Details

analyze115.0ms (2%)

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
12.4%	12.4%	75.3%	3
12.4%	12.4%	75.3%	4
18.5%	6.2%	75.3%	5
18.5%	6.2%	75.3%	6
21.6%	3.1%	75.3%	7
21.6%	3.1%	75.3%	8
23.2%	1.5%	75.3%	9
23.2%	1.5%	75.3%	10
23.9%	0.8%	75.3%	11
23.9%	0.8%	75.3%	12
24.3%	0.4%	75.3%	13
24.3%	0.4%	75.3%	14

Compiler

Compiled 35 to 18 computations (48.6% saved)

sample1.8s (31.7%)

Results

1.7s

8256×

body

128

valid

Compiler

Compiled 98 to 49 computations (50% saved)

simplify76.0ms (1.3%)

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 (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(/.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

0.2b

(/.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)

localize38.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series196.0ms (3.5%)

Counts

4 → 96

Calls

4 calls:

149.0ms	(/.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)))))
24.0ms	(.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))))
14.0ms	(*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
10.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))

rewrite83.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

726×	`prod-diff_binary32`
198×	`log1p-udef_binary32`
135×	`add-sqr-sqrt_binary32`
129×	`egg-rr`
126×	`add-log-exp_binary32`

Counts

4 → 129

Calls

4 calls:

80.0ms	(*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
80.0ms	(/.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)))))
80.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
80.0ms	(.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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	100
1	267	56
2	3163	56
3	4947	56
0	0	0
1	0	0

simplify109.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-neg_binary32`
372×	`unswap-sqr_binary32`
318×	`distribute-rgt-neg-in_binary32`
290×	`times-frac_binary32`
280×	`distribute-neg-frac_binary32`

Counts

225 → 170

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	83	1990
1	245	1934
2	678	1858
3	2886	1848
4	4741	1848
5	4865	1840
6	5046	1840

prune225.0ms (4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	226	4	230
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	227	5	232

Error

0.0b

Counts

232 → 5

Alt Table

Status	Error	Program
	13.3b	(*.f32 (exp.f32 (/.f32 x s)) (/.f32 (/.f32 1 s) (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2)))
	13.4b	(.f32 (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (pow.f32 (cbrt.f32 (.f32 s (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2))) 2)) (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (cbrt.f32 (*.f32 s (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2)))))
	14.2b	(/.f32 (pow.f32 (E.f32) (/.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)))))
▶	0.2b	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
	12.1b	(/.f32 (/.f32 1 (exp.f32 (/.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 6495 to 2509 computations (61.4% saved)

localize47.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series84.0ms (1.5%)

Counts

3 → 56

Calls

3 calls:

63.0ms	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
12.0ms	(+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)
9.0ms	(exp.f32 (/.f32 (fabs.f32 x) s))

rewrite74.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

678×	`prod-diff_binary32`
225×	`log1p-udef_binary32`
164×	`add-sqr-sqrt_binary32`
155×	`log1p-expm1-u_binary32`
155×	`expm1-log1p-u_binary32`

Counts

3 → 91

Calls

3 calls:

71.0ms	(+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)
71.0ms	(exp.f32 (/.f32 (fabs.f32 x) s))
71.0ms	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	331	33
2	3435	33
3	4992	33
0	0	0
1	0	0

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary32`
567×	`cancel-sign-sub-inv_binary32`
382×	`fma-neg_binary32`
296×	`neg-mul-1_binary32`
228×	`distribute-neg-frac_binary32`

Counts

147 → 115

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	63	1196
1	171	1160
2	476	1140
3	1911	1120
4	4422	1118
5	4979	1110
6	4996	1110
7	4938	1110

prune153.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	145	5	150

Error

0.0b

Counts

150 → 5

Alt Table

Status	Error	Program
	13.4b	(.f32 (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (pow.f32 (cbrt.f32 (.f32 s (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2))) 2)) (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (cbrt.f32 (*.f32 s (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2)))))
	11.5b	(/.f32 (/.f32 1 s) (+.f32 (pow.f32 (E.f32) (/.f32 x s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
▶	0.0b	(/.f32 1 (fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
	14.2b	(/.f32 (pow.f32 (E.f32) (/.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)))))
✓	0.2b	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

Compiler

Compiled 3351 to 1697 computations (49.4% saved)

localize36.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))))
✓	0.0b	(/.f32 1 (fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
	0.0b	(exp.f32 (/.f32 (fabs.f32 x) s))
✓	0.0b	(/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))

series162.0ms (2.9%)

Counts

3 → 56

Calls

3 calls:

95.0ms

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

42.0ms

(fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))))

25.0ms

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

rewrite94.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

578×	`prod-diff_binary32`
211×	`expm1-udef_binary32`
211×	`log1p-udef_binary32`
185×	`log-pow_binary32`
146×	`fma-def_binary32`

Counts

3 → 91

Calls

3 calls:

91.0ms

(fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))))

91.0ms

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

91.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	64
1	258	54
2	3014	54
3	4862	54
4	5183	54
0	0	0
1	0	0

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary32`
417×	`fma-neg_binary32`
363×	`cancel-sign-sub-inv_binary32`
320×	`associate-/r/_binary32`
306×	`associate-/l/_binary32`

Counts

147 → 119

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	1408
1	208	1364
2	539	1324
3	2062	1316
4	4888	1312
5	5026	1312

prune177.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	178	4	182

Error

Counts

182 → 4

Alt Table

Status	Error	Program
▶	11.5b	(/.f32 1 (fma.f32 s (+.f32 (pow.f32 (E.f32) (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
	13.4b	(.f32 (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (pow.f32 (cbrt.f32 (.f32 s (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2))) 2)) (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (cbrt.f32 (*.f32 s (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2)))))
	14.2b	(/.f32 (pow.f32 (E.f32) (/.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)))))
✓	0.2b	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

Compiler

Compiled 4079 to 1725 computations (57.7% saved)

localize48.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 1 (fma.f32 s (+.f32 (pow.f32 (E.f32) (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
	0.0b	(exp.f32 (/.f32 (fabs.f32 x) s))
	0.0b	(/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))
✓	0.0b	(pow.f32 (E.f32) (/.f32 x s))

series76.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

71.0ms	(/.f32 1 (fma.f32 s (+.f32 (pow.f32 (E.f32) (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
5.0ms	(pow.f32 (E.f32) (/.f32 x s))

rewrite118.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

382×	`prod-diff_binary32`
328×	`fma-udef_binary32`
229×	`expm1-udef_binary32`
229×	`log1p-udef_binary32`
221×	`fma-neg_binary32`

Counts

2 → 40

Calls

2 calls:

117.0ms	(/.f32 1 (fma.f32 s (+.f32 (pow.f32 (E.f32) (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
117.0ms	(pow.f32 (E.f32) (/.f32 x s))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	318	30
2	3280	30
3	4893	30
4	4892	30
5	4876	30
0	0	0
1	0	0

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary32`
642×	`times-frac_binary32`
412×	`fma-def_binary32`
337×	`associate-/l*_binary32`
248×	`associate-/r*_binary32`

Counts

88 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1416
1	328	1374
2	1108	1174
3	4408	1174
4	5001	1174

prune152.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	134	3	137

Error

Counts

137 → 3

Alt Table

Status	Error	Program
	0.0b	(/.f32 1 (fma.f32 s (+.f32 (pow.f32 (E.f32) (/.f32 x s)) 2) (/.f32 s (pow.f32 (E.f32) (/.f32 x s)))))
	13.4b	(.f32 (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (pow.f32 (cbrt.f32 (.f32 s (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2))) 2)) (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (cbrt.f32 (*.f32 s (pow.f32 (+.f32 1 (exp.f32 (/.f32 x s))) 2)))))
✓	0.2b	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))

Compiler

Compiled 3425 to 1481 computations (56.8% saved)

regimes1.5s (26.4%)

Accuracy

Total 0.0b remaining (26%)

Threshold costs 0.0b (26%)

Counts

211 → 1

Compiler

Compiled 23615 to 15322 computations (35.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary32`
1×	`1-exp_binary32`
1×	`e-exp-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	16	28
2	15	28

end59.0ms (1%)

Compiler: Compiled 119 to 69 computations (42% saved)

Details

analyze115.0ms (2%)

sample1.8s (31.7%)

simplify76.0ms (1.3%)

prune4.0ms (0.1%)

localize38.0ms (0.7%)

series196.0ms (3.5%)

rewrite83.0ms (1.5%)

simplify109.0ms (1.9%)

prune225.0ms (4%)

localize47.0ms (0.8%)

series84.0ms (1.5%)

rewrite74.0ms (1.3%)

simplify93.0ms (1.7%)

prune153.0ms (2.7%)

localize36.0ms (0.6%)

series162.0ms (2.9%)

rewrite94.0ms (1.7%)

simplify78.0ms (1.4%)

prune177.0ms (3.1%)

localize48.0ms (0.8%)

series76.0ms (1.4%)

rewrite118.0ms (2.1%)

simplify66.0ms (1.2%)

prune152.0ms (2.7%)

regimes1.5s (26.4%)

simplify2.0ms (0%)

end59.0ms (1%)

Profiling