Details

analyze239.0ms (4.4%)

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)

sample1.6s (29.8%)

Results

1.5s	8256×	body	128	valid
90.0ms	549×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify10.0ms (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

prune4.0ms (0.1%)

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)

localize12.0ms (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)))

series38.0ms (0.7%)

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)))
10.0ms	(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))

simplify372.0ms (6.9%)

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 → 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

prune131.0ms (2.4%)

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

Compiler

Compiled 2093 to 1193 computations (43% saved)

localize13.0ms (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))))

series264.0ms (4.9%)

Counts

4 → 96

Calls

4 calls:

93.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))))
88.0ms	(/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))
66.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))
16.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))

rewrite42.0ms (0.8%)

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:

9.0ms	(/.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)))

simplify368.0ms (6.8%)

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

prune499.0ms (9.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	0	2	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 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))) (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.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 (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 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 9461 to 5960 computations (37% saved)

localize15.0ms (0.3%)

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

series52.0ms (1%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
23.0ms	(log1p.f64 (expm1.f64 (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)))))

simplify252.0ms (4.7%)

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 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	1455
1	59	1377
2	74	1377
3	87	1377
4	100	1377
5	122	1377
6	170	1377
7	270	1377
8	614	1377
9	1210	1377
10	1349	1377
11	1612	1377
12	1917	1377
13	2211	1377
14	2613	1377
15	2967	1377
16	3150	1377
17	3407	1377
18	3546	1377
19	3625	1377
20	3705	1377
21	4463	1377
22	4855	1377

prune143.0ms (2.7%)

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

0.9b

Counts

123 → 4

Alt Table

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

Compiler

Compiled 2803 to 1713 computations (38.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series102.0ms (1.9%)

Counts

4 → 72

Calls

4 calls:

55.0ms	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)
24.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
23.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3))
0.0ms	(*.f64 2/3 (PI.f64))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

4 → 78

Calls

4 calls:

3.0ms	(*.f64 2/3 (PI.f64))
2.0ms	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3))
1.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))

simplify148.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

740×	`sqr-pow_binary64`
574×	`fma-def_binary64`
452×	`*-commutative_binary64`
386×	`log-prod_binary64`
384×	`exp-prod_binary64`

Counts

150 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	112	3222
1	166	2982
2	368	2966
3	1272	2966
4	2315	2963
5	4112	2963
6	4941	2963

prune122.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	100	4	104

Error

Counts

104 → 4

Alt Table

Status	Error	Program
✓	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 (.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))))
	0.1b	(.f64 2 (.f64 (cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) 3)) (cbrt.f64 (pow.f64 (cbrt.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)))))

Compiler

Compiled 2494 to 1602 computations (35.8% saved)

regimes781.0ms (14.5%)

Accuracy

Total 0.0b remaining (70.6%)

Threshold costs 0.0b (70.6%)

Counts

66 → 1

Compiler

Compiled 13121 to 11269 computations (14.1% saved)

simplify4.0ms (0.1%)

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	18	65
1	27	65
2	31	65
3	34	65
4	35	65
5	35	65

end134.0ms (2.5%)

Compiler: Compiled 207 to 147 computations (29% saved)

Details

analyze239.0ms (4.4%)

sample1.6s (29.8%)

simplify10.0ms (0.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series38.0ms (0.7%)

rewrite6.0ms (0.1%)

simplify372.0ms (6.9%)

prune131.0ms (2.4%)

localize13.0ms (0.2%)

series264.0ms (4.9%)

rewrite42.0ms (0.8%)

simplify368.0ms (6.8%)

prune499.0ms (9.3%)

localize15.0ms (0.3%)

series52.0ms (1%)

rewrite2.0ms (0%)

simplify252.0ms (4.7%)

prune143.0ms (2.7%)

localize14.0ms (0.3%)

series102.0ms (1.9%)

rewrite11.0ms (0.2%)

simplify148.0ms (2.8%)

prune122.0ms (2.3%)

regimes781.0ms (14.5%)

simplify4.0ms (0.1%)

end134.0ms (2.5%)

Profiling