Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.2s (41.4%)

Results

433.0ms	2098×	body	512	valid
403.0ms	4696×	body	128	valid
146.0ms	1021×	body	256	valid
116.0ms	441×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify64.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-def_binary64`
589×	`rules-21_binary64`
521×	`fma-neg_binary64`
366×	`rules-13_binary64`
324×	`rules-15-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	18	13
2	31	13
3	81	13
4	294	10
5	957	8
6	4255	8
7	4973	8

prune3.0ms (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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 30 to 19 computations (36.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 -1 (fma.f64 x x x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite79.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

423×	`log1p-expm1-u_binary64`
423×	`expm1-log1p-u_binary64`
377×	`prod-diff_binary64`
312×	`fma-neg_binary64`
231×	`unpow-prod-down_binary64`

Counts

1 → 39

Calls

1 calls:

79.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	110	8
2	1256	8
3	4951	8
4	5348	8
0	0	0
1	0	0

simplify105.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

657×	`rules-14-rev_binary64`
257×	`rules-15-rev_binary64`
251×	`rules-6_binary64`
229×	`fma-neg_binary64`
228×	`rules-11_binary64`

Counts

51 → 54

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	201
1	67	199
2	220	191
3	805	163
4	3489	147
5	5058	147

prune75.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	4	55

Error

0.3b

Counts

55 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
	1.4b	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 3)
▶	1.4b	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2))
	40.2b	(/.f64 (-.f64 1 x) (pow.f64 x 3))

Compiler

Compiled 751 to 439 computations (41.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2))
✓	0.3b	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
✓	0.4b	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2)
✓	14.0b	(cbrt.f64 (fma.f64 x x x))

series33.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

15.0ms	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2)
8.0ms	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
6.0ms	(cbrt.f64 (fma.f64 x x x))
3.0ms	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2))

rewrite64.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

692×	`log1p-expm1-u_binary64`
692×	`expm1-log1p-u_binary64`
235×	`prod-diff_binary64`
152×	`egg-rr`
79×	`add-sqr-sqrt_binary64`

Counts

4 → 152

Calls

4 calls:

61.0ms	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2))
60.0ms	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
60.0ms	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2)
60.0ms	(cbrt.f64 (fma.f64 x x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	55
1	198	43
2	2079	43
3	4925	43
0	0	0
1	0	0

simplify56.0ms (2%)

Algorithm

1×	egg-herbie

Rules

753×	`rules-20_binary64`
666×	`fma-def_binary64`
525×	`rules-15-rev_binary64`
297×	`rules-21_binary64`
264×	`fma-neg_binary64`

Counts

200 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1107
1	302	1087
2	950	1079
3	3343	1051
4	5495	1051

prune277.0ms (9.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	301	3	304
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	302	6	308

Error

0.3b

Counts

308 → 6

Alt Table

Status	Error	Program
	12.9b	(.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (cbrt.f64 (fma.f64 x x x)))) 2) (cbrt.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 4))))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
▶	1.4b	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 3)
	40.2b	(/.f64 (-.f64 1 x) (pow.f64 x 3))
	2.1b	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (pow.f64 (/.f64 -1 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x x))) 3)) 2))
	34.2b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (*.f64 x x))) -1) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2))

Compiler

Compiled 7957 to 4338 computations (45.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
✓	0.5b	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 3)
	14.0b	(cbrt.f64 (fma.f64 x x x))

series16.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

16.0ms

(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 3)

rewrite68.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

647×	`log1p-expm1-u_binary64`
647×	`expm1-log1p-u_binary64`
212×	`prod-diff_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Counts

1 → 49

Calls

1 calls:

67.0ms

(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	179	8
2	1928	8
3	4928	8
0	0	0
1	0	0

simplify52.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

657×	`rules-14-rev_binary64`
257×	`rules-15-rev_binary64`
251×	`rules-6_binary64`
229×	`fma-neg_binary64`
228×	`rules-11_binary64`

Counts

61 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	201
1	67	199
2	220	191
3	805	163
4	3489	147
5	5058	147

prune105.0ms (3.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	153	7	160

Error

0.2b

Counts

160 → 7

Alt Table

Status	Error	Program
▶	12.9b	(.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (cbrt.f64 (fma.f64 x x x)))) 2) (cbrt.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 4))))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
	34.5b	(pow.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) -1) 3)
✓	1.4b	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 3)
	40.2b	(/.f64 (-.f64 1 x) (pow.f64 x 3))
	30.4b	(pow.f64 (/.f64 -1 (pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 x))) 2)) 3)
	34.2b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (*.f64 x x))) -1) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2))

Compiler

Compiled 2912 to 1761 computations (39.5% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (/.f64 -1 (cbrt.f64 (cbrt.f64 (fma.f64 x x x)))) 2)
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 x x x)))
	14.0b	(cbrt.f64 (fma.f64 x x x))
✓	25.1b	(cbrt.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 4))

series29.0ms (1%)

Counts

3 → 36

Calls

3 calls:

16.0ms	(pow.f64 (/.f64 -1 (cbrt.f64 (cbrt.f64 (fma.f64 x x x)))) 2)
7.0ms	(cbrt.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 4))
6.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x x x)))

rewrite78.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

710×	`fma-neg_binary64`
449×	`fma-def_binary64`
290×	`prod-diff_binary64`
183×	`egg-rr`
177×	`expm1-udef_binary64`

Counts

3 → 183

Calls

3 calls:

72.0ms	(pow.f64 (/.f64 -1 (cbrt.f64 (cbrt.f64 (fma.f64 x x x)))) 2)
72.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x x x)))
72.0ms	(cbrt.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	284	35
2	2812	35
3	4896	35
0	0	0
1	0	0

simplify67.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-neg_binary64`
690×	`rules-20_binary64`
606×	`fma-def_binary64`
327×	`rules-21_binary64`
247×	`rules-4_binary64`

Counts

219 → 223

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	130	1030
1	269	1008
2	795	1008
3	2793	1008
4	4894	1008
5	4975	1008

prune317.0ms (11.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	364	0	364
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	364	7	371

Error

0.2b

Counts

371 → 7

Alt Table

Status	Error	Program
✓	12.9b	(.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (cbrt.f64 (fma.f64 x x x)))) 2) (cbrt.f64 (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 4))))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
	34.5b	(pow.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) -1) 3)
✓	1.4b	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 3)
	40.2b	(/.f64 (-.f64 1 x) (pow.f64 x 3))
	30.4b	(pow.f64 (/.f64 -1 (pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 x))) 2)) 3)
	34.2b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (*.f64 x x))) -1) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) 2))

Compiler

Compiled 14771 to 8204 computations (44.5% saved)

regimes55.0ms (1.9%)

Accuracy

Total 0.2b remaining (57.6%)

Threshold costs 0.2b (57.6%)

Counts

27 → 1

Compiler

Compiled 934 to 614 computations (34.3% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end94.0ms (3.3%)

Compiler: Compiled 111 to 75 computations (32.4% saved)

Details

analyze6.0ms (0.2%)

sample1.2s (41.4%)

simplify64.0ms (2.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite79.0ms (2.8%)

simplify105.0ms (3.7%)

prune75.0ms (2.6%)

localize7.0ms (0.2%)

series33.0ms (1.1%)

rewrite64.0ms (2.2%)

simplify56.0ms (2%)

prune277.0ms (9.7%)

localize6.0ms (0.2%)

series16.0ms (0.6%)

rewrite68.0ms (2.4%)

simplify52.0ms (1.8%)

prune105.0ms (3.7%)

localize14.0ms (0.5%)

series29.0ms (1%)

rewrite78.0ms (2.7%)

simplify67.0ms (2.4%)

prune317.0ms (11.1%)

regimes55.0ms (1.9%)

simplify1.0ms (0%)

end94.0ms (3.3%)

Profiling