Details

analyze118.0ms (2.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0.1%	0.1%	99.8%	3
0.1%	0.1%	99.8%	4
0.1%	0%	99.8%	5
0.1%	0%	99.8%	6
0.1%	0%	99.8%	7
0.1%	0%	99.8%	8
0.2%	0%	99.8%	9
0.2%	0%	99.8%	10
0.2%	0%	99.8%	11
0.2%	0%	99.8%	12
0.2%	0%	99.8%	13
0.2%	0%	99.8%	14

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.8s (35%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-def_binary32`
230×	`fma-neg_binary32`
88×	`cancel-sign-sub-inv_binary32`
79×	`distribute-rgt-in_binary32`
67×	`distribute-lft-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
	14.4b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Compiler

Compiled 61 to 42 computations (31.1% saved)

localize22.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

series241.0ms (4.6%)

Counts

2 → 36

Calls

2 calls:

237.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
3.0ms	(log1p.f32 (neg.f32 u0))

rewrite125.0ms (2.4%)

Algorithm

2×	egg-rewrite

Rules

55×	`egg`
35×	`egg`

Counts

2 → 90

Calls

2 calls:

76.0ms	(log1p.f32 (neg.f32 u0))
47.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	163	9
2	1403	9
3	5265	9
0	4	5
1	80	3
2	699	3
3	4885	3
4	5123	3

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

960×	`fma-neg_binary32`
468×	`fma-def_binary32`
439×	`cancel-sign-sub-inv_binary32`
366×	`times-frac_binary32`
263×	`sub-neg_binary32`

Counts

126 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	752
1	284	698
2	892	650
3	2908	644
4	4824	644
5	5251	644

prune67.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	130	10	140

Error

0.1b

Counts

140 → 10

Alt Table

Status	Error	Program
▶	1.9b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	14.4b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
	2.4b	(.f32 (.f32 alpha alpha) (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0)))
	3.6b	(.f32 (.f32 alpha (neg.f32 alpha)) (-.f32 (log.f32 (-.f32 1 (*.f32 u0 u0))) (log1p.f32 u0)))
	3.8b	(.f32 alpha (.f32 alpha (fma.f32 1/2 (*.f32 u0 u0) u0)))
	7.8b	(*.f32 u0 (pow.f32 alpha 2))
	8.6b	(.f32 (sqrt.f32 (log1p.f32 u0)) (.f32 (sqrt.f32 (log1p.f32 u0)) (*.f32 alpha alpha)))
	8.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 alpha (log1p.f32 u0))))
	8.6b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 u0)) 2) (.f32 (cbrt.f32 (log1p.f32 u0)) (*.f32 alpha alpha)))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Compiler

Compiled 2294 to 1139 computations (50.3% saved)

localize76.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 (pow.f32 u0 3) (pow.f32 alpha 2))
✓	0.3b	(*.f32 (pow.f32 u0 4) (pow.f32 alpha 2))
✓	0.3b	(*.f32 (pow.f32 u0 2) (pow.f32 alpha 2))
✓	0.4b	(.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2)))

series63.0ms (1.2%)

Counts

4 → 0

Calls

4 calls:

20.0ms	(.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2)))
17.0ms	(*.f32 (pow.f32 u0 3) (pow.f32 alpha 2))
15.0ms	(*.f32 (pow.f32 u0 4) (pow.f32 alpha 2))
11.0ms	(*.f32 (pow.f32 u0 2) (pow.f32 alpha 2))

rewrite210.0ms (4%)

Algorithm

4×	egg-rewrite

Rules

54×	`egg`
38×	`egg`
36×	`egg`
32×	`egg`

Counts

4 → 160

Calls

4 calls:

74.0ms	(*.f32 (pow.f32 u0 4) (pow.f32 alpha 2))
46.0ms	(.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2)))
45.0ms	(*.f32 (pow.f32 u0 2) (pow.f32 alpha 2))
42.0ms	(*.f32 (pow.f32 u0 3) (pow.f32 alpha 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	208	13
2	2061	13
3	4880	13
0	7	7
1	144	7
2	1405	7
3	5197	7
0	8	10
1	164	10
2	1557	10
3	4991	10
4	4945	10
0	8	10
1	165	10
2	1598	10
3	4940	10

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

160 → 156

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune197.0ms (3.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	156	10	166

Error

0.1b

Counts

166 → 10

Alt Table

Status	Error	Program
✓	1.9b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	14.4b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
▶	2.4b	(.f32 (.f32 alpha alpha) (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0)))
	3.6b	(.f32 (.f32 alpha (neg.f32 alpha)) (-.f32 (log.f32 (-.f32 1 (*.f32 u0 u0))) (log1p.f32 u0)))
	3.8b	(.f32 alpha (.f32 alpha (fma.f32 1/2 (*.f32 u0 u0) u0)))
	7.8b	(*.f32 u0 (pow.f32 alpha 2))
	8.6b	(.f32 (sqrt.f32 (log1p.f32 u0)) (.f32 (sqrt.f32 (log1p.f32 u0)) (*.f32 alpha alpha)))
	8.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 alpha (log1p.f32 u0))))
	8.6b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 u0)) 2) (.f32 (cbrt.f32 (log1p.f32 u0)) (*.f32 alpha alpha)))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Compiler

Compiled 6296 to 4546 computations (27.8% saved)

localize34.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 1/2 (*.f32 u0 u0) u0)
✓	0.1b	(fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))
✓	0.3b	(.f32 (.f32 alpha alpha) (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0)))

series36.0ms (0.7%)

Counts

3 → 48

Calls

3 calls:

30.0ms	(.f32 (.f32 alpha alpha) (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0)))
3.0ms	(fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))
2.0ms	(fma.f32 1/2 (*.f32 u0 u0) u0)

rewrite178.0ms (3.4%)

Algorithm

3×	egg-rewrite

Rules

52×	`egg`
40×	`egg`
24×	`egg`

Counts

3 → 116

Calls

3 calls:

80.0ms	(fma.f32 1/2 (*.f32 u0 u0) u0)
52.0ms	(.f32 (.f32 alpha alpha) (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0)))
44.0ms	(fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	247	21
2	2524	21
3	4838	21
0	9	15
1	187	15
2	1849	15
3	4829	15
0	5	8
1	101	8
2	1052	8
3	4672	8
4	5979	8

simplify167.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

813×	`associate-l_binary32`
655×	`distribute-rgt-out_binary32`
609×	`distribute-lft-out_binary32`
537×	`associate-r_binary32`
438×	`fma-def_binary32`

Counts

164 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	779
1	61	741
2	172	689
3	559	609
4	2148	609
5	4088	609
6	4240	609
7	4567	609
8	4742	609
9	4947	609
10	4975	609
11	4922	609

prune128.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	5	2	7
Picked	1	0	1
Done	0	2	2
Total	138	9	147

Error

0.0b

Counts

147 → 9

Alt Table

Status	Error	Program
▶	2.5b	(.f32 alpha (.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))))
	3.6b	(.f32 (.f32 alpha (neg.f32 alpha)) (-.f32 (log.f32 (-.f32 1 (*.f32 u0 u0))) (log1p.f32 u0)))
✓	1.9b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	14.4b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
	2.6b	(.f32 (.f32 alpha alpha) (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 (sqrt.f32 u0) (sqrt.f32 u0) (.f32 1/2 (.f32 u0 u0)))))
	3.7b	(.f32 u0 (.f32 alpha (*.f32 alpha (fma.f32 u0 1/2 1))))
	2.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (.f32 u0 u0) u0)))))
	2.8b	(.f32 (pow.f32 (cbrt.f32 (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (.f32 u0 u0) u0))) 2) (.f32 (cbrt.f32 (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (.f32 u0 u0) u0))) (*.f32 alpha alpha)))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Compiler

Compiled 3060 to 1753 computations (42.7% saved)

localize33.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 1/2 (*.f32 u0 u0) u0)
	0.1b	(fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))
✓	0.2b	(.f32 alpha (.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))))
✓	0.3b	(.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (.f32 u0 u0) u0)))

series56.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (.f32 u0 u0) u0)))
27.0ms	(.f32 alpha (.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))))

rewrite106.0ms (2%)

Algorithm

2×	egg-rewrite

Rules

43×	`egg`
31×	`egg`

Counts

2 → 74

Calls

2 calls:

52.0ms	(.f32 alpha (.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))))
51.0ms	(.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (.f32 u0 u0) u0)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	226	18
2	2314	18
3	5495	18
0	12	21
1	247	21
2	2584	21
3	4958	21

simplify220.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1980×	`fma-def_binary32`
643×	`sqr-pow_binary32`
534×	`*-commutative_binary32`
433×	`unswap-sqr_binary32`
338×	`cube-prod_binary32`

Counts

122 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	957
1	84	934
2	233	854
3	666	738
4	1353	738
5	2270	738
6	2258	738
7	2351	738
8	2428	738
9	2594	738
10	2820	738
11	2984	738
12	3171	738
13	3426	738
14	3751	738
15	4151	738
16	4618	738
17	4762	738
18	4893	738
19	4880	738

prune137.0ms (2.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	180	9	189

Error

0.0b

Counts

189 → 9

Alt Table

Status	Error	Program
✓	2.5b	(.f32 alpha (.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (*.f32 u0 u0) u0))))
	3.6b	(.f32 (.f32 alpha (neg.f32 alpha)) (-.f32 (log.f32 (-.f32 1 (*.f32 u0 u0))) (log1p.f32 u0)))
✓	1.9b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	14.4b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
	2.6b	(.f32 (.f32 alpha alpha) (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 (sqrt.f32 u0) (sqrt.f32 u0) (.f32 1/2 (.f32 u0 u0)))))
	3.7b	(.f32 u0 (.f32 alpha (*.f32 alpha (fma.f32 u0 1/2 1))))
	2.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (.f32 u0 u0) u0)))))
	2.7b	(.f32 (.f32 (.f32 alpha (fma.f32 1/3 (pow.f32 u0 3) (fma.f32 1/2 (.f32 u0 u0) u0))) (pow.f32 (cbrt.f32 alpha) 2)) (cbrt.f32 alpha))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Compiler

Compiled 3774 to 2272 computations (39.8% saved)

regimes912.0ms (17.4%)

Accuracy

Total 0.3b remaining (76.7%)

Threshold costs 0.3b (76.7%)

Counts

150 → 1

Compiler

Compiled 17984 to 12164 computations (32.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`
5×	`+-commutative_binary32`
5×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	28	13
3	36	13
4	41	13
5	44	13
6	45	13
7	45	13

end155.0ms (3%)

Compiler: Compiled 188 to 129 computations (31.4% saved)

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

Details

analyze118.0ms (2.3%)

sample1.8s (35%)

simplify39.0ms (0.8%)

prune4.0ms (0.1%)

localize22.0ms (0.4%)

series241.0ms (4.6%)

rewrite125.0ms (2.4%)

simplify74.0ms (1.4%)

prune67.0ms (1.3%)

localize76.0ms (1.4%)

series63.0ms (1.2%)

rewrite210.0ms (4%)

simplify10.0ms (0.2%)

prune197.0ms (3.8%)

localize34.0ms (0.6%)

series36.0ms (0.7%)

rewrite178.0ms (3.4%)

simplify167.0ms (3.2%)

prune128.0ms (2.4%)

localize33.0ms (0.6%)

series56.0ms (1.1%)

rewrite106.0ms (2%)

simplify220.0ms (4.2%)

prune137.0ms (2.6%)

regimes912.0ms (17.4%)

simplify4.0ms (0.1%)

end155.0ms (3%)

Profiling

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13