Details

analyze118.0ms (2.4%)

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)

sample1.9s (38.4%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify33.0ms (0.7%)

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)))
	14.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Compiler

Compiled 61 to 42 computations (31.1% saved)

localize30.0ms (0.6%)

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)))

series258.0ms (5.3%)

Counts

2 → 36

Calls

2 calls:

255.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
3.0ms	(log1p.f32 (neg.f32 u0))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary32`
7×	`add-exp-log_binary32`
7×	`pow1_binary32`
3×	`associate-r_binary32`
3×	`*-un-lft-identity_binary32`

Counts

2 → 32

Calls

2 calls:

7.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
0.0ms	(log1p.f32 (neg.f32 u0))

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-neg_binary32`
526×	`fma-def_binary32`
217×	`times-frac_binary32`
213×	`distribute-rgt-neg-out_binary32`
204×	`distribute-lft-neg-out_binary32`

Counts

68 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1211
1	390	1075
2	1418	1024
3	4435	1014
4	4952	1014

prune69.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Error

0.0b

Counts

94 → 8

Alt Table

Status	Error	Program
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 alpha (neg.f32 alpha))) (.f32 alpha (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.9b	(.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (log1p.f32 (neg.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)))))
	0.9b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
▶	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))

Compiler

Compiled 1846 to 865 computations (53.1% saved)

localize25.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.2b	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

series502.0ms (10.4%)

Counts

2 → 48

Calls

2 calls:

252.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
249.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`associate-l_binary32`
9×	`add-sqr-sqrt_binary32`
9×	`add-cbrt-cube_binary32`
9×	`add-exp-log_binary32`
9×	`pow1_binary32`

Counts

2 → 49

Calls

2 calls:

4.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
4.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

simplify86.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary32`
338×	`fma-neg_binary32`
288×	`distribute-rgt-neg-out_binary32`
249×	`distribute-lft-neg-out_binary32`
230×	`times-frac_binary32`

Counts

97 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1675
1	436	1509
2	1377	1427
3	4367	1415
4	4977	1415

prune121.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	159	10	169

Error

Counts

169 → 10

Alt Table

Status	Error	Program
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (neg.f32 (cbrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 alpha (neg.f32 alpha))) (.f32 alpha (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.9b	(.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
▶	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	0.8b	(.f32 alpha (.f32 (.f32 (neg.f32 alpha) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))

Compiler

Compiled 2847 to 1285 computations (54.9% saved)

localize33.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.3b	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))
✓	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))

series199.0ms (4.1%)

Counts

2 → 32

Calls

2 calls:

173.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
26.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`associate-r_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`*-un-lft-identity_binary32`
10×	`add-cube-cbrt_binary32`
9×	`associate-l_binary32`

Counts

2 → 60

Calls

2 calls:

6.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
6.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

simplify127.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary32`
490×	`*-commutative_binary32`
235×	`fma-neg_binary32`
222×	`associate-r_binary32`
220×	`distribute-rgt-neg-out_binary32`

Counts

92 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	1990
1	520	1770
2	1695	1627
3	4473	1546
4	4873	1546
5	5000	1546
6	4944	1546

prune133.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	166	9	175

Error

Counts

175 → 9

Alt Table

Status	Error	Program
	0.5b	(.f32 (.f32 (sqrt.f32 alpha) (log1p.f32 (neg.f32 u0))) (neg.f32 (pow.f32 alpha 3/2)))
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
▶	0.3b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (*.f32 alpha alpha))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.9b	(.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 alpha)) (.f32 (sqrt.f32 (sqrt.f32 alpha)) (*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))))
✓	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 3369 to 1940 computations (42.4% saved)

localize29.0ms (0.6%)

Local error

Found 2 expressions with local error:

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

series232.0ms (4.8%)

Counts

1 → 24

Calls

1 calls:

232.0ms

(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (*.f32 alpha alpha)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-r_binary32`
5×	`add-sqr-sqrt_binary32`
3×	`associate-l_binary32`
3×	`*-un-lft-identity_binary32`
3×	`add-cube-cbrt_binary32`

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (*.f32 alpha alpha)))

simplify72.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

707×	`unsub-neg_binary32`
322×	`times-frac_binary32`
298×	`fma-def_binary32`
284×	`fma-neg_binary32`
259×	`neg-sub0_binary32`

Counts

48 → 58

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	934
1	260	853
2	845	800
3	2196	786
4	4179	784
5	5230	784

prune65.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	95	9	104

Error

Counts

104 → 9

Alt Table

Status	Error	Program
	3.7b	(.f32 1 (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (.f32 u0 (pow.f32 alpha 2))))
✓	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	0.5b	(.f32 (.f32 (sqrt.f32 alpha) (log1p.f32 (neg.f32 u0))) (neg.f32 (pow.f32 alpha 3/2)))
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
✓	0.3b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (*.f32 alpha alpha))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.9b	(.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
	0.7b	(.f32 (sqrt.f32 (sqrt.f32 alpha)) (.f32 (sqrt.f32 (sqrt.f32 alpha)) (*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 1817 to 973 computations (46.5% saved)

regimes636.0ms (13.1%)

Accuracy

Total 0.3b remaining (94.5%)

Threshold costs 0.3b (94.5%)

Counts

119 → 1

Compiler

Compiled 12164 to 7914 computations (34.9% saved)

simplify3.0ms (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	11	18
1	21	18
2	31	18
3	39	18
4	44	18
5	47	18
6	48	18
7	48	18

end97.0ms (2%)

Compiler: Compiled 192 to 117 computations (39.1% 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 (2.4%)

sample1.9s (38.4%)

simplify33.0ms (0.7%)

prune4.0ms (0.1%)

localize30.0ms (0.6%)

series258.0ms (5.3%)

rewrite9.0ms (0.2%)

simplify65.0ms (1.3%)

prune69.0ms (1.4%)

localize25.0ms (0.5%)

series502.0ms (10.4%)

rewrite10.0ms (0.2%)

simplify86.0ms (1.8%)

prune121.0ms (2.5%)

localize33.0ms (0.7%)

series199.0ms (4.1%)

rewrite15.0ms (0.3%)

simplify127.0ms (2.6%)

prune133.0ms (2.7%)

localize29.0ms (0.6%)

series232.0ms (4.8%)

rewrite6.0ms (0.1%)

simplify72.0ms (1.5%)

prune65.0ms (1.3%)

regimes636.0ms (13.1%)

simplify3.0ms (0.1%)

end97.0ms (2%)

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