Details

analyze1.5s (24.5%)

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
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.6s (27.7%)

Results

1.2s	8256×	body	128	valid
354.0ms	2685×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

prune4.0ms (0.1%)

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
▶	7.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	8.6b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	7.8b	(/.f64 (*.f64 y (-.f64 z t)) a)

series59.0ms (1%)

Counts

3 → 144

Calls

3 calls:

29.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
23.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms	(*.f64 y (-.f64 z t))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

8.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))
4.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
517×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
448×	`fma-def_binary64`
124×	`associate-l_binary64`

Counts

236 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2898
1	425	2525
2	1558	2355
3	5186	2355

prune106.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	142	6	148
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	142	8	150

Error

Counts

150 → 8

Alt Table

Status	Error	Program
	7.6b	(+.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
✓	7.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	7.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	8.6b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	35.9b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
	7.2b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
▶	7.2b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	17.8b	(fma.f64 (/.f64 y a) z x)

Compiler

Compiled 2667 to 794 computations (70.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	0.0b	(*.f64 y (-.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))
✓	7.8b	(/.f64 a (*.f64 y (-.f64 z t)))

series87.0ms (1.5%)

Counts

3 → 156

Calls

3 calls:

38.0ms	(/.f64 a (*.f64 y (-.f64 z t)))
29.0ms	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
20.0ms	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
29×	`add-exp-log_binary64`
27×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 109

Calls

3 calls:

9.0ms	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
8.0ms	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))
5.0ms	(/.f64 a (*.f64 y (-.f64 z t)))

simplify162.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

476×	`fma-def_binary64`
446×	`distribute-rgt-in_binary64`
412×	`distribute-lft-in_binary64`
290×	`associate-/l/_binary64`
179×	`fma-neg_binary64`

Counts

265 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	4358
1	493	3727
2	1854	3499
3	4842	3499
4	4981	3499

prune184.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	257	8	265

Error

Counts

265 → 8

Alt Table

Status	Error	Program
	7.6b	(+.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
✓	7.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	7.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	8.6b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	35.9b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
▶	7.2b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	7.2b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	17.8b	(fma.f64 (/.f64 y a) z x)

Compiler

Compiled 5019 to 1821 computations (63.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
	0.0b	(*.f64 y (-.f64 z t))
✓	7.9b	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

series55.0ms (0.9%)

Counts

2 → 108

Calls

2 calls:

35.0ms	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
20.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`prod-exp_binary64`
10×	`*-un-lft-identity_binary64`

Counts

2 → 60

Calls

2 calls:

8.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))
3.0ms	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

627×	`distribute-rgt-in_binary64`
613×	`distribute-lft-in_binary64`
359×	`fma-def_binary64`
140×	`associate-l_binary64`
136×	`fma-neg_binary64`

Counts

168 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	2264
1	362	1850
2	1278	1848
3	4946	1848
4	4985	1848

prune132.0ms (2.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	176	8	184

Error

Counts

184 → 8

Alt Table

Status	Error	Program
▶	7.6b	(+.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
✓	7.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	7.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	8.6b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	35.9b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
✓	7.2b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	7.2b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	17.8b	(fma.f64 (/.f64 y a) z x)

Compiler

Compiled 3422 to 1314 computations (61.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 a)
✓	0.6b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	1.9b	(/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
✓	6.2b	(/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a)))

series862.0ms (14.5%)

Counts

4 → 120

Calls

4 calls:

727.0ms	(/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a)))
52.0ms	(/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
43.0ms	(cbrt.f64 a)
40.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
37×	`cbrt-prod_binary64`
36×	`add-exp-log_binary64`
32×	`*-un-lft-identity_binary64`

Counts

4 → 144

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
9.0ms	(/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a)))
5.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms	(cbrt.f64 a)

simplify144.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
337×	`distribute-rgt-in_binary64`
319×	`distribute-lft-in_binary64`
214×	`times-frac_binary64`
190×	`div-sub_binary64`

Counts

264 → 241

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	210	4571
1	480	3826
2	2144	3759
3	4432	3757
4	5083	3757

prune182.0ms (3.1%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	277	8	285

Error

Counts

285 → 8

Alt Table

Status	Error	Program
✓	7.6b	(+.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
✓	7.2b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	7.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	8.6b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	35.9b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
✓	7.2b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	7.2b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	17.8b	(fma.f64 (/.f64 y a) z x)

Compiler

Compiled 6324 to 1773 computations (72% saved)

regimes375.0ms (6.3%)

Accuracy

Total 1.5b remaining (99.1%)

Threshold costs 0b (0%)

Counts

30 → 3

Compiler

Compiled 4873 to 2987 computations (38.7% saved)

bsearch1.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	78
1	33	78
2	37	78
3	39	78
4	40	78
5	39	78

end97.0ms (1.6%)

Compiler: Compiled 239 to 124 computations (48.1% saved)

Details

analyze1.5s (24.5%)

sample1.6s (27.7%)

simplify69.0ms (1.2%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series59.0ms (1%)

rewrite23.0ms (0.4%)

simplify86.0ms (1.4%)

prune106.0ms (1.8%)

localize9.0ms (0.2%)

series87.0ms (1.5%)

rewrite29.0ms (0.5%)

simplify162.0ms (2.7%)

prune184.0ms (3.1%)

localize8.0ms (0.1%)

series55.0ms (0.9%)

rewrite15.0ms (0.3%)

simplify91.0ms (1.5%)

prune132.0ms (2.2%)

localize10.0ms (0.2%)

series862.0ms (14.5%)

rewrite41.0ms (0.7%)

simplify144.0ms (2.4%)

prune182.0ms (3.1%)

regimes375.0ms (6.3%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end97.0ms (1.6%)

Profiling