Details

analyze324.0ms (4.6%)

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)

sample1.8s (25%)

Results

1.6s	8256×	body	128	valid
82.0ms	569×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify9.0ms (0.1%)

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)

localize11.0ms (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)))

series40.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

23.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
11.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
6.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite6.0ms (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))

simplify126.0ms (1.8%)

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 → 97

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

prune156.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	3	98

Error

0.9b

Counts

98 → 3

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 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)))))
	1.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

Compiler

Compiled 2121 to 1209 computations (43% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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 (/.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))))

series249.0ms (3.5%)

Counts

4 → 96

Calls

4 calls:

100.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))))
68.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))
64.0ms	(/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))
17.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))

rewrite41.0ms (0.6%)

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:

10.0ms	(/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))
3.0ms	(/.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)))

simplify320.0ms (4.5%)

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 → 323

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	264	9313
1	501	9003
2	900	8721
3	1849	8607
4	2330	8600
5	3649	8388
6	4997	8388

prune513.0ms (7.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	321	2	323
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	322	4	326

Error

0.9b

Counts

326 → 4

Alt Table

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

Compiler

Compiled 9453 to 5952 computations (37% 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	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
✓	1.0b	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3))
✓	1.0b	(pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)

series111.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

56.0ms	(pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3)
24.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) 3))
24.0ms	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
7.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
12×	`cbrt-prod_binary64`
9×	`times-frac_binary64`

Counts

4 → 89

Calls

4 calls:

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

simplify210.0ms (3%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-def_binary64`
459×	`*-commutative_binary64`
441×	`log-prod_binary64`
384×	`exp-prod_binary64`
358×	`sqr-pow_binary64`

Counts

185 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	137	3920
1	209	3650
2	444	3634
3	1380	3634
4	2627	3631
5	4230	3631
6	4623	3631
7	4807	3631

prune113.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	124	5	129

Error

Counts

129 → 5

Alt Table

Status	Error	Program
✓	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)))))
	1.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
▶	0.1b	(.f64 2 (.f64 (cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))) (cbrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (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 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))))) 9))))

Compiler

Compiled 3245 to 2040 computations (37.1% saved)

localize15.0ms (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	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
✓	1.0b	(*.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))
✓	1.0b	(cbrt.f64 (*.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))) (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))

series1.4s (19.6%)

Counts

2 → 48

Calls

2 calls:

1.3s

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

41.0ms

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

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms

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

2.0ms

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

simplify140.0ms (2%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-def_binary64`
455×	`log-div_binary64`
372×	`sqr-pow_binary64`
316×	`*-commutative_binary64`
255×	`associate-*r/_binary64`

Counts

89 → 66

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	75	2577
1	117	2371
2	260	2074
3	712	2043
4	1224	1936
5	1534	1936
6	2962	1932
7	4602	1932
8	5030	1932

prune267.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	238	4	242

Error

Counts

242 → 4

Alt Table

Status	Error	Program
✓	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)))))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))))))
	0.1b	(.f64 2 (.f64 (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))))) 2)))) (cbrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
	1.5b	(.f64 2 (cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))))) 9))))

Compiler

Compiled 11021 to 6038 computations (45.2% saved)

regimes1.1s (15.2%)

Accuracy

Total 0.0b remaining (75.1%)

Threshold costs 0.0b (75.1%)

Counts

95 → 1

Compiler

Compiled 22155 to 17532 computations (20.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-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	24	48
1	34	48
2	38	48
3	41	48
4	42	48
5	41	48

end121.0ms (1.7%)

Compiler: Compiled 154 to 124 computations (19.5% saved)

Details

analyze324.0ms (4.6%)

sample1.8s (25%)

simplify9.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0.2%)

series40.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify126.0ms (1.8%)

prune156.0ms (2.2%)

localize12.0ms (0.2%)

series249.0ms (3.5%)

rewrite41.0ms (0.6%)

simplify320.0ms (4.5%)

prune513.0ms (7.3%)

localize13.0ms (0.2%)

series111.0ms (1.6%)

rewrite11.0ms (0.2%)

simplify210.0ms (3%)

prune113.0ms (1.6%)

localize15.0ms (0.2%)

series1.4s (19.6%)

rewrite8.0ms (0.1%)

simplify140.0ms (2%)

prune267.0ms (3.8%)

regimes1.1s (15.2%)

simplify3.0ms (0%)

end121.0ms (1.7%)

Profiling