Details

analyze271.0ms (1.8%)

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)

sample110.0ms (0.7%)

Algorithm

1×

intervals

Results

65.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 87 to 63 computations (27.6% saved)

simplify65.0ms (0.4%)

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

prune9.0ms (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
	0.6b	(.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

0.6b

(*.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)

localize180.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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)

series61.0ms (0.4%)

Counts

4 → 84

Calls

4 calls:

19.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
19.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
15.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
7.0ms	(.f32 (.f32 2 (PI.f32)) s)

rewrite50.0ms (0.3%)

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:

12.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
10.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
8.0ms	(.f32 (.f32 2 (PI.f32)) s)
8.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))

simplify158.0ms (1.1%)

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

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

prune494.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	149	6	155

Error

0.0b

Counts

155 → 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 (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 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)))
	0.1b	(+.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)))))
	0.6b	(.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 (exp.f32 (log.f32 (.f32 2 (.f32 s (PI.f32))))) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
▶	0.1b	(+.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) 3) s))) (.f32 (.f32 (.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 6216 to 3593 computations (42.2% saved)

localize176.0ms (1.2%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

17.0ms

(/.f32 (/.f32 (neg.f32 r) 3) s)

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

222×	`times-frac_binary32`
116×	`*-un-lft-identity_binary32`
116×	`add-sqr-sqrt_binary32`
116×	`add-cube-cbrt_binary32`
36×	`distribute-lft-neg-in_binary32`

Counts

1 → 158

Calls

1 calls:

15.0ms

(/.f32 (/.f32 (neg.f32 r) 3) s)

simplify303.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

756×	`div-sub_binary32`
455×	`neg-mul-1_binary32`
340×	`associate-/l/_binary32`
290×	`associate-/r/_binary32`
269×	`distribute-frac-neg_binary32`

Counts

182 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	3491
1	635	3398
2	1734	3326
3	3232	3326
4	4235	3326
5	4972	3326
6	4870	3326

prune1.2s (8.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	309	3	312
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	313	5	318

Error

0.0b

Counts

318 → 5

Alt Table

Status	Error	Program
	0.6b	(.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 2 (PI.f32)) (.f32 s r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 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 (exp.f32 (log.f32 (.f32 2 (.f32 s (PI.f32))))) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.1b	(+.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) 3) s))) (expm1.f32 (log1p.f32 (.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 (/.f32 (neg.f32 r) 3) s))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 r)))))

Compiler

Compiled 13312 to 7627 computations (42.7% saved)

localize178.0ms (1.2%)

Local error

Found 4 expressions with local error:

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

series29.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))
10.0ms	(exp.f32 (/.f32 (neg.f32 r) s))

rewrite32.0ms (0.2%)

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:

12.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))
9.0ms	(exp.f32 (/.f32 (neg.f32 r) s))

simplify145.0ms (1%)

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

prune1.4s (9.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	346	3	349
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	350	4	354

Error

0.0b

Counts

354 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r)))) (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 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 2 (PI.f32)) (.f32 s r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 3) s))) (expm1.f32 (log1p.f32 (.f32 6 (.f32 s (.f32 (PI.f32) r)))))))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (pow.f32 (exp.f32 (/.f32 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 (cbrt.f32 s) (cbrt.f32 s)))) (/.f32 (neg.f32 (cbrt.f32 r)) (cbrt.f32 s)))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 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 (neg.f32 r) 3) s))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 r)))))

Compiler

Compiled 14874 to 8162 computations (45.1% saved)

localize219.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
	0.3b	(.f32 (.f32 2 (PI.f32)) (*.f32 s r))
✓	0.3b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r)))) (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 s r))))
✓	0.5b	(.f32 (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 s r))))

series2.3s (15.7%)

Counts

2 → 48

Calls

2 calls:

2.0s

(*.f32 (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r))) (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r))))

281.0ms

(*.f32 (*.f32 (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r))) (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r)))) (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r))))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`pow1_binary32`
15×	`pow1/3_binary32`
11×	`pow-prod-up_binary32`
10×	`add-sqr-sqrt_binary32`
9×	`add-exp-log_binary32`

Counts

2 → 68

Calls

2 calls:

19.0ms

(*.f32 (*.f32 (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r))) (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r)))) (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r))))

11.0ms

(*.f32 (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r))) (cbrt.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 s r))))

simplify258.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary32`
386×	`fma-def_binary32`
322×	`*-commutative_binary32`
304×	`unswap-sqr_binary32`
233×	`log-prod_binary32`

Counts

116 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	2554
1	268	2246
2	745	1948
3	1587	1794
4	4279	1794
5	4986	1794
6	4984	1794
7	5033	1794

prune1.1s (7.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	222	4	226

Error

0.0b

Counts

226 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r)))) (cbrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 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 2 (PI.f32)) (.f32 s r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 3) s))) (expm1.f32 (log1p.f32 (.f32 6 (.f32 s (.f32 (PI.f32) r)))))))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (pow.f32 (exp.f32 (/.f32 (.f32 (cbrt.f32 r) (cbrt.f32 r)) (.f32 (cbrt.f32 s) (cbrt.f32 s)))) (/.f32 (neg.f32 (cbrt.f32 r)) (cbrt.f32 s)))) (.f32 (.f32 2 (PI.f32)) (.f32 s r))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 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 (neg.f32 r) 3) s))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 r)))))

Compiler

Compiled 12677 to 7160 computations (43.5% saved)

regimes2.3s (15.9%)

Accuracy

Total 0.0b remaining (28.7%)

Threshold costs 0.0b (28.7%)

Counts

286 → 1

Compiler

Compiled 35779 to 25687 computations (28.2% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary32`
5×	`+-commutative_binary32`
4×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	85
1	47	85
2	55	85
3	62	85
4	66	85
5	67	85
6	67	85

end2.0ms (0%)

Compiler: Compiled 54 to 36 computations (33.3% saved)

sample3.5s (23.7%)

Algorithm

1×

intervals

Results

2.0s	8000×	body	128	valid
367.0ms	8000×	pre	128	true

Compiler

Compiled 286 to 199 computations (30.4% saved)

Details

analyze271.0ms (1.8%)

sample110.0ms (0.7%)

simplify65.0ms (0.4%)

prune9.0ms (0.1%)

localize180.0ms (1.2%)

series61.0ms (0.4%)

rewrite50.0ms (0.3%)

simplify158.0ms (1.1%)

prune494.0ms (3.4%)

localize176.0ms (1.2%)

series17.0ms (0.1%)

rewrite51.0ms (0.3%)

simplify303.0ms (2.1%)

prune1.2s (8.3%)

localize178.0ms (1.2%)

series29.0ms (0.2%)

rewrite32.0ms (0.2%)

simplify145.0ms (1%)

prune1.4s (9.8%)

localize219.0ms (1.5%)

series2.3s (15.7%)

rewrite39.0ms (0.3%)

simplify258.0ms (1.8%)

prune1.1s (7.2%)

regimes2.3s (15.9%)

simplify11.0ms (0.1%)

end2.0ms (0%)

sample3.5s (23.7%)

Profiling