Details

analyze144.0ms (2.7%)

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 (32.6%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify42.0ms (0.8%)

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)))
	14.4b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 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)))

series247.0ms (4.7%)

Counts

2 → 36

Calls

2 calls:

244.0ms	(.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))

simplify63.0ms (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

prune62.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

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

Error

0.0b

Counts

94 → 9

Alt Table

Status	Error	Program
	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)))))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
	2.7b	(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)))))
	2.4b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	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)))))
	7.8b	(*.f32 u0 (pow.f32 alpha 2))
▶	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 1794 to 856 computations (52.3% 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 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
✓	0.2b	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

series484.0ms (9.1%)

Counts

2 → 48

Calls

2 calls:

252.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
232.0ms	(.f32 alpha (.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:

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

simplify74.0ms (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

prune103.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	160	10	170

Error

Counts

170 → 10

Alt Table

Status	Error	Program
	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)))))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
	2.7b	(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 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.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 alpha (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 (sqrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (neg.f32 (cbrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.4b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	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)))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 2815 to 1310 computations (53.5% saved)

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.2b	(.f32 alpha (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 (sqrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
✓	0.3b	(.f32 (sqrt.f32 alpha) (.f32 (neg.f32 (sqrt.f32 alpha)) (log1p.f32 (neg.f32 u0))))
✓	0.4b	(*.f32 (neg.f32 (sqrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))

series360.0ms (6.8%)

Counts

3 → 52

Calls

3 calls:

179.0ms

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

163.0ms

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

18.0ms

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

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`associate-l_binary32`
19×	`add-cbrt-cube_binary32`
19×	`add-exp-log_binary32`
19×	`pow1_binary32`
14×	`add-sqr-sqrt_binary32`

Counts

3 → 82

Calls

3 calls:

8.0ms

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

6.0ms

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

4.0ms

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

simplify122.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

527×	`distribute-rgt-neg-out_binary32`
463×	`distribute-lft-neg-out_binary32`
327×	`fma-neg_binary32`
308×	`associate-r_binary32`
308×	`times-frac_binary32`

Counts

134 → 190

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	2474
1	636	2194
2	2134	2182
3	4527	2176
4	4989	2176
5	4973	2176

prune139.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	228	9	237

Error

Counts

237 → 9

Alt Table

Status	Error	Program
	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)))))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
	2.7b	(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)))))
	0.7b	(.f32 alpha (.f32 (sqrt.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 alpha))) (sqrt.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 alpha)))))
	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	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	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)))))
▶	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 4583 to 1822 computations (60.2% saved)

localize31.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.3b	(.f32 (sqrt.f32 alpha) (.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0))))
✓	0.3b	(*.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0)))

series189.0ms (3.6%)

Counts

2 → 32

Calls

2 calls:

165.0ms	(.f32 (sqrt.f32 alpha) (.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0))))
23.0ms	(*.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`associate-l_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`*-un-lft-identity_binary32`
10×	`add-cube-cbrt_binary32`
9×	`add-cbrt-cube_binary32`

Counts

2 → 60

Calls

2 calls:

6.0ms	(.f32 (sqrt.f32 alpha) (.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0))))
5.0ms	(*.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0)))

simplify101.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary32`
496×	`*-commutative_binary32`
235×	`fma-neg_binary32`
223×	`distribute-rgt-neg-out_binary32`
206×	`distribute-lft-neg-out_binary32`

Counts

92 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	1993
1	508	1773
2	1620	1630
3	4476	1544
4	4863	1544
5	4948	1544

prune146.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	183	8	191

Error

Counts

191 → 8

Alt Table

Status	Error	Program
	2.7b	(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)))))
	0.7b	(.f32 alpha (.f32 (sqrt.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 alpha))) (sqrt.f32 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 alpha)))))
	0.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 (.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0))))))
	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)))))
	0.6b	(.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 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))) (.f32 (sqrt.f32 (cbrt.f32 alpha)) (.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0)))))
✓	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (neg.f32 (pow.f32 alpha 3/2)) (log1p.f32 (neg.f32 u0))))
✓	0.4b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 3530 to 2049 computations (42% saved)

regimes1.0s (19.1%)

Accuracy

Total 0.3b remaining (92.9%)

Threshold costs 0.3b (92.9%)

Counts

154 → 1

Compiler

Compiled 17262 to 11326 computations (34.4% 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

end106.0ms (2%)

Compiler: Compiled 194 to 123 computations (36.6% 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

analyze144.0ms (2.7%)

sample1.7s (32.6%)

simplify42.0ms (0.8%)

prune4.0ms (0.1%)

localize22.0ms (0.4%)

series247.0ms (4.7%)

rewrite6.0ms (0.1%)

simplify63.0ms (1.2%)

prune62.0ms (1.2%)

localize22.0ms (0.4%)

series484.0ms (9.1%)

rewrite11.0ms (0.2%)

simplify74.0ms (1.4%)

prune103.0ms (1.9%)

localize29.0ms (0.6%)

series360.0ms (6.8%)

rewrite23.0ms (0.4%)

simplify122.0ms (2.3%)

prune139.0ms (2.6%)

localize31.0ms (0.6%)

series189.0ms (3.6%)

rewrite26.0ms (0.5%)

simplify101.0ms (1.9%)

prune146.0ms (2.8%)

regimes1.0s (19.1%)

simplify3.0ms (0.1%)

end106.0ms (2%)

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