Details

analyze115.0ms (2.3%)

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)

sample1.7s (34.2%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify31.0ms (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

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)))
	15.2b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Compiler

Compiled 61 to 42 computations (31.1% saved)

localize19.0ms (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)))

series217.0ms (4.3%)

Counts

2 → 36

Calls

2 calls:

214.0ms	(.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))

simplify60.0ms (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

prune58.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Error

0.0b

Counts

94 → 8

Alt Table

Status	Error	Program
✓	0.3b	(.f32 (.f32 alpha (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)))))
	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)))))
	7.5b	(*.f32 u0 (pow.f32 alpha 2))
	2.1b	(+.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))))
▶	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)))))

Compiler

Compiled 1770 to 838 computations (52.7% saved)

localize19.0ms (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))))

series436.0ms (8.6%)

Counts

2 → 48

Calls

2 calls:

226.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
209.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

rewrite9.0ms (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)))

simplify70.0ms (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

prune96.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	161	8	169

Error

Counts

169 → 8

Alt Table

Status	Error	Program
	2.7b	(.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)))))
✓	0.3b	(.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)))))
▶	0.4b	(.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 (log1p.f32 (neg.f32 u0)) (.f32 (neg.f32 alpha) (cbrt.f32 alpha))))
	2.1b	(+.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))))
	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)))))

Compiler

Compiled 2775 to 1283 computations (53.8% saved)

localize28.0ms (0.6%)

Local error

Found 3 expressions with local error:

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

series170.0ms (3.4%)

Counts

2 → 32

Calls

2 calls:

149.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
21.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

rewrite14.0ms (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)))

simplify113.0ms (2.2%)

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 → 129

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

prune117.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	166	8	174

Error

Counts

174 → 8

Alt Table

Status	Error	Program
	2.7b	(.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)))))
✓	0.3b	(.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)))))
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 alpha)) (.f32 (log1p.f32 (neg.f32 u0)) (*.f32 (neg.f32 (pow.f32 alpha 3/2)) (sqrt.f32 (sqrt.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))))
	2.1b	(+.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)))))

Compiler

Compiled 3374 to 1983 computations (41.2% saved)

localize42.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series427.0ms (8.4%)

Counts

4 → 68

Calls

4 calls:

235.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4))
148.0ms	(.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)))))
23.0ms	(sqrt.f32 (pow.f32 alpha 3/2))
21.0ms	(.f32 (.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4)) (neg.f32 (sqrt.f32 (pow.f32 alpha 3/2))))

rewrite28.0ms (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:

8.0ms	(.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)))))
7.0ms	(.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))
1.0ms	(sqrt.f32 (pow.f32 alpha 3/2))

simplify146.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

187 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	303	4185
1	844	3751
2	3031	3237
3	4596	3119
4	4932	3119
5	4938	3119

prune174.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	250	7	257

Error

Counts

257 → 7

Alt Table

Status	Error	Program
✓	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	0.5b	(.f32 (.f32 (log1p.f32 (neg.f32 u0)) (*.f32 (pow.f32 alpha 3/4) (sqrt.f32 alpha))) (neg.f32 (sqrt.f32 (pow.f32 alpha 3/2))))
	2.7b	(.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)))))
✓	0.3b	(.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)))))
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 alpha)) (.f32 (log1p.f32 (neg.f32 u0)) (*.f32 (neg.f32 (pow.f32 alpha 3/2)) (sqrt.f32 (sqrt.f32 alpha)))))
	2.1b	(+.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)))))

Compiler

Compiled 5935 to 3686 computations (37.9% saved)

regimes842.0ms (16.6%)

Accuracy

Total 0.3b remaining (92.4%)

Threshold costs 0.3b (92.4%)

Counts

152 → 1

Compiler

Compiled 17597 to 11988 computations (31.9% 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	8	13
1	18	13
2	28	13
3	36	13
4	41	13
5	44	13
6	45	13
7	45	13

end85.0ms (1.7%)

Compiler: Compiled 160 to 111 computations (30.6% 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

analyze115.0ms (2.3%)

sample1.7s (34.2%)

simplify31.0ms (0.6%)

prune4.0ms (0.1%)

localize19.0ms (0.4%)

series217.0ms (4.3%)

rewrite6.0ms (0.1%)

simplify60.0ms (1.2%)

prune58.0ms (1.1%)

localize19.0ms (0.4%)

series436.0ms (8.6%)

rewrite9.0ms (0.2%)

simplify70.0ms (1.4%)

prune96.0ms (1.9%)

localize28.0ms (0.6%)

series170.0ms (3.4%)

rewrite14.0ms (0.3%)

simplify113.0ms (2.2%)

prune117.0ms (2.3%)

localize42.0ms (0.8%)

series427.0ms (8.4%)

rewrite28.0ms (0.6%)

simplify146.0ms (2.9%)

prune174.0ms (3.4%)

regimes842.0ms (16.6%)

simplify3.0ms (0.1%)

end85.0ms (1.7%)

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