Details

analyze156.0ms (2.5%)

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 44 to 32 computations (27.3% saved)

sample55.0ms (0.9%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 81 to 59 computations (27.2% saved)

simplify74.0ms (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 → 1

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

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 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)))
	0.5b	(.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)))

0.5b

(*.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 136 to 98 computations (27.9% saved)

localize127.0ms (2.1%)

Local error

Found 4 expressions with local error:

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

rewrite232.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

62×	`pow1_binary32`
40×	`pow-prod-down_binary32`
36×	`add-exp-log_binary32`
28×	`add-sqr-sqrt_binary32`
22×	`add-cbrt-cube_binary32`

Counts

4 → 164

Calls

4 calls:

16.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
16.0ms	(.f32 (.f32 (*.f32 6 PI.f32) s) r)
15.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
14.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 5102 to 3059 computations (40% saved)

series62.0ms (1%)

Error

0.1b

Counts

4 → 21

Calls

4 calls:

17.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
17.0ms	(.f32 (.f32 (*.f32 6 PI.f32) s) r)
15.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
8.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 1591 to 1130 computations (29% saved)

simplify151.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

419×	`unswap-sqr_binary32`
321×	`associate-l_binary32`
303×	`fma-def_binary32`
278×	`distribute-rgt-neg-out_binary32`
277×	`associate-r_binary32`

Counts

185 → 103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	183	1918
1	460	1629
2	2004	1629
3	4865	1629
4	4980	1629

prune155.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	101	4	105

Error

0.0b

Counts

105 → 4

Alt Table

Status	Error	Program
	0.5b	(.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 (/.f32 (neg.f32 r) s) 3))) (.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 (cbrt.f32 (.f32 (.f32 s (.f32 PI.f32 r)) 6)) (cbrt.f32 (.f32 (.f32 s (.f32 PI.f32 r)) 6))) (cbrt.f32 (.f32 (.f32 s (*.f32 PI.f32 r)) 6)))))
	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 (.f32 s (*.f32 PI.f32 r)) 6)))))

Compiler

Compiled 2980 to 1728 computations (42% saved)

localize80.0ms (1.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (.f32 (*.f32 6 PI.f32) s) r)
0.3b	(/.f32 (/.f32 (neg.f32 r) s) 3)
0.3b	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
0.3b	(.f32 (.f32 2 PI.f32) s)

rewrite282.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

62×	`pow1_binary32`
40×	`pow-prod-down_binary32`
36×	`add-exp-log_binary32`
28×	`add-sqr-sqrt_binary32`
27×	`add-cube-cbrt_binary32`

Counts

4 → 163

Calls

4 calls:

22.0ms	(/.f32 (/.f32 (neg.f32 r) s) 3)
17.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
15.0ms	(.f32 (.f32 (*.f32 6 PI.f32) s) r)
14.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 5153 to 2946 computations (42.8% saved)

series65.0ms (1.1%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

18.0ms	(.f32 (.f32 (*.f32 6 PI.f32) s) r)
17.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
16.0ms	(/.f32 (/.f32 (neg.f32 r) s) 3)
8.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 1591 to 1097 computations (31% saved)

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Rules

945×	`fma-def_binary32`
444×	`times-frac_binary32`
357×	`unswap-sqr_binary32`
296×	`associate-l_binary32`
236×	`associate-r_binary32`

Counts

184 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	1957
1	452	1671
2	1763	1661
3	4774	1661
4	5569	1661

prune115.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	102	3	105

Error

0.0b

Counts

105 → 3

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

Compiler

Compiled 2870 to 1604 computations (44.1% saved)

localize79.0ms (1.3%)

Local error

Found 4 expressions with local error:

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

rewrite279.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

69×	`pow1_binary32`
45×	`pow-prod-down_binary32`
34×	`add-exp-log_binary32`
32×	`add-sqr-sqrt_binary32`
20×	`add-cbrt-cube_binary32`

Counts

4 → 144

Calls

4 calls:

19.0ms	(.f32 (.f32 s (*.f32 PI.f32 r)) 6)
18.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
14.0ms	(*.f32 PI.f32 r)
14.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 4310 to 2241 computations (48% saved)

series53.0ms (0.9%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

17.0ms	(.f32 (.f32 s (*.f32 PI.f32 r)) 6)
17.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
7.0ms	(.f32 (.f32 2 PI.f32) s)
6.0ms	(*.f32 PI.f32 r)

Compiler

Compiled 1394 to 910 computations (34.7% saved)

simplify183.0ms (3%)

Algorithm

1×	egg-herbie

Rules

603×	`fma-def_binary32`
455×	`unswap-sqr_binary32`
427×	`log-prod_binary32`
382×	`prod-exp_binary32`
294×	`associate-l_binary32`

Counts

162 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	1562
1	324	1400
2	1339	1388
3	3163	1388
4	4735	1388
5	4966	1388
6	4986	1388
7	4993	1388
8	4985	1388

prune100.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	90	4	94

Error

0.0b

Counts

94 → 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 (/.f32 (neg.f32 r) s) 3))) (.f32 (.f32 s (.f32 PI.f32 r)) 6)))
	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 (neg.f32 r) s) 3))) (exp.f32 (log.f32 (.f32 (.f32 s (.f32 PI.f32 r)) 6)))))
	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 (cbrt.f32 (.f32 (.f32 s (.f32 PI.f32 r)) 6)) (cbrt.f32 (.f32 (.f32 s (.f32 PI.f32 r)) 6))) (cbrt.f32 (.f32 (.f32 s (*.f32 PI.f32 r)) 6)))))
▶	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 (neg.f32 r) s) 3))) (.f32 (.f32 s (.f32 (sqrt.f32 (.f32 PI.f32 r)) (sqrt.f32 (.f32 PI.f32 r)))) 6)))

Compiler

Compiled 2424 to 1275 computations (47.4% saved)

localize112.0ms (1.8%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (.f32 2 PI.f32) s)
0.3b	(*.f32 PI.f32 r)
0.3b	(*.f32 PI.f32 r)
0.5b	(.f32 (sqrt.f32 (.f32 PI.f32 r)) (sqrt.f32 (*.f32 PI.f32 r)))

rewrite523.0ms (8.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`pow1_binary32`
37×	`add-sqr-sqrt_binary32`
26×	`add-exp-log_binary32`
23×	`pow-prod-down_binary32`
21×	`add-cube-cbrt_binary32`

Counts

4 → 159

Calls

4 calls:

16.0ms	(.f32 (sqrt.f32 (.f32 PI.f32 r)) (sqrt.f32 (*.f32 PI.f32 r)))
15.0ms	(.f32 (.f32 2 PI.f32) s)
15.0ms	(*.f32 PI.f32 r)
13.0ms	(*.f32 PI.f32 r)

Compiler

Compiled 5266 to 2411 computations (54.2% saved)

series32.0ms (0.5%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f32 PI.f32 r)
7.0ms	(.f32 (.f32 2 PI.f32) s)
7.0ms	(.f32 (sqrt.f32 (.f32 PI.f32 r)) (sqrt.f32 (*.f32 PI.f32 r)))
6.0ms	(*.f32 PI.f32 r)

Compiler

Compiled 1081 to 690 computations (36.2% saved)

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

703×	`prod-exp_binary32`
396×	`unswap-sqr_binary32`
359×	`*-commutative_binary32`
339×	`exp-prod_binary32`
317×	`fma-def_binary32`

Counts

171 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	122	1230
1	230	1114
2	816	1096
3	1811	1085
4	4050	1071
5	5038	1071

prune93.0ms (1.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	79	4	83

Error

0.0b

Counts

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

Compiler

Compiled 2118 to 1043 computations (50.8% saved)

regimes1.0s (16.7%)

Accuracy

Total 0.0b remaining (25%)

Threshold costs 0.0b (25%)

Compiler

Compiled 26908 to 18532 computations (31.1% saved)

simplify6.0ms (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	28	67
1	44	67
2	50	67
3	55	67
4	58	67
5	59	67
6	59	67

end1.0ms (0%)

Compiler: Compiled 42 to 27 computations (35.7% saved)

sample1.9s (30.4%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
212.0ms	8000×	pre	128	true

Compiler

Compiled 255 to 171 computations (32.9% saved)

Details

analyze156.0ms (2.5%)

sample55.0ms (0.9%)

simplify74.0ms (1.2%)

prune4.0ms (0.1%)

localize127.0ms (2.1%)

rewrite232.0ms (3.8%)

series62.0ms (1%)

simplify151.0ms (2.5%)

prune155.0ms (2.5%)

localize80.0ms (1.3%)

rewrite282.0ms (4.6%)

series65.0ms (1.1%)

simplify125.0ms (2%)

prune115.0ms (1.9%)

localize79.0ms (1.3%)

rewrite279.0ms (4.6%)

series53.0ms (0.9%)

simplify183.0ms (3%)

prune100.0ms (1.6%)

localize112.0ms (1.8%)

rewrite523.0ms (8.5%)

series32.0ms (0.5%)

simplify100.0ms (1.6%)

prune93.0ms (1.5%)

regimes1.0s (16.7%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.9s (30.4%)

Profiling