Details

analyze122.0ms (2.5%)

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 (40.5%)

Results

1.7s

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

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

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Compiler

Compiled 39 to 26 computations (33.3% saved)

localize23.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.4b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

series196.0ms (4.1%)

Counts

2 → 36

Calls

2 calls:

192.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
4.0ms	(log1p.f32 (neg.f32 u0))

rewrite6.0ms (0.1%)

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:

4.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
0.0ms	(log1p.f32 (neg.f32 u0))

simplify71.0ms (1.5%)

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

prune76.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Error

0.0b

Counts

93 → 7

Alt Table

Status	Error	Program
	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)))))
	2.9b	(+.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)))))
	0.4b	(.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) 1) (log1p.f32 (neg.f32 u0)))
	2.2b	(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)))))
▶	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	0.8b	(.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 (.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))))

Compiler

Compiled 1770 to 839 computations (52.6% saved)

localize23.0ms (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))))

series443.0ms (9.2%)

Counts

2 → 48

Calls

2 calls:

228.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
215.0ms	(*.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)))

simplify88.0ms (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

prune123.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	156	5	161
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	158	10	168

Error

0.0b

Counts

168 → 10

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.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)))))
	2.2b	(cbrt.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.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))))))
	2.9b	(+.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)))))
	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	2.9b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)) (.f32 1/4 (.f32 (pow.f32 u0 4) alpha))))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	0.8b	(.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)))))
▶	0.4b	(.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))
	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))))

Compiler

Compiled 2869 to 1337 computations (53.4% saved)

localize24.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.4b	(.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))

series196.0ms (4.1%)

Counts

1 → 24

Calls

1 calls:

196.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary32`
6×	`add-exp-log_binary32`
6×	`pow1_binary32`
3×	`associate-l_binary32`
3×	`cbrt-unprod_binary32`

Counts

1 → 21

Calls

1 calls:

4.0ms

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

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Rules

940×	`unsub-neg_binary32`
356×	`fma-def_binary32`
298×	`fma-neg_binary32`
290×	`neg-sub0_binary32`
285×	`neg-mul-1_binary32`

Counts

45 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	905
1	265	801
2	943	748
3	3086	738
4	4940	738
5	4995	738
6	4988	738
7	4932	738

prune61.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	90	9	99

Error

0.0b

Counts

99 → 9

Alt Table

Status	Error	Program
	2.9b	(+.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 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (.f32 alpha (neg.f32 alpha))))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.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)))))
▶	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	2.9b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)) (.f32 1/4 (.f32 (pow.f32 u0 4) alpha))))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	0.8b	(.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)))))
✓	0.4b	(.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))

Compiler

Compiled 1767 to 880 computations (50.2% saved)

localize36.0ms (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))))

series166.0ms (3.5%)

Counts

2 → 32

Calls

2 calls:

146.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
19.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

rewrite16.0ms (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:

8.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
5.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

simplify122.0ms (2.5%)

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

prune169.0ms (3.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	165	9	174

Error

Counts

174 → 9

Alt Table

Status	Error	Program
	2.9b	(+.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 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (.f32 alpha (neg.f32 alpha))))
	0.6b	(.f32 (sqrt.f32 alpha) (.f32 (*.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4)) (neg.f32 (sqrt.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))))
	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)))))
	2.9b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)) (.f32 1/4 (.f32 (pow.f32 u0 4) alpha))))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	0.8b	(.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)))))
✓	0.4b	(.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))

Compiler

Compiled 3256 to 1891 computations (41.9% saved)

regimes621.0ms (12.9%)

Accuracy

Total 0.3b remaining (95.2%)

Threshold costs 0.3b (95.2%)

Counts

102 → 1

Compiler

Compiled 10994 to 7036 computations (36% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	31	13
3	41	13
4	46	13
5	48	13
6	48	13

end123.0ms (2.6%)

Compiler: Compiled 212 to 132 computations (37.7% 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

analyze122.0ms (2.5%)

sample1.9s (40.5%)

simplify33.0ms (0.7%)

prune3.0ms (0.1%)

localize23.0ms (0.5%)

series196.0ms (4.1%)

rewrite6.0ms (0.1%)

simplify71.0ms (1.5%)

prune76.0ms (1.6%)

localize23.0ms (0.5%)

series443.0ms (9.2%)

rewrite10.0ms (0.2%)

simplify88.0ms (1.8%)

prune123.0ms (2.6%)

localize24.0ms (0.5%)

series196.0ms (4.1%)

rewrite5.0ms (0.1%)

simplify98.0ms (2%)

prune61.0ms (1.3%)

localize36.0ms (0.7%)

series166.0ms (3.5%)

rewrite16.0ms (0.3%)

simplify122.0ms (2.5%)

prune169.0ms (3.5%)

regimes621.0ms (12.9%)

simplify2.0ms (0.1%)

end123.0ms (2.6%)

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