Details

analyze1.3s (15.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	24.7%	75.3%	0
0%	24.7%	75.3%	1
0%	24.7%	75.3%	2
0%	24.7%	75.3%	3
0%	24.7%	75.3%	4
6.2%	18.5%	75.3%	5
7.7%	17%	75.3%	6
11.6%	13.1%	75.3%	7
12.7%	12%	75.3%	8
14.9%	9.8%	75.3%	9
15.5%	9.2%	75.3%	10
16.3%	8.4%	75.3%	11
16.7%	8.1%	75.3%	12
17%	7.7%	75.3%	13
17.2%	7.5%	75.3%	14

Compiler

Compiled 35 to 18 computations (48.6% saved)

sample1.9s (22.8%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 98 to 49 computations (50% saved)

simplify77.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-def_binary32`
440×	`times-frac_binary32`
349×	`distribute-rgt-in_binary32`
300×	`fma-neg_binary32`
273×	`distribute-rgt-out_binary32`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	38	43
2	82	41
3	181	41
4	357	39
5	772	30
6	2292	29
7	3341	29
8	4243	29
9	4922	29
10	4875	29

prune4.0ms (0%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
▶	0.1b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))

Status

Error

Program

0.3b

(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

▶

0.1b

(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))

Compiler

Compiled 142 to 75 computations (47.2% saved)

localize42.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))
✓	0.0b	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
✓	0.0b	(.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
✓	0.1b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))

series196.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

143.0ms	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
29.0ms	(.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
13.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))
11.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))

rewrite73.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`exp-prod_binary32`
57×	`times-frac_binary32`
48×	`add-sqr-sqrt_binary32`
46×	`*-un-lft-identity_binary32`
42×	`add-cube-cbrt_binary32`

Counts

4 → 153

Calls

4 calls:

27.0ms	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
16.0ms	(.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
8.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
6.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))

simplify140.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

857×	`distribute-rgt-in_binary32`
838×	`fma-def_binary32`
248×	`times-frac_binary32`
170×	`associate-l_binary32`
162×	`associate-/l*_binary32`

Counts

249 → 261

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	306	5813
1	750	5303
2	2630	5170
3	5339	5170

prune663.0ms (8.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	493	4	497
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	494	5	499

Error

0.0b

Counts

499 → 5

Alt Table

Status	Error	Program
	0.3b	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
	0.1b	(/.f32 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
	0.1b	(/.f32 1 (/.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) 1) 2)) (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))))
▶	0.1b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 s (+.f32 1 (+.f32 (.f32 2 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
	0.7b	(exp.f32 (-.f32 (neg.f32 (/.f32 (fabs.f32 x) s)) (fma.f32 2 (log1p.f32 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))) (log.f32 s))))

Compiler

Compiled 17584 to 5396 computations (69.3% saved)

localize64.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
✓	0.0b	(.f32 s (+.f32 1 (+.f32 (.f32 2 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s))) 2))))
✓	0.1b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 s (+.f32 1 (+.f32 (.f32 2 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
✓	0.1b	(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)

series269.0ms (3.3%)

Counts

3 → 40

Calls

3 calls:

204.0ms

(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))

46.0ms

(*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2))))

19.0ms

(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary32`
11×	`add-sqr-sqrt_binary32`
10×	`add-cbrt-cube_binary32`
9×	`add-cube-cbrt_binary32`
8×	`add-exp-log_binary32`

Counts

3 → 74

Calls

3 calls:

20.0ms

(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))

8.0ms

(*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2))))

2.0ms

(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)

simplify117.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

554×	`distribute-rgt-in_binary32`
516×	`distribute-lft-in_binary32`
453×	`fma-def_binary32`
187×	`fma-neg_binary32`
152×	`associate-/l/_binary32`

Counts

114 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	4153
1	450	3512
2	1596	3343
3	4648	3343
4	4961	3343

prune332.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	247	4	251

Error

0.0b

Counts

251 → 4

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (*.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s) (exp.f32 (/.f32 (fabs.f32 x) s))))
	0.2b	(/.f32 (/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s))) (neg.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s)))
✓	0.1b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 s (+.f32 1 (+.f32 (.f32 2 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
	0.7b	(exp.f32 (-.f32 (neg.f32 (/.f32 (fabs.f32 x) s)) (fma.f32 2 (log1p.f32 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))) (log.f32 s))))

Compiler

Compiled 9703 to 4745 computations (51.1% saved)

localize53.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (/.f32 (fabs.f32 x) s))
✓	0.0b	(exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))
✓	0.1b	(pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)
✓	0.2b	(*.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s) (exp.f32 (/.f32 (fabs.f32 x) s)))

series156.0ms (1.9%)

Counts

4 → 64

Calls

4 calls:

102.0ms	(*.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s) (exp.f32 (/.f32 (fabs.f32 x) s)))
32.0ms	(pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)
12.0ms	(exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))
10.0ms	(exp.f32 (/.f32 (fabs.f32 x) s))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`exp-prod_binary32`
84×	`times-frac_binary32`
79×	`add-sqr-sqrt_binary32`
65×	`*-un-lft-identity_binary32`
65×	`add-cube-cbrt_binary32`

Counts

4 → 166

Calls

4 calls:

10.0ms	(*.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s) (exp.f32 (/.f32 (fabs.f32 x) s)))
6.0ms	(exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))
6.0ms	(pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)
4.0ms	(exp.f32 (/.f32 (fabs.f32 x) s))

simplify140.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

434×	`associate-l_binary32`
301×	`times-frac_binary32`
300×	`associate-/l*_binary32`
284×	`exp-prod_binary32`
267×	`fma-def_binary32`

Counts

230 → 268

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	4328
1	624	3983
2	1604	3686
3	4615	3686
4	4922	3686

prune398.0ms (4.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	319	4	323

Error

0.0b

Counts

323 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f32 1 (*.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s) (exp.f32 (/.f32 (fabs.f32 x) s))))
▶	0.2b	(/.f32 (/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s))) (neg.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s)))
✓	0.1b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 s (+.f32 1 (+.f32 (.f32 2 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
	0.7b	(exp.f32 (-.f32 (neg.f32 (/.f32 (fabs.f32 x) s)) (fma.f32 2 (log1p.f32 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))) (log.f32 s))))

Compiler

Compiled 11083 to 3746 computations (66.2% saved)

localize57.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))
✓	0.1b	(/.f32 (/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s))) (neg.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s)))
	0.1b	(pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)
✓	0.1b	(/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s)))

series274.0ms (3.3%)

Counts

2 → 32

Calls

2 calls:

247.0ms

(/.f32 (/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s))) (neg.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s)))

27.0ms

(/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s)))

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`times-frac_binary32`
129×	`*-un-lft-identity_binary32`
129×	`add-sqr-sqrt_binary32`
129×	`add-cube-cbrt_binary32`
42×	`distribute-lft-neg-in_binary32`

Counts

2 → 199

Calls

2 calls:

13.0ms

(/.f32 (/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s))) (neg.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s)))

7.0ms

(/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s)))

simplify441.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

938×	`times-frac_binary32`
492×	`fma-def_binary32`
343×	`associate-/l/_binary32`
307×	`associate-/r*_binary32`
144×	`distribute-rgt-in_binary32`

Counts

231 → 327

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	350	15455
1	840	14895
2	2375	14850
3	4482	14847
4	4995	14847
5	4902	14847

prune629.0ms (7.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	498	0	498
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	498	4	502

Error

0.0b

Counts

502 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f32 1 (*.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s) (exp.f32 (/.f32 (fabs.f32 x) s))))
✓	0.2b	(/.f32 (/.f32 -1 (exp.f32 (/.f32 (fabs.f32 x) s))) (neg.f32 (fma.f32 s (fma.f32 2 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s))) (pow.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) -2)) s)))
✓	0.1b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 s (+.f32 1 (+.f32 (.f32 2 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
	0.7b	(exp.f32 (-.f32 (neg.f32 (/.f32 (fabs.f32 x) s)) (fma.f32 2 (log1p.f32 (exp.f32 (neg.f32 (/.f32 (fabs.f32 x) s)))) (log.f32 s))))

Compiler

Compiled 23295 to 8900 computations (61.8% saved)

regimes690.0ms (8.4%)

Accuracy

Total 0.1b remaining (58.7%)

Threshold costs 0.1b (58.7%)

Counts

132 → 1

Compiler

Compiled 18133 to 10589 computations (41.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary32`
4×	`*-commutative_binary32`
2×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
1×	`distribute-neg-frac_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	24	46
2	27	46
3	30	46
4	33	46
5	34	46
6	33	46

end86.0ms (1%)

Compiler: Compiled 169 to 95 computations (43.8% saved)

Details

analyze1.3s (15.9%)

sample1.9s (22.8%)

simplify77.0ms (0.9%)

prune4.0ms (0%)

localize42.0ms (0.5%)

series196.0ms (2.4%)

rewrite73.0ms (0.9%)

simplify140.0ms (1.7%)

prune663.0ms (8.1%)

localize64.0ms (0.8%)

series269.0ms (3.3%)

rewrite35.0ms (0.4%)

simplify117.0ms (1.4%)

prune332.0ms (4%)

localize53.0ms (0.6%)

series156.0ms (1.9%)

rewrite41.0ms (0.5%)

simplify140.0ms (1.7%)

prune398.0ms (4.8%)

localize57.0ms (0.7%)

series274.0ms (3.3%)

rewrite60.0ms (0.7%)

simplify441.0ms (5.4%)

prune629.0ms (7.6%)

regimes690.0ms (8.4%)

simplify3.0ms (0%)

end86.0ms (1%)

Profiling