Details

analyze227.0ms (3.8%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
2.0ms	20×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify14.0ms (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 → 1

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

1.0b

Counts

2 → 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 45 to 39 computations (13.3% saved)

localize10.0ms (0.2%)

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))
✓	0.9b	(/.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

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:

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

series95.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

59.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
23.0ms	(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)

simplify144.0ms (2.4%)

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 → 123

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

prune61.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	2	124

Error

1.0b

Counts

124 → 2

Alt Table

Status	Error	Program
▶	1.0b	(.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))))
	1.0b	(.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 PI.f64))))))

Status

Error

Program

▶

1.0b

(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))))

1.0b

(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 PI.f64))))))

Compiler

Compiled 1049 to 614 computations (41.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))
✓	0.9b	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3)))
✓	1.0b	(cos.f64 (fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3)))))
✓	1.0b	(/.f64 1 (sqrt.f64 3))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

15.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3)))
3.0ms	(/.f64 1 (sqrt.f64 3))
1.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3)))))
0.0ms	(fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))

series255.0ms (4.2%)

Counts

4 → 72

Calls

4 calls:

108.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3)))))
88.0ms	(fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))
58.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3)))
0.0ms	(/.f64 1 (sqrt.f64 3))

simplify258.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
551×	`fma-def_binary64`
469×	`times-frac_binary64`
379×	`associate-/l*_binary64`
296×	`*-commutative_binary64`

Counts

224 → 224

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	4593
1	332	3862
2	931	3699
3	2133	3651
4	2661	3651
5	4263	3651
6	4935	3651
7	5167	3651

prune97.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	224	2	226

Error

1.0b

Counts

226 → 2

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))))
▶	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))

Status

Error

Program

✓

1.0b

(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))))

▶

1.0b

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

Compiler

Compiled 2147 to 1442 computations (32.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

3.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)
1.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
0.0ms	(expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))

series1.3s (22.3%)

Counts

4 → 96

Calls

4 calls:

1.2s	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
64.0ms	(expm1.f64 (cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))
55.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
14.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)

simplify201.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
554×	`fma-def_binary64`
471×	`associate-/l/_binary64`
407×	`distribute-rgt-in_binary64`
395×	`associate-/l*_binary64`

Counts

159 → 159

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	122	3045
1	160	2884
2	239	2884
3	336	2884
4	590	2872
5	855	2872
6	1513	2872
7	4074	2872
8	4453	2872
9	4872	2872

prune56.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	159	2	161

Error

1.0b

Counts

161 → 2

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))))
▶	1.0b	(.f64 2 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1)))

Status

Error

Program

✓

1.0b

(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))))

▶

1.0b

(*.f64 2 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1)))

Compiler

Compiled 1295 to 790 computations (39% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))
✓	1.0b	(-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1)
✓	1.0b	(cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))
✓	1.0b	(log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 75

Calls

4 calls:

4.0ms	(-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1)
3.0ms	(*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))
1.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))
1.0ms	(log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1))

series1.3s (21.8%)

Counts

4 → 80

Calls

4 calls:

1.2s	(log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1))
64.0ms	(-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1)
53.0ms	(cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))
13.0ms	(*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))

simplify175.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

439×	`sub-neg_binary64`
327×	`*-commutative_binary64`
304×	`times-frac_binary64`
294×	`associate-l_binary64`
275×	`unsub-neg_binary64`

Counts

155 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	3187
1	179	2915
2	288	2902
3	621	2900
4	1959	2900
5	3776	2900
6	4493	2900
7	5061	2900

prune46.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	155	2	157

Error

1.0b

Counts

157 → 2

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))))
	1.0b	(.f64 2 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1)))

Status

Error

Program

1.0b

(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) (sqrt.f64 3))))))

1.0b

(*.f64 2 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 2/3 PI.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))) 1)))

Compiler

Compiled 1293 to 833 computations (35.6% saved)

regimes429.0ms (7.1%)

Accuracy

Total 0.0b remaining (0.7%)

Threshold costs 0.0b (0.7%)

Compiler

Compiled 8750 to 7662 computations (12.4% 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	18	31
1	27	31
2	31	31
3	34	31
4	35	31
5	34	31

end1.0ms (0%)

Compiler: Compiled 21 to 19 computations (9.5% saved)

sample1.1s (18.9%)

Algorithm

1×

intervals

Results

775.0ms	8000×	body	128	valid
47.0ms	569×	body	128	nan

Compiler

Compiled 82 to 74 computations (9.8% saved)

Details

analyze227.0ms (3.8%)

sample38.0ms (0.6%)

simplify14.0ms (0.2%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite7.0ms (0.1%)

series95.0ms (1.6%)

simplify144.0ms (2.4%)

prune61.0ms (1%)

localize18.0ms (0.3%)

rewrite30.0ms (0.5%)

series255.0ms (4.2%)

simplify258.0ms (4.3%)

prune97.0ms (1.6%)

localize13.0ms (0.2%)

rewrite8.0ms (0.1%)

series1.3s (22.3%)

simplify201.0ms (3.4%)

prune56.0ms (0.9%)

localize15.0ms (0.3%)

rewrite14.0ms (0.2%)

series1.3s (21.8%)

simplify175.0ms (2.9%)

prune46.0ms (0.8%)

regimes429.0ms (7.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (18.9%)

Profiling