Details

analyze99.0ms (1.6%)

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)

sample275.0ms (4.5%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify33.0ms (0.5%)

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
	14.6b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
▶	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 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)))

series257.0ms (4.2%)

Counts

2 → 36

Calls

2 calls:

252.0ms	(.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))

simplify66.0ms (1.1%)

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

prune63.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Error

0.0b

Counts

94 → 9

Alt Table

Status	Error	Program
	1.8b	(+.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 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	7.6b	(*.f32 u0 (pow.f32 alpha 2))
	0.8b	(.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)))))
	2.4b	(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)))))
	0.8b	(.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))))
	14.6b	(.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)))))
	2.4b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))

Compiler

Compiled 1806 to 867 computations (52% saved)

localize22.0ms (0.4%)

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))))

series498.0ms (8.1%)

Counts

2 → 48

Calls

2 calls:

256.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
242.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

rewrite13.0ms (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:

7.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
4.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

simplify73.0ms (1.2%)

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

prune104.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	163	7	170

Error

Counts

170 → 7

Alt Table

Status	Error	Program
	1.8b	(+.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 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)))))
▶	0.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.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)))))
	2.6b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)))))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))

Compiler

Compiled 2735 to 1263 computations (53.8% saved)

localize30.0ms (0.5%)

Local error

Found 4 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 (sqrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
✓	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))

series199.0ms (3.2%)

Counts

2 → 32

Calls

2 calls:

175.0ms	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
24.0ms	(.f32 (sqrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
16×	`pow1_binary32`
12×	`associate-l_binary32`
9×	`cbrt-unprod_binary32`

Counts

2 → 51

Calls

2 calls:

8.0ms	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
5.0ms	(.f32 (sqrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary32`
369×	`distribute-rgt-neg-out_binary32`
279×	`distribute-lft-neg-out_binary32`
262×	`fma-neg_binary32`
250×	`associate-r_binary32`

Counts

83 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	1882
1	473	1603
2	1622	1468
3	4463	1416
4	4984	1416
5	4975	1416

prune142.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	228	6	234

Error

Counts

234 → 6

Alt Table

Status	Error	Program
	1.8b	(+.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 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)))))
✓	0.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.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)))))
▶	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))) (sqrt.f32 (cbrt.f32 alpha))))

Compiler

Compiled 4556 to 1946 computations (57.3% saved)

localize53.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))
✓	0.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))) (sqrt.f32 (cbrt.f32 alpha))))
✓	0.3b	(.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))) (sqrt.f32 (cbrt.f32 alpha)))
✓	0.5b	(*.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))

series491.0ms (8%)

Counts

4 → 64

Calls

4 calls:

240.0ms	(.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))) (sqrt.f32 (cbrt.f32 alpha)))
185.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))) (sqrt.f32 (cbrt.f32 alpha))))
41.0ms	(*.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))
25.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`associate-r_binary32`
32×	`add-sqr-sqrt_binary32`
27×	`pow1_binary32`
22×	`*-un-lft-identity_binary32`
22×	`add-cube-cbrt_binary32`

Counts

4 → 130

Calls

4 calls:

14.0ms	(.f32 (sqrt.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))) (sqrt.f32 (cbrt.f32 alpha))))
7.0ms	(.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))) (sqrt.f32 (cbrt.f32 alpha)))
5.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))
5.0ms	(*.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))

simplify157.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

401×	`associate-l_binary32`
390×	`associate-r_binary32`
339×	`distribute-rgt-neg-out_binary32`
289×	`distribute-lft-neg-out_binary32`
257×	`times-frac_binary32`

Counts

194 → 254

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	306	4104
1	817	3468
2	2661	3379
3	4655	3372
4	4964	3372
5	4992	3372

prune217.0ms (3.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	254	6	260

Error

Counts

260 → 6

Alt Table

Status	Error	Program
	1.8b	(+.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 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)))))
✓	0.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.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)))))
✓	0.6b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))) (sqrt.f32 (cbrt.f32 alpha))))

Compiler

Compiled 6778 to 3096 computations (54.3% saved)

regimes1.7s (28.1%)

Accuracy

Total 0.3b remaining (88.7%)

Threshold costs 0.3b (88.7%)

Counts

255 → 1

Compiler

Compiled 32566 to 20940 computations (35.7% saved)

simplify3.0ms (0%)

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

end0.0ms (0%)

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

sample1.4s (23.4%)

Algorithm

1×

intervals

Results

624.0ms	8000×	body	128	valid
238.0ms	8000×	pre	128	true

Compiler

Compiled 172 to 107 computations (37.8% 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

analyze99.0ms (1.6%)

sample275.0ms (4.5%)

simplify33.0ms (0.5%)

prune4.0ms (0.1%)

localize22.0ms (0.4%)

series257.0ms (4.2%)

rewrite6.0ms (0.1%)

simplify66.0ms (1.1%)

prune63.0ms (1%)

localize22.0ms (0.4%)

series498.0ms (8.1%)

rewrite13.0ms (0.2%)

simplify73.0ms (1.2%)

prune104.0ms (1.7%)

localize30.0ms (0.5%)

series199.0ms (3.2%)

rewrite17.0ms (0.3%)

simplify98.0ms (1.6%)

prune142.0ms (2.3%)

localize53.0ms (0.9%)

series491.0ms (8%)

rewrite39.0ms (0.6%)

simplify157.0ms (2.6%)

prune217.0ms (3.5%)

regimes1.7s (28.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (23.4%)

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