Details

analyze110.0ms (2.2%)

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)

sample2.2s (43.6%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify34.0ms (0.7%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

Compiler

Compiled 39 to 26 computations (33.3% saved)

localize26.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

series217.0ms (4.3%)

Counts

1 → 24

Calls

1 calls:

216.0ms

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

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`expm1-log1p-u_binary32`
521×	`log1p-expm1-u_binary32`
447×	`unpow-prod-down_binary32`
318×	`log-prod_binary32`
153×	`pow2_binary32`

Counts

1 → 21

Calls

1 calls:

40.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	163	9
2	1403	9
3	5265	9

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

352×	`times-frac_binary32`
297×	`fma-def_binary32`
250×	`associate-/l*_binary32`
219×	`distribute-rgt-out_binary32`
205×	`unswap-sqr_binary32`

Counts

45 → 47

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	530
1	171	498
2	501	448
3	1692	434
4	4528	432
5	4729	432
6	5008	432

prune37.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	41	6	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	7	48

Error

0.1b

Counts

48 → 7

Alt Table

Status	Error	Program
	8.8b	(pow.f32 (cbrt.f32 (.f32 (.f32 alpha alpha) (log1p.f32 u0))) 3)
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
▶	2.2b	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 u0 (.f32 u0 (+.f32 (*.f32 u0 1/3) 1/2)))))
	2.3b	(+.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)))))
	4.2b	(.f32 alpha (.f32 alpha (fma.f32 1/2 (*.f32 u0 u0) u0)))
	9.4b	(exp.f32 (log.f32 (.f32 (.f32 alpha alpha) (log1p.f32 u0))))
	8.7b	(pow.f32 (*.f32 alpha (sqrt.f32 (log1p.f32 u0))) 2)

Compiler

Compiled 890 to 548 computations (38.4% saved)

localize48.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 u0 (.f32 u0 (+.f32 (*.f32 u0 1/3) 1/2)))
✓	0.3b	(.f32 u0 (+.f32 (.f32 u0 1/3) 1/2))
✓	0.3b	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 u0 (.f32 u0 (+.f32 (*.f32 u0 1/3) 1/2)))))
✓	0.4b	(*.f32 u0 1/3)

series43.0ms (0.8%)

Counts

4 → 60

Calls

4 calls:

35.0ms	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 u0 (.f32 u0 (+.f32 (*.f32 u0 1/3) 1/2)))))
3.0ms	(.f32 u0 (.f32 u0 (+.f32 (*.f32 u0 1/3) 1/2)))
2.0ms	(.f32 u0 (+.f32 (.f32 u0 1/3) 1/2))
2.0ms	(*.f32 u0 1/3)

rewrite83.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

300×	`expm1-udef_binary32`
300×	`log1p-udef_binary32`
171×	`add-sqr-sqrt_binary32`
170×	`log1p-expm1-u_binary32`
170×	`expm1-log1p-u_binary32`

Counts

4 → 90

Calls

4 calls:

75.0ms	(.f32 u0 (.f32 u0 (+.f32 (*.f32 u0 1/3) 1/2)))
75.0ms	(.f32 u0 (+.f32 (.f32 u0 1/3) 1/2))
75.0ms	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 u0 (.f32 u0 (+.f32 (*.f32 u0 1/3) 1/2)))))
75.0ms	(*.f32 u0 1/3)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	50
1	362	48
2	4325	48
3	5043	48

simplify221.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

777×	`*-commutative_binary32`
694×	`unswap-sqr_binary32`
675×	`sqr-pow_binary32`
585×	`distribute-rgt-out_binary32`
363×	`associate-+l+_binary32`

Counts

150 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	978
1	107	946
2	302	890
3	992	871
4	1631	871
5	2341	871
6	3073	871
7	3059	871
8	3150	871
9	3263	871
10	3405	871
11	3242	871
12	3420	871
13	3726	871
14	4024	871
15	4436	871
16	4912	871
17	4908	871

prune135.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	5	0	5
Picked	1	0	1
Done	0	1	1
Total	118	6	124

Error

0.0b

Counts

124 → 6

Alt Table

Status	Error	Program
	2.4b	(/.f32 (.f32 (+.f32 (pow.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) 3) (pow.f32 (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))) 3)) (.f32 alpha alpha)) (+.f32 (pow.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) 2) (.f32 (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))) (-.f32 (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2))) (fma.f32 1/4 (pow.f32 u0 4) u0)))))
	3.0b	(.f32 u0 (.f32 (.f32 alpha alpha) (+.f32 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)) 1)))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
▶	2.2b	(fma.f32 (.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 alpha alpha) (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)))))
	2.5b	(pow.f32 (.f32 alpha (sqrt.f32 (fma.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)))) 2)
	2.2b	(sqrt.f32 (.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)))

Compiler

Compiled 3090 to 1951 computations (36.9% saved)

localize52.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)))
✓	0.3b	(fma.f32 (.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 alpha alpha) (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)))))
✓	0.3b	(*.f32 u0 (fma.f32 u0 1/3 1/2))
✓	0.3b	(.f32 (.f32 alpha alpha) (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))))

series63.0ms (1.2%)

Counts

4 → 72

Calls

4 calls:

33.0ms	(fma.f32 (.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 alpha alpha) (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)))))
24.0ms	(.f32 (.f32 alpha alpha) (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))))
3.0ms	(.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)))
2.0ms	(*.f32 u0 (fma.f32 u0 1/3 1/2))

rewrite127.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

371×	`prod-diff_binary32`
311×	`fma-udef_binary32`
255×	`expm1-udef_binary32`
255×	`log1p-udef_binary32`
214×	`fma-neg_binary32`

Counts

4 → 75

Calls

4 calls:

126.0ms	(.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)))
126.0ms	(fma.f32 (.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 alpha alpha) (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)))))
126.0ms	(*.f32 u0 (fma.f32 u0 1/3 1/2))
126.0ms	(.f32 (.f32 alpha alpha) (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	67
1	312	62
2	3344	62
3	4896	62
4	4909	62
5	4837	62

simplify161.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

694×	`unswap-sqr_binary32`
507×	`associate-+l+_binary32`
443×	`associate-+r+_binary32`
405×	`distribute-rgt-out_binary32`
342×	`*-commutative_binary32`

Counts

147 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	1326
1	118	1247
2	338	1166
3	1121	1164
4	1844	1164
5	3516	1164
6	4633	1164
7	4747	1164
8	4836	1164
9	4949	1164
10	4920	1164

prune120.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	105	7	112

Error

0.0b

Counts

112 → 7

Alt Table

Status	Error	Program
	2.4b	(/.f32 (.f32 (+.f32 (pow.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) 3) (pow.f32 (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))) 3)) (.f32 alpha alpha)) (+.f32 (pow.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) 2) (.f32 (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))) (-.f32 (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2))) (fma.f32 1/4 (pow.f32 u0 4) u0)))))
	3.0b	(.f32 u0 (.f32 (.f32 alpha alpha) (+.f32 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)) 1)))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
✓	2.2b	(fma.f32 (.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 alpha alpha) (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)))))
	5.0b	(fma.f32 (.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 alpha alpha) (log.f32 (pow.f32 (exp.f32 u0) (.f32 u0 (fma.f32 u0 1/3 1/2))))))
	2.5b	(pow.f32 (.f32 alpha (sqrt.f32 (fma.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)))) 2)
▶	2.2b	(sqrt.f32 (.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)))

Compiler

Compiled 2860 to 1752 computations (38.7% saved)

localize53.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)))
	0.3b	(*.f32 u0 (fma.f32 u0 1/3 1/2))
✓	0.4b	(.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2))
✓	0.4b	(pow.f32 (fma.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)

series92.0ms (1.8%)

Counts

3 → 60

Calls

3 calls:

56.0ms

(*.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2))

32.0ms

(sqrt.f32 (*.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)))

3.0ms

(pow.f32 (fma.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)

rewrite107.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`expm1-udef_binary32`
272×	`log1p-udef_binary32`
246×	`log-pow_binary32`
155×	`add-sqr-sqrt_binary32`
155×	`log1p-expm1-u_binary32`

Counts

3 → 65

Calls

3 calls:

105.0ms

(sqrt.f32 (*.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)))

105.0ms

(*.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2))

105.0ms

(pow.f32 (fma.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	80
1	350	75
2	3453	75
3	4922	75
4	4807	75

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary32`
601×	`distribute-rgt-out_binary32`
570×	`associate-l_binary32`
437×	`associate-r_binary32`
304×	`associate-+l+_binary32`

Counts

125 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1618
1	246	1530
2	790	1430
3	3327	1428
4	4965	1428
5	4955	1428

prune149.0ms (2.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	135	7	142

Error

0.0b

Counts

142 → 7

Alt Table

Status	Error	Program
	2.4b	(/.f32 (.f32 (+.f32 (pow.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) 3) (pow.f32 (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))) 3)) (.f32 alpha alpha)) (+.f32 (pow.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) 2) (.f32 (.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2))) (-.f32 (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2))) (fma.f32 1/4 (pow.f32 u0 4) u0)))))
	3.0b	(.f32 u0 (.f32 (.f32 alpha alpha) (+.f32 (.f32 u0 (+.f32 (*.f32 1/3 u0) 1/2)) 1)))
✓	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
✓	2.2b	(fma.f32 (.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 alpha alpha) (.f32 u0 (*.f32 u0 (fma.f32 u0 1/3 1/2)))))
	5.0b	(fma.f32 (.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 alpha alpha) (log.f32 (pow.f32 (exp.f32 u0) (.f32 u0 (fma.f32 u0 1/3 1/2))))))
	2.5b	(pow.f32 (.f32 alpha (sqrt.f32 (fma.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)))) 2)
✓	2.2b	(sqrt.f32 (.f32 (pow.f32 alpha 4) (pow.f32 (fma.f32 u0 (.f32 u0 (fma.f32 u0 1/3 1/2)) (fma.f32 1/4 (pow.f32 u0 4) u0)) 2)))

Compiler

Compiled 3392 to 2427 computations (28.4% saved)

regimes655.0ms (12.9%)

Accuracy

Total 0.2b remaining (75.3%)

Threshold costs 0.2b (75.3%)

Counts

84 → 1

Compiler

Compiled 11786 to 8168 computations (30.7% 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

end127.0ms (2.5%)

Compiler: Compiled 200 to 137 computations (31.5% 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

analyze110.0ms (2.2%)

sample2.2s (43.6%)

simplify34.0ms (0.7%)

prune3.0ms (0.1%)

localize26.0ms (0.5%)

series217.0ms (4.3%)

rewrite40.0ms (0.8%)

simplify69.0ms (1.4%)

prune37.0ms (0.7%)

localize48.0ms (1%)

series43.0ms (0.8%)

rewrite83.0ms (1.6%)

simplify221.0ms (4.3%)

prune135.0ms (2.7%)

localize52.0ms (1%)

series63.0ms (1.2%)

rewrite127.0ms (2.5%)

simplify161.0ms (3.2%)

prune120.0ms (2.4%)

localize53.0ms (1%)

series92.0ms (1.8%)

rewrite107.0ms (2.1%)

simplify86.0ms (1.7%)

prune149.0ms (2.9%)

regimes655.0ms (12.9%)

simplify3.0ms (0.1%)

end127.0ms (2.5%)

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