Details

analyze103.0ms (1.9%)

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)

sample273.0ms (5.1%)

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 (0.6%)

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)

localize22.0ms (0.4%)

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)))

series244.0ms (4.6%)

Counts

2 → 36

Calls

2 calls:

241.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
3.0ms	(log1p.f32 (neg.f32 u0))

rewrite7.0ms (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:

5.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
0.0ms	(log1p.f32 (neg.f32 u0))

simplify65.0ms (1.2%)

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 (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Error

0.0b

Counts

93 → 9

Alt Table

Status	Error	Program
	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)))))
	1.6b	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 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)))))
	0.8b	(.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))))
	3.1b	(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)))))
	3.6b	(+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))
	2.4b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	0.7b	(.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)))))

Compiler

Compiled 1816 to 857 computations (52.8% saved)

localize21.0ms (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))))

series527.0ms (9.9%)

Counts

2 → 48

Calls

2 calls:

264.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
264.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

rewrite11.0ms (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:

5.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
4.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

simplify76.0ms (1.4%)

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

prune111.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	156	5	161
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	159	11	170

Error

Counts

170 → 11

Alt Table

Status	Error	Program
	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)))))
	1.6b	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))))
	0.7b	(.f32 alpha (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 (sqrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
▶	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	3.1b	(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))))))
	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)))))
	0.7b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
	0.6b	(.f32 (sqrt.f32 (.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))) (sqrt.f32 (.f32 alpha (*.f32 (neg.f32 alpha) (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))))
	3.6b	(+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))

Compiler

Compiled 2855 to 1313 computations (54% saved)

localize32.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f32 alpha 3/2)
	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))))

series220.0ms (4.1%)

Counts

3 → 44

Calls

3 calls:

172.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
24.0ms	(pow.f32 alpha 3/2)
23.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`associate-r_binary32`
15×	`add-sqr-sqrt_binary32`
13×	`*-un-lft-identity_binary32`
13×	`add-cube-cbrt_binary32`
11×	`add-exp-log_binary32`

Counts

3 → 79

Calls

3 calls:

8.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))
7.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
1.0ms	(pow.f32 alpha 3/2)

simplify127.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-def_binary32`
225×	`associate-r_binary32`
223×	`distribute-rgt-neg-out_binary32`
212×	`fma-neg_binary32`
194×	`associate-l_binary32`

Counts

123 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	212	2247
1	557	2024
2	1779	1760
3	4532	1742
4	4974	1742
5	4995	1742
6	4978	1742

prune154.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	6	3	9
Picked	0	1	1
Done	0	1	1
Total	193	8	201

Error

Counts

201 → 8

Alt Table

Status	Error	Program
	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)))))
	0.7b	(.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)))))
	1.6b	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))))
✓	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	3.1b	(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))))))
	3.6b	(.f32 (sqrt.f32 alpha) (+.f32 (.f32 u0 (sqrt.f32 (pow.f32 alpha 3))) (.f32 1/2 (.f32 (pow.f32 u0 2) (sqrt.f32 (pow.f32 alpha 3))))))
▶	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)))))

Compiler

Compiled 3724 to 2163 computations (41.9% saved)

localize46.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (pow.f32 alpha 3/2))
✓	0.3b	(.f32 (.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4)) (neg.f32 (sqrt.f32 (pow.f32 alpha 3/2))))
✓	0.3b	(*.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4))
✓	0.4b	(.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)))))

series531.0ms (10%)

Counts

4 → 68

Calls

4 calls:

280.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4))
197.0ms	(.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)))))
27.0ms	(sqrt.f32 (pow.f32 alpha 3/2))
27.0ms	(.f32 (.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4)) (neg.f32 (sqrt.f32 (pow.f32 alpha 3/2))))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary32`
32×	`associate-r_binary32`
25×	`add-sqr-sqrt_binary32`
24×	`sqrt-prod_binary32`
22×	`prod-exp_binary32`

Counts

4 → 119

Calls

4 calls:

11.0ms	(.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)))))
8.0ms	(.f32 (.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4)) (neg.f32 (sqrt.f32 (pow.f32 alpha 3/2))))
4.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4))
2.0ms	(sqrt.f32 (pow.f32 alpha 3/2))

simplify180.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

423×	`associate-l_binary32`
402×	`associate-r_binary32`
361×	`distribute-rgt-neg-out_binary32`
315×	`fma-neg_binary32`
239×	`*-commutative_binary32`

Counts

187 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	303	4185
1	844	3751
2	3031	3237
3	4591	3095
4	4927	3095
5	4995	3095
6	4940	3095

prune188.0ms (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	248	8	256

Error

Counts

256 → 8

Alt Table

Status	Error	Program
	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)))))
	0.7b	(.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)))))
	1.6b	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))))
✓	0.5b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	3.1b	(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))))))
	3.6b	(.f32 (sqrt.f32 alpha) (+.f32 (.f32 u0 (sqrt.f32 (pow.f32 alpha 3))) (.f32 1/2 (.f32 (pow.f32 u0 2) (sqrt.f32 (pow.f32 alpha 3))))))
✓	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)))))

Compiler

Compiled 5916 to 3672 computations (37.9% saved)

regimes812.0ms (15.3%)

Accuracy

Total 0.3b remaining (91.2%)

Threshold costs 0.3b (91.2%)

Counts

140 → 1

Compiler

Compiled 14648 to 10284 computations (29.8% saved)

simplify3.0ms (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	11	18
1	21	18
2	34	18
3	44	18
4	49	18
5	51	18
6	51	18

end0.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

sample1.4s (26.4%)

Algorithm

1×

intervals

Results

581.0ms	8000×	body	128	valid
225.0ms	8000×	pre	128	true

Compiler

Compiled 194 to 130 computations (33% 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

analyze103.0ms (1.9%)

sample273.0ms (5.1%)

simplify33.0ms (0.6%)

prune3.0ms (0.1%)

localize22.0ms (0.4%)

series244.0ms (4.6%)

rewrite7.0ms (0.1%)

simplify65.0ms (1.2%)

prune69.0ms (1.3%)

localize21.0ms (0.4%)

series527.0ms (9.9%)

rewrite11.0ms (0.2%)

simplify76.0ms (1.4%)

prune111.0ms (2.1%)

localize32.0ms (0.6%)

series220.0ms (4.1%)

rewrite20.0ms (0.4%)

simplify127.0ms (2.4%)

prune154.0ms (2.9%)

localize46.0ms (0.9%)

series531.0ms (10%)

rewrite33.0ms (0.6%)

simplify180.0ms (3.4%)

prune188.0ms (3.5%)

regimes812.0ms (15.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (26.4%)

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