Details

analyze109.0ms (1.7%)

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)

sample1.6s (25.5%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 98 to 49 computations (50% saved)

simplify89.0ms (1.4%)

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)

localize40.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series157.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

109.0ms	(/.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)))))
26.0ms	(.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 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
10.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))

rewrite92.0ms (1.5%)

Algorithm

1×	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:

89.0ms	(/.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)))))
89.0ms	(*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
89.0ms	(.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))))
89.0ms	(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))

Iterations

Useful iterations: 1 (0.0ms)

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

simplify118.0ms (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

prune288.0ms (4.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

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

Error

0.0b

Counts

232 → 5

Alt Table

Status	Error	Program
✓	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)))))
▶	0.0b	(/.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)))))
	11.6b	(/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))
	4.7b	(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
	11.6b	(.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 2) (.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) (/.f32 (/.f32 1 s) (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))))

Compiler

Compiled 6447 to 2481 computations (61.5% saved)

localize77.0ms (1.2%)

Local error

Found 4 expressions with local error:

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

series58.0ms (0.9%)

Counts

3 → 24

Calls

3 calls:

29.0ms

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

18.0ms

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

10.0ms

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

rewrite103.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`prod-diff_binary32`
351×	`fma-def_binary32`
218×	`fma-neg_binary32`
184×	`expm1-udef_binary32`
184×	`log1p-udef_binary32`

Counts

3 → 100

Calls

3 calls:

101.0ms

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

101.0ms

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

101.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	255	32
2	2637	32
3	4850	32
4	5047	32

simplify36.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

706×	`associate-/r*_binary32`
568×	`fma-def_binary32`
310×	`fma-neg_binary32`
262×	`associate-/r/_binary32`
256×	`distribute-rgt-neg-in_binary32`

Counts

124 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	478
1	133	450
2	412	416
3	1753	400
4	5549	400

prune243.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	184	5	189

Error

0.0b

Counts

189 → 5

Alt Table

Status	Error	Program
✓	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)))))
✓	0.0b	(/.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)))))
	11.6b	(/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))
▶	4.7b	(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
	11.6b	(.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 2) (.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) (/.f32 (/.f32 1 s) (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))))

Compiler

Compiled 6111 to 2854 computations (53.3% saved)

localize38.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)
✓	0.7b	(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
✓	0.9b	(log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))
✓	4.0b	(-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))))

series596.0ms (9.5%)

Counts

4 → 96

Calls

4 calls:

443.0ms	(log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))
108.0ms	(-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))))
35.0ms	(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
9.0ms	(pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)

rewrite107.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`prod-diff_binary32`
228×	`log1p-udef_binary32`
209×	`egg-rr`
130×	`add-sqr-sqrt_binary32`
127×	`log1p-expm1-u_binary32`

Counts

4 → 209

Calls

4 calls:

101.0ms	(pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)
101.0ms	(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
101.0ms	(log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))
101.0ms	(-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	75
1	272	73
2	3302	73
3	5074	73

simplify108.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary32`
561×	`fma-neg_binary32`
353×	`associate-/l*_binary32`
345×	`fma-def_binary32`
314×	`associate-/r*_binary32`

Counts

305 → 282

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2384
1	459	2203
2	1360	2013
3	4087	1950
4	4932	1950
5	5033	1950

prune236.0ms (3.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	2	0	2
Picked	0	1	1
Done	0	2	2
Total	283	4	287

Error

0.0b

Counts

287 → 4

Alt Table

Status	Error	Program
✓	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)))))
✓	0.0b	(/.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)))))
✓	4.7b	(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
▶	11.6b	(/.f32 (/.f32 (exp.f32 (/.f32 x s)) (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)) s)

Compiler

Compiled 8902 to 4217 computations (52.6% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (exp.f32 (/.f32 x s)) 1)
✓	0.0b	(exp.f32 (/.f32 x s))
	0.1b	(pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)
✓	1.1b	(/.f32 (exp.f32 (/.f32 x s)) (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))

series59.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

49.0ms	(/.f32 (exp.f32 (/.f32 x s)) (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))
5.0ms	(+.f32 (exp.f32 (/.f32 x s)) 1)
5.0ms	(exp.f32 (/.f32 x s))

rewrite97.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

493×	`prod-diff_binary32`
477×	`log-prod_binary32`
176×	`expm1-udef_binary32`
176×	`log1p-udef_binary32`
159×	`fma-def_binary32`

Counts

3 → 111

Calls

3 calls:

95.0ms	(+.f32 (exp.f32 (/.f32 x s)) 1)
95.0ms	(exp.f32 (/.f32 x s))
95.0ms	(/.f32 (exp.f32 (/.f32 x s)) (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	213	34
2	2517	34
3	4947	34
4	5451	34

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Rules

947×	`fma-neg_binary32`
723×	`fma-def_binary32`
333×	`cancel-sign-sub-inv_binary32`
296×	`times-frac_binary32`
287×	`associate-/r/_binary32`

Counts

171 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	1002
1	130	978
2	365	948
3	1744	903
4	4499	903
5	5286	903

prune217.0ms (3.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	215	4	219

Error

0.0b

Counts

219 → 4

Alt Table

Status	Error	Program
✓	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)))))
✓	0.0b	(/.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)))))
✓	4.7b	(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
✓	11.6b	(/.f32 (/.f32 (exp.f32 (/.f32 x s)) (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)) s)

Compiler

Compiled 4834 to 2262 computations (53.2% saved)

regimes1.3s (21.5%)

Accuracy

Total 0.0b remaining (33.3%)

Threshold costs 0.0b (33.3%)

Counts

259 → 1

Compiler

Compiled 30222 to 19423 computations (35.7% 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-frac-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	46
1	28	46
2	31	46
3	33	46
4	34	46
5	33	46

end349.0ms (5.6%)

Compiler: Compiled 155 to 87 computations (43.9% saved)

Details

analyze109.0ms (1.7%)

sample1.6s (25.5%)

simplify89.0ms (1.4%)

prune4.0ms (0.1%)

localize40.0ms (0.6%)

series157.0ms (2.5%)

rewrite92.0ms (1.5%)

simplify118.0ms (1.9%)

prune288.0ms (4.6%)

localize77.0ms (1.2%)

series58.0ms (0.9%)

rewrite103.0ms (1.7%)

simplify36.0ms (0.6%)

prune243.0ms (3.9%)

localize38.0ms (0.6%)

series596.0ms (9.5%)

rewrite107.0ms (1.7%)

simplify108.0ms (1.7%)

prune236.0ms (3.8%)

localize30.0ms (0.5%)

series59.0ms (0.9%)

rewrite97.0ms (1.6%)

simplify63.0ms (1%)

prune217.0ms (3.5%)

regimes1.3s (21.5%)

simplify3.0ms (0%)

end349.0ms (5.6%)

Profiling