Details

analyze138.0ms (2.8%)

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)

sample1.8s (36.3%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify32.0ms (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
	14.5b	(.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)

localize45.0ms (0.9%)

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)))

series241.0ms (4.8%)

Counts

2 → 36

Calls

2 calls:

238.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
3.0ms	(log1p.f32 (neg.f32 u0))

rewrite9.0ms (0.2%)

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:

7.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
0.0ms	(log1p.f32 (neg.f32 u0))

simplify63.0ms (1.3%)

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

prune64.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Error

0.0b

Counts

94 → 8

Alt Table

Status	Error	Program
	1.9b	(+.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 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)))))
	0.8b	(.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)))))
▶	0.3b	(.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) 1) (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))))
	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (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)))))
	2.4b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 alpha (neg.f32 alpha))) (.f32 alpha (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))

Compiler

Compiled 1828 to 865 computations (52.7% saved)

localize30.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.3b	(.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) 1) (log1p.f32 (neg.f32 u0)))

series236.0ms (4.7%)

Counts

1 → 24

Calls

1 calls:

236.0ms

(*.f32 (*.f32 (*.f32 alpha (neg.f32 alpha)) 1) (log1p.f32 (neg.f32 u0)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary32`
11×	`prod-exp_binary32`
10×	`add-cbrt-cube_binary32`
10×	`pow1_binary32`
6×	`cbrt-unprod_binary32`

Counts

1 → 26

Calls

1 calls:

6.0ms

(*.f32 (*.f32 (*.f32 alpha (neg.f32 alpha)) 1) (log1p.f32 (neg.f32 u0)))

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

932×	`unsub-neg_binary32`
472×	`fma-def_binary32`
368×	`fma-neg_binary32`
331×	`neg-sub0_binary32`
323×	`neg-mul-1_binary32`

Counts

50 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1001
1	287	874
2	1086	821
3	3495	811
4	5423	811

prune73.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Error

0.0b

Counts

106 → 8

Alt Table

Status	Error	Program
	1.9b	(+.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 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)))))
	0.8b	(.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)))))
✓	0.3b	(.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) 1) (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))))
▶	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (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)))))
	2.4b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 alpha (neg.f32 alpha))) (.f32 alpha (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))

Compiler

Compiled 2054 to 1032 computations (49.8% saved)

localize44.0ms (0.9%)

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))))

series561.0ms (11.3%)

Counts

2 → 48

Calls

2 calls:

309.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
252.0ms	(.f32 alpha (.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)))

simplify74.0ms (1.5%)

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

prune150.0ms (3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	154	7	161
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	157	12	169

Error

Counts

169 → 12

Alt Table

Status	Error	Program
	2.5b	(.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 (.f32 (*.f32 alpha (neg.f32 alpha)) 1) (log1p.f32 (neg.f32 u0)))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (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 (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 alpha (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 (sqrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	1.9b	(.f32 alpha (.f32 alpha (+.f32 (fma.f32 1/2 (.f32 u0 u0) (.f32 1/4 (pow.f32 u0 4))) (fma.f32 1/3 (pow.f32 u0 3) u0))))
	0.7b	(.f32 alpha (.f32 (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (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))))
✓	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))))
	0.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))

Compiler

Compiled 2869 to 1330 computations (53.6% saved)

localize68.0ms (1.4%)

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))))

series248.0ms (5%)

Counts

2 → 32

Calls

2 calls:

223.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
25.0ms	(*.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:

7.0ms	(.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)))

simplify121.0ms (2.4%)

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

prune141.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	6	3	9
Picked	1	0	1
Done	1	1	2
Total	170	7	177

Error

Counts

177 → 7

Alt Table

Status	Error	Program
	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)))))
	0.5b	(.f32 (.f32 (sqrt.f32 alpha) (log1p.f32 (neg.f32 u0))) (neg.f32 (pow.f32 alpha 3/2)))
	0.6b	(.f32 (sqrt.f32 alpha) (.f32 (*.f32 (log1p.f32 (neg.f32 u0)) (pow.f32 alpha 3/4)) (neg.f32 (pow.f32 alpha (/.f32 3/2 2)))))
	0.5b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))) (.f32 (sqrt.f32 (cbrt.f32 alpha)) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))))
	0.7b	(.f32 alpha (.f32 (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))
✓	0.3b	(.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) 1) (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 3198 to 1854 computations (42% saved)

regimes648.0ms (13%)

Accuracy

Total 0.3b remaining (91.6%)

Threshold costs 0.3b (91.6%)

Counts

114 → 1

Compiler

Compiled 11703 to 7784 computations (33.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
8×	`neg-sub0_binary32`
8×	`neg-mul-1_binary32`
5×	`+-commutative_binary32`
5×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	22	13
2	36	13
3	43	13
4	48	13
5	51	13
6	52	13
7	50	13

end85.0ms (1.7%)

Compiler: Compiled 154 to 95 computations (38.3% 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

analyze138.0ms (2.8%)

sample1.8s (36.3%)

simplify32.0ms (0.6%)

prune4.0ms (0.1%)

localize45.0ms (0.9%)

series241.0ms (4.8%)

rewrite9.0ms (0.2%)

simplify63.0ms (1.3%)

prune64.0ms (1.3%)

localize30.0ms (0.6%)

series236.0ms (4.7%)

rewrite8.0ms (0.2%)

simplify65.0ms (1.3%)

prune73.0ms (1.5%)

localize44.0ms (0.9%)

series561.0ms (11.3%)

rewrite10.0ms (0.2%)

simplify74.0ms (1.5%)

prune150.0ms (3%)

localize68.0ms (1.4%)

series248.0ms (5%)

rewrite16.0ms (0.3%)

simplify121.0ms (2.4%)

prune141.0ms (2.8%)

regimes648.0ms (13%)

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