Details

analyze347.0ms (7.8%)

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)

sample41.0ms (0.9%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 39 to 29 computations (25.6% 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)))
	13.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Compiler

Compiled 61 to 42 computations (31.1% saved)

localize21.0ms (0.5%)

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)))

series261.0ms (5.8%)

Counts

2 → 36

Calls

2 calls:

258.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
3.0ms	(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))

simplify69.0ms (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

prune66.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Error

0.0b

Counts

94 → 10

Alt Table

Status	Error	Program
	0.8b	(.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))))
	8.3b	(*.f32 u0 (pow.f32 alpha 2))
	13.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 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)))))
	2.6b	(+.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)))))
	1.4b	(.f32 (.f32 alpha (neg.f32 alpha)) (expm1.f32 (log1p.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)))))
	2.6b	(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)))))
	2.2b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))

Compiler

Compiled 1830 to 883 computations (51.7% saved)

localize25.0ms (0.6%)

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))))

series513.0ms (11.5%)

Counts

2 → 48

Calls

2 calls:

261.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
253.0ms	(*.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))))
3.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

simplify84.0ms (1.9%)

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

prune98.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	163	8	171

Error

Counts

171 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	2.6b	(+.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)))))
	0.8b	(.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))))
	8.3b	(*.f32 u0 (pow.f32 alpha 2))
▶	0.3b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha))))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (log1p.f32 (neg.f32 u0)) (.f32 (neg.f32 alpha) (cbrt.f32 alpha))))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	13.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Compiler

Compiled 2685 to 1257 computations (53.2% 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)) (.f32 alpha (neg.f32 alpha)))

series245.0ms (5.5%)

Counts

1 → 24

Calls

1 calls:

245.0ms

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

rewrite7.0ms (0.2%)

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)))

simplify101.0ms (2.3%)

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 (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	89	8	97

Error

Counts

97 → 8

Alt Table

Status	Error	Program
▶	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	2.6b	(+.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)))))
✓	0.3b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha))))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (log1p.f32 (neg.f32 u0)) (.f32 (neg.f32 alpha) (cbrt.f32 alpha))))
	8.3b	(*.f32 u0 (pow.f32 alpha 2))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	13.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
	0.6b	(.f32 1 (.f32 (sqrt.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))) (sqrt.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha))))))

Compiler

Compiled 1821 to 1006 computations (44.8% saved)

localize34.0ms (0.8%)

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))))

series196.0ms (4.4%)

Counts

2 → 32

Calls

2 calls:

170.0ms	(.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))))
5.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

simplify124.0ms (2.8%)

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

prune137.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	166	7	173

Error

Counts

173 → 7

Alt Table

Status	Error	Program
✓	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	2.6b	(+.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)))))
	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))) (.f32 (log1p.f32 (neg.f32 u0)) (.f32 (neg.f32 (pow.f32 alpha 3/2)) (sqrt.f32 (cbrt.f32 alpha)))))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (log1p.f32 (neg.f32 u0)) (.f32 (neg.f32 alpha) (cbrt.f32 alpha))))
	8.3b	(*.f32 u0 (pow.f32 alpha 2))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	13.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Compiler

Compiled 3180 to 1856 computations (41.6% saved)

regimes524.0ms (11.7%)

Accuracy

Total 0.3b remaining (87.6%)

Threshold costs 0.3b (87.6%)

Counts

90 → 1

Compiler

Compiled 9800 to 6530 computations (33.4% 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	8	13
1	18	13
2	28	13
3	36	13
4	41	13
5	44	13
6	45	13
7	45	13

end0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

sample1.4s (31.6%)

Algorithm

1×

intervals

Results

618.0ms	8000×	body	128	valid
215.0ms	8000×	pre	128	true

Compiler

Compiled 154 to 111 computations (27.9% 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

analyze347.0ms (7.8%)

sample41.0ms (0.9%)

simplify33.0ms (0.7%)

prune4.0ms (0.1%)

localize21.0ms (0.5%)

series261.0ms (5.8%)

rewrite6.0ms (0.1%)

simplify69.0ms (1.5%)

prune66.0ms (1.5%)

localize25.0ms (0.6%)

series513.0ms (11.5%)

rewrite10.0ms (0.2%)

simplify84.0ms (1.9%)

prune98.0ms (2.2%)

localize29.0ms (0.6%)

series245.0ms (5.5%)

rewrite7.0ms (0.2%)

simplify101.0ms (2.3%)

prune61.0ms (1.4%)

localize34.0ms (0.8%)

series196.0ms (4.4%)

rewrite15.0ms (0.3%)

simplify124.0ms (2.8%)

prune137.0ms (3.1%)

regimes524.0ms (11.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (31.6%)

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