Details

analyze126.0ms (2.4%)

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)

sample1.4s (27.7%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 98 to 49 computations (50% saved)

simplify79.0ms (1.5%)

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

0.2b

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)))
	0.2b	(/.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)))

0.2b

(/.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 (0.8%)

Local error

Found 4 expressions with local error:

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

series105.0ms (2%)

Counts

4 → 80

Calls

4 calls:

64.0ms	(/.f32 (/.f32 1 s) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2)))
21.0ms	(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2))
10.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
10.0ms	(exp.f32 (/.f32 (fabs.f32 x) s))

rewrite83.0ms (1.6%)

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

4 → 114

Calls

4 calls:

80.0ms	(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) 2))
80.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
80.0ms	(exp.f32 (/.f32 (fabs.f32 x) s))
80.0ms	(/.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	68
1	331	42
2	3435	42
3	4992	42
0	0	0
1	0	0

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

567×	`cancel-sign-sub-inv_binary32`
382×	`times-frac_binary32`
368×	`unswap-sqr_binary32`
292×	`fma-neg_binary32`
228×	`distribute-neg-frac_binary32`

Counts

194 → 125

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	75	1698
1	202	1650
2	571	1630
3	2676	1596
4	4940	1596
5	4978	1588
6	4936	1588

prune134.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	122	5	127

Error

0.1b

Counts

127 → 5

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))
	0.2b	(/.f32 (/.f32 1 s) (exp.f32 (log.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	0.2b	(/.f32 (/.f32 1 s) (expm1.f32 (log1p.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	0.8b	(expm1.f32 (log1p.f32 (/.f32 (/.f32 1 s) (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	0.2b	(.f32 (/.f32 1 (sqrt.f32 (+.f32 2 (.f32 2 (cosh.f32 (/.f32 x s)))))) (/.f32 (/.f32 1 s) (sqrt.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))

Compiler

Compiled 2974 to 1646 computations (44.7% saved)

localize32.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series169.0ms (3.2%)

Counts

3 → 56

Calls

3 calls:

99.0ms

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

45.0ms

(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)))

rewrite93.0ms (1.8%)

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 → 88

Calls

3 calls:

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)))

91.0ms

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

simplify69.0ms (1.3%)

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

144 → 116

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	1408
1	208	1364
2	538	1324
3	2062	1316
4	4888	1312
5	5026	1312

prune188.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	172	5	177

Error

0.1b

Counts

177 → 5

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (expm1.f32 (log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))))))
	0.2b	(.f32 (/.f32 1 (sqrt.f32 (+.f32 2 (.f32 2 (cosh.f32 (/.f32 x s)))))) (/.f32 (/.f32 1 s) (sqrt.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	26.9b	(/.f32 1 (/.f32 (+.f32 (pow.f32 (.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2)) 3) (pow.f32 (/.f32 s (exp.f32 (/.f32 x s))) 3)) (fma.f32 (.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2)) (.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2)) (-.f32 (pow.f32 (/.f32 s (exp.f32 (/.f32 x s))) 2) (.f32 (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2)) (/.f32 s (exp.f32 (/.f32 x s))))))))
	0.2b	(/.f32 (/.f32 1 s) (exp.f32 (log.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	0.2b	(/.f32 (/.f32 1 s) (expm1.f32 (log1p.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))

Compiler

Compiled 4092 to 1758 computations (57% saved)

localize35.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f32 (log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))))
✓	0.1b	(exp.f32 (/.f32 x s))
✓	0.1b	(fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))
✓	2.1b	(log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))))

series567.0ms (10.8%)

Counts

4 → 84

Calls

4 calls:

495.0ms	(log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))))
35.0ms	(expm1.f32 (log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))))
32.0ms	(fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))
5.0ms	(exp.f32 (/.f32 x s))

rewrite102.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

670×	`prod-diff_binary32`
200×	`expm1-udef_binary32`
200×	`log1p-udef_binary32`
176×	`log-pow_binary32`
155×	`fma-def_binary32`

Counts

4 → 128

Calls

4 calls:

98.0ms	(expm1.f32 (log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))))
98.0ms	(exp.f32 (/.f32 x s))
98.0ms	(fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))
98.0ms	(log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	71
1	217	71
2	2819	71
3	4955	71
4	5478	71
0	0	0
1	0	0

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

635×	`associate-/l*_binary32`
274×	`fma-def_binary32`
263×	`cancel-sign-sub-inv_binary32`
241×	`associate-+r+_binary32`
195×	`+-commutative_binary32`

Counts

212 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	2581
1	708	2547
2	2759	2469
3	5117	2469

prune193.0ms (3.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	174	5	179

Error

0.1b

Counts

179 → 5

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (expm1.f32 (log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (pow.f32 (exp.f32 1) (/.f32 x s)))))))
	0.2b	(.f32 (/.f32 1 (sqrt.f32 (+.f32 2 (.f32 2 (cosh.f32 (/.f32 x s)))))) (/.f32 (/.f32 1 s) (sqrt.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	29.2b	(/.f32 1 (expm1.f32 (-.f32 (log1p.f32 (pow.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))) 3)) (log.f32 (+.f32 1 (-.f32 (pow.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))) 2) (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))))))))
	0.2b	(/.f32 (/.f32 1 s) (exp.f32 (log.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	0.2b	(/.f32 (/.f32 1 s) (expm1.f32 (log1p.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))

Compiler

Compiled 5479 to 2862 computations (47.8% saved)

localize44.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f32 (exp.f32 1) (/.f32 x s))
	0.1b	(exp.f32 (/.f32 x s))
✓	0.1b	(fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (pow.f32 (exp.f32 1) (/.f32 x s))))
✓	2.1b	(log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (pow.f32 (exp.f32 1) (/.f32 x s)))))

series550.0ms (10.5%)

Counts

3 → 72

Calls

3 calls:

507.0ms

(log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (pow.f32 (exp.f32 1) (/.f32 x s)))))

37.0ms

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

6.0ms

(pow.f32 (exp.f32 1) (/.f32 x s))

rewrite118.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

424×	`prod-diff_binary32`
340×	`fma-udef_binary32`
224×	`fma-neg_binary32`
217×	`expm1-udef_binary32`
217×	`log1p-udef_binary32`

Counts

3 → 60

Calls

3 calls:

116.0ms

(pow.f32 (exp.f32 1) (/.f32 x s))

116.0ms

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

116.0ms

(log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (pow.f32 (exp.f32 1) (/.f32 x s)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	252	50
2	3062	50
3	4829	50
4	4834	50
5	4985	50
0	0	0
1	0	0

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

635×	`associate-/l*_binary32`
274×	`fma-def_binary32`
263×	`cancel-sign-sub-inv_binary32`
241×	`associate-+r+_binary32`
195×	`+-commutative_binary32`

Counts

132 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	2149
1	708	2121
2	2759	2043
3	5117	2043

prune145.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Error

0.1b

Counts

140 → 5

Alt Table

Status	Error	Program
✓	0.2b	(/.f32 1 (expm1.f32 (log1p.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (pow.f32 (exp.f32 1) (/.f32 x s)))))))
	0.2b	(.f32 (/.f32 1 (sqrt.f32 (+.f32 2 (.f32 2 (cosh.f32 (/.f32 x s)))))) (/.f32 (/.f32 1 s) (sqrt.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	29.2b	(/.f32 1 (expm1.f32 (-.f32 (log1p.f32 (pow.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))) 3)) (log.f32 (+.f32 1 (-.f32 (pow.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))) 2) (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))))))))
	0.2b	(/.f32 (/.f32 1 s) (exp.f32 (log.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))
	0.2b	(/.f32 (/.f32 1 s) (expm1.f32 (log1p.f32 (+.f32 2 (*.f32 2 (cosh.f32 (/.f32 x s)))))))

Compiler

Compiled 4330 to 2445 computations (43.5% saved)

regimes595.0ms (11.4%)

Accuracy

Total 0.0b remaining (28.2%)

Threshold costs 0.0b (28.2%)

Counts

130 → 1

Compiler

Compiled 13626 to 9458 computations (30.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary32`
1×	`sub-neg_binary32`
1×	`exp-1-e_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	25	37
2	26	37
3	24	37

end95.0ms (1.8%)

Compiler: Compiled 188 to 124 computations (34% saved)

Details

analyze126.0ms (2.4%)

sample1.4s (27.7%)

simplify79.0ms (1.5%)

prune4.0ms (0.1%)

localize42.0ms (0.8%)

series105.0ms (2%)

rewrite83.0ms (1.6%)

simplify94.0ms (1.8%)

prune134.0ms (2.6%)

localize32.0ms (0.6%)

series169.0ms (3.2%)

rewrite93.0ms (1.8%)

simplify69.0ms (1.3%)

prune188.0ms (3.6%)

localize35.0ms (0.7%)

series567.0ms (10.8%)

rewrite102.0ms (1.9%)

simplify66.0ms (1.3%)

prune193.0ms (3.7%)

localize44.0ms (0.8%)

series550.0ms (10.5%)

rewrite118.0ms (2.2%)

simplify58.0ms (1.1%)

prune145.0ms (2.8%)

regimes595.0ms (11.4%)

simplify2.0ms (0%)

end95.0ms (1.8%)

Profiling