Details

analyze115.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	2.1%	97.9%	0
0%	2.1%	97.9%	1
1%	1%	97.9%	2
1%	1%	97.9%	3
1.5%	0.5%	97.9%	4
1.5%	0.5%	97.9%	5
1.8%	0.3%	97.9%	6
1.8%	0.3%	97.9%	7
1.9%	0.1%	97.9%	8
1.9%	0.1%	97.9%	9
2%	0.1%	97.9%	10
2%	0.1%	97.9%	11
2%	0%	97.9%	12
2%	0%	97.9%	13
2%	0%	97.9%	14

Compiler

Compiled 50 to 36 computations (28% saved)

sample2.2s (33.5%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-neg_binary32`
634×	`associate-l_binary32`
530×	`associate-r_binary32`
445×	`associate-/r*_binary32`
406×	`*-commutative_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	66	43
2	237	35
3	864	32
4	2572	32
5	3890	32
6	4293	32
7	4871	32
8	4870	32

prune5.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	1.3b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Status

Error

Program

▶

0.1b

(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))

1.3b

(*.f32 (/.f32 (/.f32 1/8 (*.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Compiler

Compiled 169 to 117 computations (30.8% saved)

localize84.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
✓	0.2b	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
✓	0.2b	(/.f32 (neg.f32 r) (*.f32 3 s))
✓	0.4b	(.f32 (.f32 2 (PI.f32)) s)

series28.0ms (0.4%)

Counts

4 → 84

Calls

4 calls:

8.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
8.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
7.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
5.0ms	(.f32 (.f32 2 (PI.f32)) s)

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary32`
32×	`add-exp-log_binary32`
27×	`pow1_binary32`
16×	`cbrt-unprod_binary32`
16×	`prod-exp_binary32`

Counts

4 → 105

Calls

4 calls:

31.0ms	(.f32 (.f32 2 (PI.f32)) s)
6.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
5.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
4.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

512×	`associate-/l*_binary32`
418×	`associate-l_binary32`
326×	`associate-/r*_binary32`
318×	`distribute-rgt-neg-out_binary32`
310×	`associate-r_binary32`

Counts

189 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	2248
1	442	1951
2	1885	1945
3	4571	1945
4	4935	1945

prune238.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	152	4	156

Error

0.0b

Counts

156 → 4

Alt Table

Status	Error	Program
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (exp.f32 (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 r)))))
▶	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (.f32 6 (PI.f32)) s) r)))
	1.3b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Compiler

Compiled 6119 to 3516 computations (42.5% saved)

localize105.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)
	0.2b	(/.f32 (neg.f32 r) (*.f32 3 s))
✓	0.4b	(.f32 (.f32 2 (PI.f32)) (sqrt.f32 s))
✓	0.4b	(.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s))

series31.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

12.0ms	(.f32 (.f32 2 (PI.f32)) (sqrt.f32 s))
12.0ms	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)
7.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary32`
31×	`add-exp-log_binary32`
31×	`pow1_binary32`
19×	`cbrt-unprod_binary32`
19×	`prod-exp_binary32`

Counts

3 → 75

Calls

3 calls:

8.0ms	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)
7.0ms	(.f32 (.f32 2 (PI.f32)) (sqrt.f32 s))
7.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s))

simplify111.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

530×	`*-commutative_binary32`
468×	`distribute-rgt-in_binary32`
397×	`sqr-pow_binary32`
346×	`associate-l_binary32`
292×	`unswap-sqr_binary32`

Counts

103 → 92

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	1354
1	249	1165
2	990	1165
3	1553	1165
4	2083	1165
5	3240	1165
6	4907	1165
7	5003	1165

prune264.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Error

0.0b

Counts

157 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (exp.f32 (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 r)))))
✓	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (.f32 6 (PI.f32)) s) r)))
	1.3b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Compiler

Compiled 6665 to 3631 computations (45.5% saved)

localize113.0ms (1.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (neg.f32 r) (*.f32 3 s))
	0.4b	(.f32 (.f32 2 (PI.f32)) s)
✓	0.4b	(+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r))
✓	2.7b	(exp.f32 (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))

series1.5s (23.2%)

Counts

2 → 48

Calls

2 calls:

773.0ms	(+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r))
750.0ms	(exp.f32 (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`pow1_binary32`
23×	`log-pow_binary32`
17×	`*-un-lft-identity_binary32`
16×	`distribute-lft-out_binary32`
15×	`pow-prod-down_binary32`

Counts

2 → 54

Calls

2 calls:

9.0ms	(+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r))
6.0ms	(exp.f32 (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))

simplify115.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

443×	`distribute-rgt-in_binary32`
408×	`distribute-lft-in_binary32`
384×	`fma-neg_binary32`
328×	`exp-sum_binary32`
303×	`associate-+l+_binary32`

Counts

102 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1338
1	201	1270
2	690	1243
3	3893	1243
4	4852	1243
5	4948	1243
6	4841	1243

prune347.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	162	6	168

Error

0.0b

Counts

168 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 s (PI.f32))))) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (exp.f32 (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))))
▶	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (exp.f32 (log.f32 (.f32 (*.f32 6 (PI.f32)) s))) (exp.f32 (log.f32 r)))))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (.f32 -1/3 r) s))) (exp.f32 (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (pow.f32 (E.f32) (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))))
✓	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (.f32 6 (PI.f32)) s) r)))
	1.3b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Compiler

Compiled 7120 to 4234 computations (40.5% saved)

localize110.0ms (1.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (neg.f32 r) (*.f32 3 s))
	0.4b	(.f32 (.f32 2 (PI.f32)) s)
✓	1.3b	(exp.f32 (log.f32 r))
✓	2.8b	(exp.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(exp.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)))
1.0ms	(exp.f32 (log.f32 r))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`exp-prod_binary32`
9×	`pow1_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-sqr-sqrt_binary32`
5×	`add-cube-cbrt_binary32`

Counts

2 → 33

Calls

2 calls:

7.0ms	(exp.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)))
2.0ms	(exp.f32 (log.f32 r))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary32`
460×	`prod-exp_binary32`
305×	`*-commutative_binary32`
284×	`unswap-sqr_binary32`
257×	`times-frac_binary32`

Counts

57 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	364
1	76	344
2	177	344
3	652	340
4	1294	340
5	1766	340
6	2161	340
7	3665	340
8	4897	340
9	5138	340

prune346.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	139	6	145

Error

0.0b

Counts

145 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (pow.f32 (E.f32) (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 6 (*.f32 s (PI.f32))) (exp.f32 (log.f32 r)))))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (.f32 -1/3 r) s))) (.f32 (exp.f32 (log.f32 (.f32 (*.f32 6 (PI.f32)) s))) (exp.f32 (log.f32 r)))))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (expm1.f32 (log1p.f32 (.f32 2 (.f32 s (PI.f32))))) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (exp.f32 (+.f32 (log.f32 (.f32 (.f32 6 (PI.f32)) s)) (log.f32 r)))))
✓	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (.f32 6 (PI.f32)) s) r)))
	1.3b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Compiler

Compiled 5953 to 3443 computations (42.2% saved)

regimes323.0ms (4.9%)

Accuracy

Total 0.1b remaining (38.3%)

Threshold costs 0.1b (38.3%)

Counts

78 → 1

Compiler

Compiled 8872 to 6466 computations (27.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary32`
3×	`+-commutative_binary32`
2×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	45	58
2	49	58
3	52	58
4	53	58
5	53	58

end155.0ms (2.4%)

Compiler: Compiled 291 to 212 computations (27.1% saved)

Details

analyze115.0ms (1.7%)

sample2.2s (33.5%)

simplify64.0ms (1%)

prune5.0ms (0.1%)

localize84.0ms (1.3%)

series28.0ms (0.4%)

rewrite50.0ms (0.8%)

simplify93.0ms (1.4%)

prune238.0ms (3.6%)

localize105.0ms (1.6%)

series31.0ms (0.5%)

rewrite27.0ms (0.4%)

simplify111.0ms (1.7%)

prune264.0ms (4%)

localize113.0ms (1.7%)

series1.5s (23.2%)

rewrite19.0ms (0.3%)

simplify115.0ms (1.7%)

prune347.0ms (5.3%)

localize110.0ms (1.7%)

series5.0ms (0.1%)

rewrite10.0ms (0.2%)

simplify81.0ms (1.2%)

prune346.0ms (5.3%)

regimes323.0ms (4.9%)

simplify3.0ms (0.1%)

end155.0ms (2.4%)

Profiling