Details

analyze150.0ms (3.1%)

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 44 to 32 computations (27.3% saved)

sample55.0ms (1.1%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 81 to 59 computations (27.2% saved)

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-l_binary32`
530×	`associate-r_binary32`
445×	`associate-/r*_binary32`
406×	`*-commutative_binary32`
367×	`associate-/l*_binary32`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	66	45
2	235	35
3	850	32
4	2524	32
5	3762	32
6	4029	32
7	4426	32
8	4756	32
9	4857	32
10	4783	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

0.0b

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)))
	0.8b	(.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)))

0.8b

(*.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)

localize89.0ms (1.8%)

Local error

Found 4 expressions with local error:

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

rewrite164.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

32×	`add-cbrt-cube_binary32`
32×	`add-exp-log_binary32`
27×	`pow1_binary32`
16×	`cbrt-unprod_binary32`
16×	`prod-exp_binary32`

Counts

4 → 97

Calls

4 calls:

8.0ms	(.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)

Compiler

Compiled 3367 to 1941 computations (42.4% saved)

series67.0ms (1.4%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

19.0ms	(.f32 (.f32 (*.f32 6 PI.f32) s) r)
19.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
16.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
8.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 1591 to 1130 computations (29% saved)

simplify102.0ms (2.1%)

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

118 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	1560
1	434	1267
2	1877	1261
3	4562	1261
4	5000	1261
5	4926	1261

prune79.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	83	3	86

Error

0.0b

Counts

86 → 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 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (sqrt.f32 r) (.f32 s (.f32 PI.f32 6))) (sqrt.f32 r))))
	0.8b	(.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 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (*.f32 PI.f32 6))) (cbrt.f32 r))))

Compiler

Compiled 2025 to 1157 computations (42.9% saved)

localize91.0ms (1.9%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
0.3b	(.f32 (.f32 (sqrt.f32 r) (.f32 s (.f32 PI.f32 6))) (sqrt.f32 r))
0.3b	(.f32 (sqrt.f32 r) (.f32 s (*.f32 PI.f32 6)))
0.3b	(.f32 (.f32 2 PI.f32) s)

rewrite148.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

41×	`add-cbrt-cube_binary32`
41×	`add-exp-log_binary32`
41×	`pow1_binary32`
25×	`cbrt-unprod_binary32`
25×	`prod-exp_binary32`

Counts

4 → 90

Calls

4 calls:

9.0ms	(.f32 (.f32 (sqrt.f32 r) (.f32 s (.f32 PI.f32 6))) (sqrt.f32 r))
6.0ms	(.f32 (sqrt.f32 r) (.f32 s (*.f32 PI.f32 6)))
5.0ms	(.f32 (.f32 2 PI.f32) s)
5.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)

Compiler

Compiled 3369 to 1817 computations (46.1% saved)

series127.0ms (2.6%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

75.0ms	(.f32 (.f32 (sqrt.f32 r) (.f32 s (.f32 PI.f32 6))) (sqrt.f32 r))
20.0ms	(.f32 (sqrt.f32 r) (.f32 s (*.f32 PI.f32 6)))
19.0ms	(.f32 (.f32 (*.f32 2 PI.f32) s) r)
7.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 1788 to 1241 computations (30.6% saved)

simplify134.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

497×	`associate-l_binary32`
433×	`associate-r_binary32`
390×	`sqr-pow_binary32`
369×	`unswap-sqr_binary32`
261×	`associate-/l*_binary32`

Counts

111 → 78

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	153	1812
1	390	1410
2	1678	1410
3	2137	1410
4	3006	1410
5	4757	1410
6	4997	1410
7	4948	1410

prune65.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Error

0.0b

Counts

81 → 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 (.f32 (sqrt.f32 r) (.f32 s (.f32 PI.f32 6))) (sqrt.f32 r))))
	0.8b	(.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 (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r)))) (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r))))) (sqrt.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 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (*.f32 PI.f32 6))) (cbrt.f32 r))))

Compiler

Compiled 1894 to 1020 computations (46.1% saved)

localize94.0ms (1.9%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (.f32 PI.f32 6)))
0.3b	(.f32 (.f32 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (*.f32 PI.f32 6))) (cbrt.f32 r))
0.3b	(.f32 (.f32 2 PI.f32) s)
0.5b	(*.f32 (cbrt.f32 r) (cbrt.f32 r))

rewrite214.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

66×	`pow1_binary32`
61×	`add-exp-log_binary32`
42×	`pow-prod-down_binary32`
41×	`cbrt-unprod_binary32`
41×	`prod-exp_binary32`

Counts

4 → 122

Calls

4 calls:

13.0ms	(.f32 (.f32 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (*.f32 PI.f32 6))) (cbrt.f32 r))
10.0ms	(.f32 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (.f32 PI.f32 6)))
5.0ms	(*.f32 (cbrt.f32 r) (cbrt.f32 r))
4.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 4857 to 2417 computations (50.2% saved)

series118.0ms (2.4%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

49.0ms	(.f32 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (.f32 PI.f32 6)))
28.0ms	(.f32 (.f32 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (*.f32 PI.f32 6))) (cbrt.f32 r))
17.0ms	(*.f32 (cbrt.f32 r) (cbrt.f32 r))
10.0ms	(.f32 (.f32 2 PI.f32) s)

Compiler

Compiled 1741 to 1232 computations (29.2% saved)

simplify131.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

462×	`associate-l_binary32`
451×	`sqr-pow_binary32`
408×	`log-prod_binary32`
389×	`associate-r_binary32`
361×	`unswap-sqr_binary32`

Counts

140 → 119

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	174	2722
1	421	1766
2	1605	1694
3	2237	1660
4	3666	1568
5	4478	1568
6	4959	1568

prune79.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	119	4	123

Error

0.0b

Counts

123 → 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 (.f32 (sqrt.f32 r) (.f32 s (.f32 PI.f32 6))) (sqrt.f32 r))))
	0.8b	(.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 (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r)))) (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r))))) (sqrt.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 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (*.f32 PI.f32 6))) (cbrt.f32 r))))

Compiler

Compiled 2126 to 1150 computations (45.9% saved)

localize99.0ms (2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f32 s PI.f32)
0.3b	(.f32 (.f32 s PI.f32) (sqrt.f32 r))
0.3b	(.f32 (.f32 2 PI.f32) s)
0.5b	(.f32 (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r)))) (sqrt.f32 (.f32 6 (.f32 (*.f32 s PI.f32) (sqrt.f32 r)))))

rewrite197.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

283×	`pow1_binary32`
181×	`pow-prod-down_binary32`
104×	`sqrt-pow1_binary32`
26×	`pow-prod-up_binary32`
18×	`pow-sqr_binary32`

Counts

4 → 146

Calls

4 calls:

14.0ms	(.f32 (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r)))) (sqrt.f32 (.f32 6 (.f32 (*.f32 s PI.f32) (sqrt.f32 r)))))
6.0ms	(.f32 (.f32 s PI.f32) (sqrt.f32 r))
4.0ms	(.f32 (.f32 2 PI.f32) s)
3.0ms	(*.f32 s PI.f32)

Compiler

Compiled 4561 to 2251 computations (50.6% saved)

series70.0ms (1.4%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

28.0ms	(.f32 (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r)))) (sqrt.f32 (.f32 6 (.f32 (*.f32 s PI.f32) (sqrt.f32 r)))))
21.0ms	(.f32 (.f32 s PI.f32) (sqrt.f32 r))
8.0ms	(.f32 (.f32 2 PI.f32) s)
8.0ms	(*.f32 s PI.f32)

Compiler

Compiled 1930 to 1295 computations (32.9% saved)

simplify157.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

567×	`sqr-pow_binary32`
312×	`associate-l_binary32`
275×	`associate-r_binary32`
238×	`pow-sqr_binary32`
235×	`log-prod_binary32`

Counts

164 → 128

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	144	1743
1	321	1585
2	1185	1571
3	1619	1552
4	2538	1516
5	3654	1516
6	4678	1514
7	4992	1514
8	4910	1514

prune74.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	128	4	132

Error

0.0b

Counts

132 → 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 (.f32 (sqrt.f32 r) (.f32 s (.f32 PI.f32 6))) (sqrt.f32 r))))
	0.8b	(.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 (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r)))) (sqrt.f32 (.f32 6 (.f32 (.f32 s PI.f32) (sqrt.f32 r))))) (sqrt.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 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 s (*.f32 PI.f32 6))) (cbrt.f32 r))))

Compiler

Compiled 2142 to 1141 computations (46.7% saved)

regimes491.0ms (10%)

Accuracy

Total 0.0b remaining (31.8%)

Threshold costs 0.0b (31.8%)

Compiler

Compiled 10186 to 7225 computations (29.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-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	60
1	47	60
2	53	60
3	58	60
4	60	60
5	60	60

end1.0ms (0%)

Compiler: Compiled 39 to 27 computations (30.8% saved)

sample1.8s (36.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
182.0ms	8000×	pre	128	true

Compiler

Compiled 238 to 164 computations (31.1% saved)

Details

analyze150.0ms (3.1%)

sample55.0ms (1.1%)

simplify92.0ms (1.9%)

prune4.0ms (0.1%)

localize89.0ms (1.8%)

rewrite164.0ms (3.3%)

series67.0ms (1.4%)

simplify102.0ms (2.1%)

prune79.0ms (1.6%)

localize91.0ms (1.9%)

rewrite148.0ms (3%)

series127.0ms (2.6%)

simplify134.0ms (2.7%)

prune65.0ms (1.3%)

localize94.0ms (1.9%)

rewrite214.0ms (4.4%)

series118.0ms (2.4%)

simplify131.0ms (2.7%)

prune79.0ms (1.6%)

localize99.0ms (2%)

rewrite197.0ms (4%)

series70.0ms (1.4%)

simplify157.0ms (3.2%)

prune74.0ms (1.5%)

regimes491.0ms (10%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.8s (36.9%)

Profiling