Details

analyze1.1s (16.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.8%	0.1%	8
21.1%	78%	0.9%	9
37.3%	60.3%	2.5%	10
39.7%	56.1%	4.2%	11
45.6%	48.7%	5.7%	12
55.9%	35.1%	8.9%	13
57.6%	32.1%	10.3%	14

Compiler

Compiled 13 to 8 computations (38.5% saved)

sample1.9s (28.2%)

Results

1.5s	8256×	body	128	valid
198.0ms	1123×	body	128	invalid

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify135.0ms (2%)

Algorithm

1×	egg-herbie

Rules

2064×	`fma-neg_binary64`
381×	`div-sub_binary64`
365×	`associate-/l*_binary64`
334×	`distribute-neg-frac_binary64`
322×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	12	11
2	25	11
3	47	11
4	82	11
5	143	11
6	228	11
7	442	11
8	1041	11
9	2472	11
10	2805	11
11	2944	11
12	3273	11
13	3441	11
14	3513	11
15	4986	11

prune5.0ms (0.1%)

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

12.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.3b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

Compiler

Compiled 42 to 21 computations (50% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 z x) x)
✓	11.6b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

series40.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

27.0ms	(/.f64 (fma.f64 y (-.f64 z x) x) z)
13.0ms	(fma.f64 y (-.f64 z x) x)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 y (-.f64 z x) x) z)
1.0ms	(fma.f64 y (-.f64 z x) x)

simplify207.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

615×	`distribute-rgt-in_binary64`
602×	`distribute-lft-in_binary64`
415×	`times-frac_binary64`
355×	`fma-def_binary64`
346×	`fma-neg_binary64`

Counts

111 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1462
1	170	1315
2	385	1259
3	1042	1259
4	4436	1259
5	4999	1259
6	4955	1259

prune67.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	5	66

Error

0.0b

Counts

66 → 5

Alt Table

Status	Error	Program
	38.5b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)))
▶	3.9b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))
✓	12.3b	(/.f64 (fma.f64 y (-.f64 z x) x) z)
	13.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 y (-.f64 z x) x) (cbrt.f64 z)))
	12.5b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))

Compiler

Compiled 992 to 260 computations (73.8% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.7b	(fma.f64 (/.f64 (-.f64 1 y) z) x y)

series27.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

27.0ms

(fma.f64 (/.f64 (-.f64 1 y) z) x y)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 (/.f64 (-.f64 1 y) z) x y)

simplify102.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

731×	`distribute-rgt-neg-out_binary64`
555×	`distribute-neg-out_binary64`
397×	`unsub-neg_binary64`
368×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`

Counts

46 → 29

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	574
1	77	497
2	184	497
3	447	497
4	2234	497
5	4465	497
6	5104	497

prune42.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	29	5	34

Error

0.0b

Counts

34 → 5

Alt Table

Status	Error	Program
✓	3.9b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))
✓	12.3b	(/.f64 (fma.f64 y (-.f64 z x) x) z)
	13.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 y (-.f64 z x) x) (cbrt.f64 z)))
	1.3b	(.f64 1 (.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))))
▶	0.1b	(*.f64 1 (fma.f64 (/.f64 x z) (-.f64 1 y) y))

Compiler

Compiled 551 to 324 computations (41.2% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 x z) (-.f64 1 y) y)

series24.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

23.0ms

(fma.f64 (/.f64 x z) (-.f64 1 y) y)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 (/.f64 x z) (-.f64 1 y) y)

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

705×	`distribute-rgt-neg-out_binary64`
469×	`distribute-neg-out_binary64`
368×	`unsub-neg_binary64`
332×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`

Counts

46 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	586
1	78	509
2	194	497
3	424	497
4	2300	497
5	4502	497
6	5263	497

prune57.0ms (0.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	23	5	28

Error

0.0b

Counts

28 → 5

Alt Table

Status	Error	Program
✓	3.9b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))
✓	12.3b	(/.f64 (fma.f64 y (-.f64 z x) x) z)
	13.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 y (-.f64 z x) x) (cbrt.f64 z)))
▶	1.3b	(.f64 1 (.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))))
✓	0.1b	(*.f64 1 (fma.f64 (/.f64 x z) (-.f64 1 y) y))

Compiler

Compiled 438 to 250 computations (42.9% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (/.f64 x z) (-.f64 1 y) y)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)))
✓	0.5b	(cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))

series471.0ms (7%)

Counts

3 → 108

Calls

3 calls:

334.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)))

107.0ms

(cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))

28.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

13.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)))

11.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)))

1.0ms

(cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))

simplify407.0ms (6%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-/l*_binary64`
699×	`fma-def_binary64`
351×	`*-commutative_binary64`
160×	`+-commutative_binary64`
132×	`sub-neg_binary64`

Counts

201 → 226

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	861	14503
1	2846	13436
2	5666	13436

prune1.4s (20.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	429	2	431
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	430	6	436

Error

Counts

436 → 6

Alt Table

Status	Error	Program
	1.5b	(.f64 1 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))))))
✓	3.9b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))
✓	12.3b	(/.f64 (fma.f64 y (-.f64 z x) x) z)
	13.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 y (-.f64 z x) x) (cbrt.f64 z)))
	4.9b	(.f64 1 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y)) (cbrt.f64 (fma.f64 (/.f64 x z) (-.f64 1 y) y))) (cbrt.f64 (+.f64 (.f64 x (/.f64 (-.f64 1 y) z)) y))))
✓	0.1b	(*.f64 1 (fma.f64 (/.f64 x z) (-.f64 1 y) y))

Compiler

Compiled 31830 to 18841 computations (40.8% saved)

regimes337.0ms (5%)

Accuracy

Total 0.0b remaining (85.7%)

Threshold costs 0.0b (85.7%)

Counts

41 → 1

Compiler

Compiled 3424 to 2000 computations (41.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	14	11
2	18	11
3	20	11
4	21	11
5	20	11

end197.0ms (2.9%)

Compiler: Compiled 170 to 103 computations (39.4% saved)

Details

analyze1.1s (16.8%)

sample1.9s (28.2%)

simplify135.0ms (2%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

series40.0ms (0.6%)

rewrite8.0ms (0.1%)

simplify207.0ms (3.1%)

prune67.0ms (1%)

localize12.0ms (0.2%)

series27.0ms (0.4%)

rewrite1.0ms (0%)

simplify102.0ms (1.5%)

prune42.0ms (0.6%)

localize12.0ms (0.2%)

series24.0ms (0.4%)

rewrite1.0ms (0%)

simplify91.0ms (1.4%)

prune57.0ms (0.9%)

localize19.0ms (0.3%)

series471.0ms (7%)

rewrite41.0ms (0.6%)

simplify407.0ms (6%)

prune1.4s (20.6%)

regimes337.0ms (5%)

simplify3.0ms (0.1%)

end197.0ms (2.9%)

Profiling