Details

analyze105.0ms (2.2%)

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)

sample2.5s (52.2%)

Results

2.4s

8256×

body

128

valid

Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify59.0ms (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
	1.1b	(.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 (.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

1.1b

(*.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 (*.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)

localize86.0ms (1.8%)

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 (*.f32 6 (PI.f32)) s) r)
✓	0.3b	(.f32 (.f32 2 (PI.f32)) s)

series29.0ms (0.6%)

Counts

4 → 84

Calls

4 calls:

10.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
9.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
7.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
3.0ms	(.f32 (.f32 2 (PI.f32)) s)

rewrite24.0ms (0.5%)

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:

6.0ms	(.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)

simplify126.0ms (2.6%)

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

prune304.0ms (6.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Error

0.1b

Counts

155 → 7

Alt Table

Status	Error	Program
	1.1b	(.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 (.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)))))
	0.2b	(+.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)))) (.f32 (.f32 6 (PI.f32)) (*.f32 s r))))
	0.3b	(+.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 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) 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 (.f32 r -1/3) s))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) 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 1 (.f32 -3 (/.f32 s r))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 6276 to 3637 computations (42% saved)

localize86.0ms (1.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 (*.f32 r -1/3) s)
	0.3b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
	0.3b	(.f32 (.f32 2 (PI.f32)) s)
✓	0.3b	(*.f32 r -1/3)

series9.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

7.0ms	(/.f32 (*.f32 r -1/3) s)
2.0ms	(*.f32 r -1/3)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary32`
9×	`add-exp-log_binary32`
8×	`add-sqr-sqrt_binary32`
6×	`*-un-lft-identity_binary32`
6×	`add-cube-cbrt_binary32`

Counts

2 → 43

Calls

2 calls:

4.0ms	(*.f32 r -1/3)
3.0ms	(/.f32 (*.f32 r -1/3) s)

simplify106.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-neg_binary32`
647×	`div-sub_binary32`
394×	`associate-/l*_binary32`
365×	`*-commutative_binary32`
345×	`times-frac_binary32`

Counts

79 → 67

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	73	617
1	148	560
2	527	560
3	2107	560
4	2408	560
5	2615	560
6	3221	560
7	4307	560
8	4976	560
9	4837	560

prune248.0ms (5.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Error

0.1b

Counts

134 → 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 (.f32 r -1/3) s))) (.f32 (.f32 6 (PI.f32)) (*.f32 s 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 1 (.f32 -3 (/.f32 s r))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	1.1b	(.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 (.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)))))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.3b	(+.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 r -1/3) s))) (exp.f32 (log.f32 (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))))

Compiler

Compiled 5065 to 3067 computations (39.4% saved)

localize89.0ms (1.9%)

Local error

Found 4 expressions with local error:

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

6.0ms	(.f32 6 (.f32 s (*.f32 (PI.f32) r)))
3.0ms	(*.f32 (PI.f32) r)

simplify82.0ms (1.7%)

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

prune257.0ms (5.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	134	5	139

Error

0.1b

Counts

139 → 5

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

Compiler

Compiled 5337 to 2875 computations (46.1% saved)

localize93.0ms (1.9%)

Local error

Found 4 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

7.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary32`
6×	`add-exp-log_binary32`
6×	`pow1_binary32`
3×	`associate-l_binary32`
3×	`cbrt-unprod_binary32`

Counts

1 → 20

Calls

1 calls:

4.0ms

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

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

580×	`log-div_binary32`
514×	`associate-/l*_binary32`
411×	`*-commutative_binary32`
409×	`associate-l_binary32`
339×	`cube-div_binary32`

Counts

20 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	245
1	87	194
2	275	194
3	770	194
4	976	194
5	1185	194
6	1422	194
7	1902	194
8	3020	194
9	4714	194
10	4982	194

prune227.0ms (4.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	135	5	140

Error

0.1b

Counts

140 → 5

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

Compiler

Compiled 5277 to 2767 computations (47.6% saved)

regimes108.0ms (2.3%)

Accuracy

Total 0.0b remaining (31.2%)

Threshold costs 0.0b (31.2%)

Counts

28 → 1

Compiler

Compiled 3085 to 2254 computations (26.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	26	51
1	42	51
2	46	51
3	49	51
4	50	51
5	50	51

end122.0ms (2.5%)

Compiler: Compiled 246 to 180 computations (26.8% saved)

Details

analyze105.0ms (2.2%)

sample2.5s (52.2%)

simplify59.0ms (1.2%)

prune5.0ms (0.1%)

localize86.0ms (1.8%)

series29.0ms (0.6%)

rewrite24.0ms (0.5%)

simplify126.0ms (2.6%)

prune304.0ms (6.4%)

localize86.0ms (1.8%)

series9.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify106.0ms (2.2%)

prune248.0ms (5.2%)

localize89.0ms (1.9%)

series11.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify82.0ms (1.7%)

prune257.0ms (5.4%)

localize93.0ms (1.9%)

series7.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify70.0ms (1.5%)

prune227.0ms (4.8%)

regimes108.0ms (2.3%)

simplify3.0ms (0.1%)

end122.0ms (2.5%)

Profiling