Details

analyze222.0ms (5.6%)

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)

sample56.0ms (1.4%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
2.0ms	20×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify8.0ms (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)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(acos.f64 (/.f64 (neg.f64 g) h))
✓	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)))

series41.0ms (1%)

Counts

4 → 96

Calls

4 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))
5.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
3.0ms	(acos.f64 (/.f64 (neg.f64 g) h))

rewrite7.0ms (0.2%)

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 → 62

Calls

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

simplify139.0ms (3.5%)

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

158 → 118

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	108	2519
1	152	2386
2	248	2386
3	413	2386
4	876	2386
5	2201	2386
6	4686	2386
7	5111	2386

prune131.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	4	119

Error

0.9b

Counts

119 → 4

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

Compiler

Compiled 2497 to 1401 computations (43.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series51.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
22.0ms	(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)))))

simplify240.0ms (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 → 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 (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	119	4	123

Error

0.9b

Counts

123 → 4

Alt Table

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

Compiler

Compiled 2788 to 1708 computations (38.7% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(expm1.f64 (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	(log1p.f64 (expm1.f64 (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	(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))

series303.0ms (7.6%)

Counts

4 → 72

Calls

4 calls:

110.0ms	(expm1.f64 (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))))))
98.0ms	(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)))))
95.0ms	(log1p.f64 (expm1.f64 (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	(/.f64 1 (sqrt.f64 3))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

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	(expm1.f64 (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	(log1p.f64 (expm1.f64 (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)))))))

simplify149.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
406×	`sub-neg_binary64`
382×	`fma-neg_binary64`
236×	`*-commutative_binary64`
215×	`times-frac_binary64`

Counts

151 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	2999
1	135	2705
2	168	2482
3	258	2482
4	566	2482
5	1421	2482
6	2234	2482
7	4351	2482
8	4790	2482

prune144.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	2	2
Picked	0	1	1
Done	1	0	1
Total	105	4	109

Error

0.9b

Counts

109 → 4

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (log1p.f64 (expm1.f64 (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 (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 (log.f64 (exp.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))))
	1.0b	(.f64 2 (cbrt.f64 (.f64 (.f64 (log1p.f64 (expm1.f64 (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))))))) (log1p.f64 (expm1.f64 (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)))))))) (log1p.f64 (expm1.f64 (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))))))))))

Compiler

Compiled 3088 to 2294 computations (25.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series103.0ms (2.6%)

Counts

4 → 72

Calls

4 calls:

54.0ms	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)
25.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
24.0ms	(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 (0.3%)

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))))

simplify144.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

740×	`sqr-pow_binary64`
574×	`fma-def_binary64`
454×	`*-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

prune126.0ms (3.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	99	5	104

Error

0.0b

Counts

104 → 5

Alt Table

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

Compiler

Compiled 2564 to 1670 computations (34.9% saved)

regimes615.0ms (15.5%)

Accuracy

Total 0.0b remaining (72.2%)

Threshold costs 0.0b (72.2%)

Counts

62 → 1

Compiler

Compiled 13596 to 11640 computations (14.4% 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

end1.0ms (0%)

Compiler: Compiled 41 to 27 computations (34.1% saved)

sample1.3s (32%)

Algorithm

1×

intervals

Results

786.0ms	8000×	body	128	valid
50.0ms	576×	body	128	nan

Compiler

Compiled 227 to 177 computations (22% saved)

Details

analyze222.0ms (5.6%)

sample56.0ms (1.4%)

simplify8.0ms (0.2%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series41.0ms (1%)

rewrite7.0ms (0.2%)

simplify139.0ms (3.5%)

prune131.0ms (3.3%)

localize15.0ms (0.4%)

series51.0ms (1.3%)

rewrite2.0ms (0%)

simplify240.0ms (6%)

prune143.0ms (3.6%)

localize16.0ms (0.4%)

series303.0ms (7.6%)

rewrite8.0ms (0.2%)

simplify149.0ms (3.7%)

prune144.0ms (3.6%)

localize12.0ms (0.3%)

series103.0ms (2.6%)

rewrite11.0ms (0.3%)

simplify144.0ms (3.6%)

prune126.0ms (3.2%)

regimes615.0ms (15.5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.3s (32%)

Profiling