Details

analyze126.0ms (2.6%)

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 (46.9%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify56.0ms (1.2%)

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
	0.7b	(.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 (*.f32 6 (PI.f32)) s) r)))

Status

Error

Program

0.7b

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

Compiler

Compiled 169 to 117 computations (30.8% saved)

localize81.0ms (1.7%)

Local error

Found 4 expressions with local error:

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

series27.0ms (0.6%)

Counts

4 → 84

Calls

4 calls:

9.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
9.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
6.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
3.0ms	(.f32 (.f32 2 (PI.f32)) s)

rewrite28.0ms (0.6%)

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:

9.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
5.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
4.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
4.0ms	(.f32 (.f32 2 (PI.f32)) s)

simplify86.0ms (1.8%)

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

prune244.0ms (5.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	5	155

Error

0.0b

Counts

155 → 5

Alt Table

Status	Error	Program
	26.4b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (log.f32 (exp.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)))
	0.1b	(+.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 6 (.f32 s (.f32 (PI.f32) r)))) (sqrt.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 (.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)))) (.f32 6 (.f32 s (*.f32 (PI.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)))) (exp.f32 (log.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))))

Compiler

Compiled 6186 to 3565 computations (42.4% saved)

localize82.0ms (1.7%)

Local error

Found 4 expressions with local error:

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

series11.0ms (0.2%)

Counts

2 → 0

Calls

2 calls:

9.0ms	(.f32 6 (.f32 s (*.f32 (PI.f32) r)))
2.0ms	(*.f32 (PI.f32) r)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary32`
13×	`add-exp-log_binary32`
13×	`pow1_binary32`
7×	`add-sqr-sqrt_binary32`
7×	`cbrt-unprod_binary32`

Counts

2 → 43

Calls

2 calls:

5.0ms	(.f32 6 (.f32 s (*.f32 (PI.f32) r)))
4.0ms	(*.f32 (PI.f32) r)

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

448×	`log-div_binary32`
334×	`fma-def_binary32`
333×	`*-commutative_binary32`
333×	`sqr-pow_binary32`
304×	`cube-div_binary32`

Counts

43 → 44

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	541
1	153	439
2	546	439
3	887	439
4	1173	439
5	1714	439
6	2400	439
7	3647	439
8	4859	439
9	4977	439

prune245.0ms (5.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	133	5	138

Error

0.0b

Counts

138 → 5

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 6 (.f32 s (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (*.f32 (cbrt.f32 (PI.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 (sqrt.f32 (.f32 6 (.f32 s (.f32 (PI.f32) r)))) (sqrt.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 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 6 (.f32 s (exp.f32 (log.f32 (*.f32 (PI.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 (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)))))))

Compiler

Compiled 5408 to 2914 computations (46.1% saved)

localize81.0ms (1.7%)

Local error

Found 4 expressions with local error:

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

series8.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite7.0ms (0.2%)

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:

6.0ms

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

simplify67.0ms (1.4%)

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

prune278.0ms (5.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	3	4
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)))) (.f32 (sqrt.f32 (.f32 6 (.f32 s (.f32 (PI.f32) r)))) (sqrt.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 (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)))) (.f32 6 (.f32 s (exp.f32 (log.f32 (*.f32 (PI.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)))) (exp.f32 (log.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))))

Compiler

Compiled 6047 to 3335 computations (44.8% saved)

localize73.0ms (1.5%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))
5.0ms	(exp.f32 (/.f32 (neg.f32 r) s))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`exp-prod_binary32`
30×	`times-frac_binary32`
22×	`*-un-lft-identity_binary32`
22×	`add-sqr-sqrt_binary32`
22×	`add-cube-cbrt_binary32`

Counts

2 → 70

Calls

2 calls:

6.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))
4.0ms	(exp.f32 (/.f32 (neg.f32 r) s))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary32`
352×	`*-commutative_binary32`
335×	`unswap-sqr_binary32`
306×	`fma-neg_binary32`
249×	`associate-/l/_binary32`

Counts

118 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1469
1	320	1342
2	990	1331
3	2126	1325
4	4857	1325
5	4988	1325

prune308.0ms (6.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	188	4	192

Error

0.0b

Counts

192 → 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)))) (.f32 (sqrt.f32 (.f32 6 (.f32 s (.f32 (PI.f32) r)))) (sqrt.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 (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)))) (.f32 6 (.f32 s (exp.f32 (log.f32 (*.f32 (PI.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)))) (exp.f32 (log.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))))

Compiler

Compiled 7437 to 3885 computations (47.8% saved)

regimes416.0ms (8.7%)

Accuracy

Total 0.0b remaining (27.2%)

Threshold costs 0.0b (27.2%)

Counts

116 → 1

Compiler

Compiled 12844 to 9271 computations (27.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-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	25	51
1	40	51
2	44	51
3	47	51
4	48	51
5	48	51

end109.0ms (2.3%)

Compiler: Compiled 222 to 156 computations (29.7% saved)

Details

analyze126.0ms (2.6%)

sample2.2s (46.9%)

simplify56.0ms (1.2%)

prune5.0ms (0.1%)

localize81.0ms (1.7%)

series27.0ms (0.6%)

rewrite28.0ms (0.6%)

simplify86.0ms (1.8%)

prune244.0ms (5.1%)

localize82.0ms (1.7%)

series11.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify77.0ms (1.6%)

prune245.0ms (5.1%)

localize81.0ms (1.7%)

series8.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify67.0ms (1.4%)

prune278.0ms (5.8%)

localize73.0ms (1.5%)

series13.0ms (0.3%)

rewrite15.0ms (0.3%)

simplify78.0ms (1.6%)

prune308.0ms (6.4%)

regimes416.0ms (8.7%)

simplify3.0ms (0.1%)

end109.0ms (2.3%)

Profiling