 (/.f64 a z) (/.f64 y z)))))
	2.9b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 135038 to 23532 computations (82.6% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) y)
✓	0.0b	(+.f64 (*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z)))) x)
✓	0.8b	(/.f64 1 (/.f64 (-.f64 a z) y))
✓	3.4b	(*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z))))

series114.0ms (0.4%)

Counts

4 → 172

Calls

4 calls:

46.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z)))) x)
43.0ms	(*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z))))
16.0ms	(/.f64 1 (/.f64 (-.f64 a z) y))
9.0ms	(/.f64 (-.f64 a z) y)

rewrite3.0s (11.4%)

Algorithm

1×	rewrite-expression-head

Rules

12501×	`times-frac_binary64`
9379×	`add-sqr-sqrt_binary64`
9360×	`*-un-lft-identity_binary64`
6288×	`add-cube-cbrt_binary64`
5208×	`prod-diff_binary64`

Counts

4 → 5489

Calls

4 calls:

229.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z)))) x)
122.0ms	(*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z))))
9.0ms	(/.f64 1 (/.f64 (-.f64 a z) y))
4.0ms	(/.f64 (-.f64 a z) y)

simplify9.3s (34.9%)

Algorithm

1×	egg-herbie

Rules

825×	`times-frac_binary64`
446×	`*-commutative_binary64`
369×	`distribute-rgt-in_binary64`
323×	`fma-udef_binary64`
261×	`unsub-neg_binary64`

Counts

5661 → 6247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1575	358753
1	2673	241807
2	4625	240131
3	5740	240131

prune5.2s (19.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	6247	0	6247
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	6247	5	6252

Error

0.0b

Counts

6252 → 5

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 (*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z)))) x)
	27.3b	(+.f64 t (+.f64 x (*.f64 t (-.f64 (/.f64 a z) (/.f64 y z)))))
▶	2.9b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 411268 to 100531 computations (75.6% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) t)
✓	0.5b	(/.f64 1 (/.f64 (-.f64 a z) t))
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)

series62.0ms (0.2%)

Counts

3 → 124

Calls

3 calls:

35.0ms	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
16.0ms	(/.f64 1 (/.f64 (-.f64 a z) t))
10.0ms	(/.f64 (-.f64 a z) t)

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`times-frac_binary64`
101×	`*-un-lft-identity_binary64`
101×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

3 → 152

Calls

3 calls:

6.0ms	(/.f64 1 (/.f64 (-.f64 a z) t))
5.0ms	(/.f64 (-.f64 a z) t)
0.0ms	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)

simplify142.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

748×	`fma-def_binary64`
289×	`cancel-sign-sub-inv_binary64`
249×	`associate-/l/_binary64`
217×	`fma-neg_binary64`
206×	`distribute-rgt-in_binary64`

Counts

276 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	5419
1	622	5057
2	2193	4377
3	4627	4377
4	5157	4377

prune162.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	248	5	253

Error

0.0b

Counts

253 → 5

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 (*.f64 t (-.f64 (/.f64 1 (/.f64 (-.f64 a z) y)) (/.f64 z (-.f64 a z)))) x)
	27.3b	(+.f64 t (+.f64 x (*.f64 t (-.f64 (/.f64 a z) (/.f64 y z)))))
✓	2.9b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) t)) x)
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 5418 to 1700 computations (68.6% saved)

regimes673.0ms (2.5%)

Accuracy

Total 0.3b remaining (95.5%)

Threshold costs 0.3b (95.5%)

Counts

64 → 3

Compiler

Compiled 7611 to 4853 computations (36.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	94
1	41	94
2	50	94
3	54	94
4	56	94
5	55	94

end74.0ms (0.3%)

Compiler: Compiled 226 to 108 computations (52.2% saved)

Details

analyze1.2s (4.6%)

sample1.1s (4.2%)

simplify116.0ms (0.4%)

prune4.0ms (0%)

localize8.0ms (0%)

series55.0ms (0.2%)

rewrite7.0ms (0%)

simplify71.0ms (0.3%)

prune78.0ms (0.3%)

localize8.0ms (0%)

series111.0ms (0.4%)

rewrite856.0ms (3.2%)

simplify2.6s (9.6%)

prune1.6s (6%)

localize10.0ms (0%)

series114.0ms (0.4%)

rewrite3.0s (11.4%)

simplify9.3s (34.9%)

prune5.2s (19.6%)

localize9.0ms (0%)

series62.0ms (0.2%)

rewrite25.0ms (0.1%)

simplify142.0ms (0.5%)

prune162.0ms (0.6%)

regimes673.0ms (2.5%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end74.0ms (0.3%)

Profiling