Details

analyze807.0ms (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	2.1%	97.9%	0
0%	2.1%	97.9%	1
0%	2.1%	97.9%	2
0%	2.1%	97.9%	3
0.8%	1.3%	97.9%	4
0.9%	1.2%	97.9%	5
1.3%	0.7%	97.9%	6
1.4%	0.7%	97.9%	7
1.6%	0.5%	97.9%	8
1.6%	0.5%	97.9%	9
1.7%	0.4%	97.9%	10
1.7%	0.4%	97.9%	11
1.7%	0.3%	97.9%	12
1.7%	0.3%	97.9%	13
1.8%	0.3%	97.9%	14

Compiler

Compiled 50 to 36 computations (28% saved)

sample2.7s (41.5%)

Results

2.6s

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)))
	0.4b	(.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)))

0.4b

(*.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)

localize86.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (neg.f32 r) (*.f32 3 s))
✓	0.3b	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
✓	0.3b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
✓	0.3b	(.f32 (.f32 2 (PI.f32)) s)

series33.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

12.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
9.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
9.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
3.0ms	(.f32 (.f32 2 (PI.f32)) s)

rewrite26.0ms (0.4%)

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:

5.0ms	(.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))
4.0ms	(.f32 (.f32 2 (PI.f32)) s)

simplify92.0ms (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 → 153

Iterations

Useful iterations: 2 (0.0ms)

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

prune317.0ms (4.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	149	6	155

Error

0.0b

Counts

155 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) 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 (PI.f32)) (*.f32 s 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)))) (exp.f32 (log.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))))
	0.4b	(.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)))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) s) (sqrt.f32 r)) (sqrt.f32 r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (.f32 6 (PI.f32)) s) 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 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)) (sqrt.f32 (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))))

Compiler

Compiled 6234 to 3601 computations (42.2% saved)

localize87.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (neg.f32 r) (*.f32 3 s))
	0.3b	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
✓	0.3b	(.f32 (.f32 6 (PI.f32)) (*.f32 s r))
	0.3b	(.f32 (.f32 2 (PI.f32)) s)

series9.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary32`
13×	`add-exp-log_binary32`
13×	`pow1_binary32`
8×	`cbrt-unprod_binary32`
8×	`prod-exp_binary32`

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

407×	`associate-/l/_binary32`
395×	`*-commutative_binary32`
338×	`sqr-pow_binary32`
336×	`associate-/l*_binary32`
287×	`associate-*r/_binary32`

Counts

48 → 30

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	665
1	132	565
2	487	565
3	756	565
4	1012	565
5	1447	565
6	2224	565
7	3813	565
8	4955	565

prune303.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	151	6	157

Error

0.0b

Counts

157 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) 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 (PI.f32)) (*.f32 s 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)))) (exp.f32 (log.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))))
	0.4b	(.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)))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) s) (sqrt.f32 r)) (sqrt.f32 r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (.f32 6 (PI.f32)) s) 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 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)) (sqrt.f32 (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))))

Compiler

Compiled 6130 to 3398 computations (44.6% saved)

localize102.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r))
	0.3b	(/.f32 (neg.f32 r) (*.f32 3 s))
	0.3b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
✓	0.4b	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))

series38.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r))
9.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cbrt-cube_binary32`
42×	`add-exp-log_binary32`
24×	`cbrt-unprod_binary32`
24×	`prod-exp_binary32`
14×	`pow1_binary32`

Counts

2 → 58

Calls

2 calls:

12.0ms	(/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r))
7.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))

simplify123.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

730×	`associate-*l/_binary32`
496×	`associate-/l/_binary32`
357×	`times-frac_binary32`
316×	`associate-l_binary32`
253×	`associate-r_binary32`

Counts

106 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2780
1	499	2031
2	2472	1978
3	4940	1978
4	4940	1978

prune391.0ms (6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	181	7	188

Error

Counts

188 → 7

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 (log.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))))
▶	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (.f32 (/.f32 3/4 (.f32 (.f32 6 (PI.f32)) s)) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s))) r)))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (/.f32 (/.f32 -3/4 (cbrt.f32 (exp.f32 (/.f32 r s)))) (.f32 -6 (.f32 s (*.f32 (PI.f32) r)))))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (/.f32 (/.f32 (/.f32 1/8 (cbrt.f32 (exp.f32 (/.f32 r s)))) (*.f32 s (PI.f32))) r))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (exp.f32 (+.f32 (log.f32 (/.f32 1/8 (.f32 s (.f32 (PI.f32) r)))) (*.f32 -1/3 (/.f32 r s)))))
	0.4b	(.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)))
✓	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 (PI.f32)) (*.f32 s r))))

Compiler

Compiled 7562 to 4140 computations (45.3% saved)

localize91.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (/.f32 3/4 (.f32 (.f32 6 (PI.f32)) s)) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s))) r))
✓	0.2b	(/.f32 3/4 (.f32 (.f32 6 (PI.f32)) s))
	0.3b	(/.f32 (neg.f32 r) (*.f32 3 s))
	0.4b	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))

series35.0ms (0.5%)

Counts

2 → 36

Calls

2 calls:

28.0ms	(.f32 (/.f32 3/4 (.f32 (.f32 6 (PI.f32)) s)) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s))) r))
7.0ms	(/.f32 3/4 (.f32 (.f32 6 (PI.f32)) s))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-cbrt-cube_binary32`
39×	`add-exp-log_binary32`
18×	`add-sqr-sqrt_binary32`
17×	`cbrt-unprod_binary32`
17×	`prod-exp_binary32`

Counts

2 → 77

Calls

2 calls:

14.0ms	(.f32 (/.f32 3/4 (.f32 (.f32 6 (PI.f32)) s)) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s))) r))
5.0ms	(/.f32 3/4 (.f32 (.f32 6 (PI.f32)) s))

simplify121.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary32`
528×	`*-commutative_binary32`
308×	`fma-neg_binary32`
246×	`cancel-sign-sub-inv_binary32`
223×	`sub-neg_binary32`

Counts

113 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	2938
1	511	2317
2	1972	2299
3	3179	2243
4	4694	2243
5	5012	2243

prune485.0ms (7.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	224	6	230

Error

Counts

230 → 6

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 (log.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (/.f32 (/.f32 -3/4 (cbrt.f32 (exp.f32 (/.f32 r s)))) (.f32 -6 (.f32 s (*.f32 (PI.f32) r)))))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (exp.f32 (+.f32 (log.f32 (/.f32 1/8 (.f32 s (.f32 (PI.f32) r)))) (*.f32 -1/3 (/.f32 r s)))))
	0.4b	(.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)))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (.f32 3/4 (/.f32 (/.f32 (/.f32 1/6 (PI.f32)) s) (.f32 r (cbrt.f32 (exp.f32 (/.f32 r s)))))))
✓	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 (PI.f32)) (*.f32 s r))))

Compiler

Compiled 9120 to 4997 computations (45.2% saved)

regimes303.0ms (4.7%)

Accuracy

Total 0.1b remaining (53.3%)

Threshold costs 0.1b (53.3%)

Counts

82 → 1

Compiler

Compiled 9037 to 6478 computations (28.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary32`
4×	`+-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	43	53
2	49	53
3	54	53
4	56	53
5	56	53

end133.0ms (2.1%)

Compiler: Compiled 263 to 190 computations (27.8% saved)

Details

analyze807.0ms (12.5%)

sample2.7s (41.5%)

simplify64.0ms (1%)

prune5.0ms (0.1%)

localize86.0ms (1.3%)

series33.0ms (0.5%)

rewrite26.0ms (0.4%)

simplify92.0ms (1.4%)

prune317.0ms (4.9%)

localize87.0ms (1.3%)

series9.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify70.0ms (1.1%)

prune303.0ms (4.7%)

localize102.0ms (1.6%)

series38.0ms (0.6%)

rewrite27.0ms (0.4%)

simplify123.0ms (1.9%)

prune391.0ms (6%)

localize91.0ms (1.4%)

series35.0ms (0.5%)

rewrite30.0ms (0.5%)

simplify121.0ms (1.9%)

prune485.0ms (7.5%)

regimes303.0ms (4.7%)

simplify3.0ms (0.1%)

end133.0ms (2.1%)

Profiling