Details

analyze239.0ms (3.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	68.7%	6.3%	5
25%	65.6%	9.5%	6
37.5%	39%	23.5%	7
37.5%	36.7%	25.9%	8
43.7%	20.7%	35.6%	9
43.7%	19.3%	37%	10
46.8%	10.6%	42.5%	11
46.8%	9.9%	43.3%	12
48.4%	5.4%	46.2%	13
48.4%	5%	46.6%	14

Compiler

Compiled 19 to 17 computations (10.5% saved)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
1.0ms	16×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	26	23
2	40	21
3	49	21
4	56	21
5	63	21
6	74	21
7	73	21
8	62	21

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 61 to 49 computations (19.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
✓	1.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	1.0b	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

8.0ms	(fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
2.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series96.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

57.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
26.0ms	(fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
13.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

simplify137.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

516×	`distribute-rgt-in_binary64`
515×	`fma-neg_binary64`
508×	`associate-/l/_binary64`
495×	`distribute-lft-in_binary64`
420×	`distribute-rgt-out_binary64`

Counts

123 → 239

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	105	2186
1	150	2070
2	246	2070
3	411	2070
4	874	2070
5	2199	2070
6	4684	2070
7	5109	2070

prune128.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	235	4	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	4	240

Error

0.9b

Counts

240 → 4

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
▶	1.0b	(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2193 to 1251 computations (43% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))
✓	0.0b	(fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))
✓	0.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
✓	1.0b	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
156×	`add-cube-cbrt_binary64`
144×	`sqrt-prod_binary64`

Counts

4 → 242

Calls

4 calls:

8.0ms	(/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))
4.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
1.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))))
0.0ms	(fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))

series270.0ms (3.7%)

Counts

4 → 96

Calls

4 calls:

107.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))))
71.0ms	(fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))
59.0ms	(/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))
32.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))

simplify344.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

692×	`distribute-rgt-in_binary64`
495×	`associate-/l/_binary64`
371×	`fma-def_binary64`
308×	`*-commutative_binary64`
304×	`fma-neg_binary64`

Counts

338 → 665

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	262	9313
1	500	9003
2	900	8721
3	1849	8607
4	2330	8600
5	3649	8388
6	4997	8388

prune410.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	665	0	665
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	665	4	669

Error

0.9b

Counts

669 → 4

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
▶	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 9427 to 5914 computations (37.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
	1.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	1.0b	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
	1.0b	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

series1.2s (16.9%)

Counts

2 → 48

Calls

2 calls:

1.2s	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
65.0ms	(expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

simplify265.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1392×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
592×	`cube-prod_binary64`
500×	`fabs-mul_binary64`
470×	`pow-sqr_binary64`

Counts

70 → 134

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	1455
1	60	1377
2	75	1377
3	88	1377
4	101	1377
5	123	1377
6	171	1377
7	271	1377
8	615	1377
9	1211	1377
10	1350	1377
11	1613	1377
12	1918	1377
13	2212	1377
14	2614	1377
15	2968	1377
16	3151	1377
17	3408	1377
18	3547	1377
19	3626	1377
20	3706	1377
21	4464	1377
22	4856	1377

prune138.0ms (1.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	307	4	311

Error

0.9b

Counts

311 → 4

Alt Table

Status	Error	Program
▶	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2791 to 1689 computations (39.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(*.f64 (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
	1.0b	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
	1.0b	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
	1.0b	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`

Counts

1 → 42

Calls

1 calls:

5.0ms

(*.f64 (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

series1.2s (16.5%)

Counts

1 → 24

Calls

1 calls:

1.2s	(*.f64 (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

simplify134.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

882×	`fma-def_binary64`
454×	`unswap-sqr_binary64`
352×	`sqr-pow_binary64`
272×	`*-commutative_binary64`
256×	`associate-+l+_binary64`

Counts

66 → 128

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	2311
1	103	2279
2	217	1839
3	437	1791
4	788	1518
5	1362	1518
6	2610	1518
7	4588	1518
8	5098	1518

prune118.0ms (1.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1051	1	1052
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	1051	5	1056

Error

Counts

1056 → 5

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	0.1b	(.f64 2 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))) 6)) (cbrt.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 5868 to 3386 computations (42.3% saved)

regimes1.1s (15.6%)

Accuracy

Total 0.1b remaining (81.8%)

Threshold costs 0.1b (81.8%)

Compiler

Compiled 26062 to 20837 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	50
1	32	50
2	36	50
3	38	50
4	38	50

end1.0ms (0%)

Compiler: Compiled 32 to 24 computations (25% saved)

sample1.3s (17.5%)

Algorithm

1×

intervals

Results

819.0ms	8000×	body	128	valid
45.0ms	535×	body	128	nan

Compiler

Compiled 203 to 156 computations (23.2% saved)

Details

analyze239.0ms (3.3%)

sample37.0ms (0.5%)

simplify12.0ms (0.2%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite13.0ms (0.2%)

series96.0ms (1.3%)

simplify137.0ms (1.9%)

prune128.0ms (1.7%)

localize12.0ms (0.2%)

rewrite29.0ms (0.4%)

series270.0ms (3.7%)

simplify344.0ms (4.7%)

prune410.0ms (5.6%)

localize15.0ms (0.2%)

rewrite2.0ms (0%)

series1.2s (16.9%)

simplify265.0ms (3.6%)

prune138.0ms (1.9%)

localize15.0ms (0.2%)

rewrite7.0ms (0.1%)

series1.2s (16.5%)

simplify134.0ms (1.8%)

prune118.0ms (1.6%)

regimes1.1s (15.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.3s (17.5%)

Profiling