Details

analyze94.0ms (2.1%)

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)

sample109.0ms (2.4%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 87 to 63 computations (27.6% saved)

simplify62.0ms (1.4%)

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)))
	0.9b	(.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)))

0.9b

(*.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 (1.9%)

Local error

Found 4 expressions with local error:

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

series28.0ms (0.6%)

Counts

4 → 84

Calls

4 calls:

9.0ms	(.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))
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:

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)

simplify89.0ms (2%)

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

prune242.0ms (5.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	151	5	156

Error

0.0b

Counts

156 → 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 (.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 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)) (sqrt.f32 (.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)))) (exp.f32 (+.f32 (+.f32 (log.f32 (*.f32 6 (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 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)))))
	0.9b	(.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 6203 to 3578 computations (42.3% saved)

localize82.0ms (1.8%)

Local error

Found 4 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite6.0ms (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))

simplify71.0ms (1.6%)

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

prune330.0ms (7.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	2	2	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 2 (.f32 s (.f32 (PI.f32) 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 (+.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 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (exp.f32 (+.f32 (log.f32 (*.f32 6 (PI.f32))) (+.f32 (log.f32 s) (log.f32 r))))))
	0.9b	(.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 6011 to 3319 computations (44.8% saved)

localize87.0ms (1.9%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.2%)

Counts

2 → 0

Calls

2 calls:

8.0ms	(.f32 s (.f32 (PI.f32) r))
2.0ms	(*.f32 (PI.f32) r)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary32`
9×	`add-exp-log_binary32`
9×	`pow1_binary32`
7×	`add-sqr-sqrt_binary32`
6×	`associate-l_binary32`

Counts

2 → 40

Calls

2 calls:

4.0ms	(.f32 s (.f32 (PI.f32) r))
3.0ms	(*.f32 (PI.f32) r)

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

533×	`associate-/l/_binary32`
503×	`times-frac_binary32`
479×	`associate-l_binary32`
382×	`*-commutative_binary32`
359×	`associate-r_binary32`

Counts

40 → 51

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	418
1	117	345
2	365	345
3	1001	345
4	1221	345
5	1572	345
6	2901	345
7	4953	345
8	5164	345

prune265.0ms (5.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	141	5	146

Error

0.0b

Counts

146 → 5

Alt Table

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

Compiler

Compiled 5721 to 2897 computations (49.4% saved)

localize91.0ms (2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (neg.f32 r) (*.f32 3 s))
	0.3b	(.f32 (.f32 6 (PI.f32)) (*.f32 s r))
	0.3b	(*.f32 (PI.f32) r)
✓	1.1b	(exp.f32 (log.f32 (*.f32 (PI.f32) r)))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(exp.f32 (log.f32 (*.f32 (PI.f32) r)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 16

Calls

1 calls:

2.0ms

(exp.f32 (log.f32 (*.f32 (PI.f32) r)))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary32`
689×	`associate-l_binary32`
482×	`associate-r_binary32`
461×	`associate-/l*_binary32`
258×	`associate-/l/_binary32`

Counts

28 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	186
1	35	175
2	75	175
3	174	175
4	292	175
5	450	175
6	788	175
7	1918	175
8	2715	175
9	4259	175
10	4924	175

prune237.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	136	4	140

Error

0.0b

Counts

140 → 4

Alt Table

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

Compiler

Compiled 5502 to 2679 computations (51.3% saved)

regimes400.0ms (8.8%)

Accuracy

Total 0.0b remaining (15.8%)

Threshold costs 0.0b (15.8%)

Counts

110 → 1

Compiler

Compiled 12607 to 9241 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-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	44	53
2	50	53
3	55	53
4	57	53
5	57	53

end1.0ms (0%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

sample2.0s (45.2%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
377.0ms	8000×	pre	128	true

Compiler

Compiled 244 to 176 computations (27.9% saved)

Details

analyze94.0ms (2.1%)

sample109.0ms (2.4%)

simplify62.0ms (1.4%)

prune5.0ms (0.1%)

localize86.0ms (1.9%)

series28.0ms (0.6%)

rewrite24.0ms (0.5%)

simplify89.0ms (2%)

prune242.0ms (5.3%)

localize82.0ms (1.8%)

series9.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify71.0ms (1.6%)

prune330.0ms (7.3%)

localize87.0ms (1.9%)

series10.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify69.0ms (1.5%)

prune265.0ms (5.9%)

localize91.0ms (2%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify63.0ms (1.4%)

prune237.0ms (5.2%)

regimes400.0ms (8.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.0s (45.2%)

Profiling