Details

analyze249.0ms (4.8%)

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)

sample40.0ms (0.8%)

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)

simplify41.0ms (0.8%)

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 (0.1%)

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)

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)))

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))

series102.0ms (2%)

Counts

3 → 72

Calls

3 calls:

60.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
27.0ms	(fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
15.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

simplify161.0ms (3.1%)

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

prune134.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	234	5	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	235	5	240

Error

0.9b

Counts

240 → 5

Alt Table

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

Compiler

Compiled 2251 to 1293 computations (42.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`

Counts

4 → 127

Calls

4 calls:

4.0ms	(/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))
2.0ms	(/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))
1.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))))
0.0ms	(fma.f64 PI.f64 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))))

series147.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

60.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))))
46.0ms	(/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))
26.0ms	(fma.f64 PI.f64 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))))
14.0ms	(/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h))))

simplify265.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-def_binary64`
415×	`times-frac_binary64`
410×	`distribute-lft-out_binary64`
402×	`distribute-rgt-out_binary64`
350×	`fma-neg_binary64`

Counts

223 → 437

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	4210
1	212	3935
2	450	3916
3	931	3916
4	1586	3916
5	3047	3916
6	3475	3916
7	4739	3916
8	4876	3916

prune276.0ms (5.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	437	0	437
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	437	5	442

Error

0.9b

Counts

442 → 5

Alt Table

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

Compiler

Compiled 5187 to 3051 computations (41.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	1.0b	(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)))
✓	1.0b	(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)))))

series1.3s (25.2%)

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)))))
68.0ms	(expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

simplify280.0ms (5.4%)

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

prune141.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	307	5	312

Error

0.9b

Counts

312 → 5

Alt Table

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

Compiler

Compiled 2851 to 1733 computations (39.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(sin.f64 (*.f64 PI.f64 2/3))
	1.0b	(*.f64 PI.f64 2/3)
✓	1.0b	(*.f64 PI.f64 2/3)
✓	1.6b	(cos.f64 (*.f64 PI.f64 2/3))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 38

Calls

3 calls:

3.0ms	(*.f64 PI.f64 2/3)
1.0ms	(cos.f64 (*.f64 PI.f64 2/3))
1.0ms	(sin.f64 (*.f64 PI.f64 2/3))

series0.0ms (0%)

Counts

3 → 0

Calls

3 calls:

0.0ms	(cos.f64 (*.f64 PI.f64 2/3))
0.0ms	(*.f64 PI.f64 2/3)
0.0ms	(sin.f64 (*.f64 PI.f64 2/3))

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

603×	`unswap-sqr_binary64`
428×	`associate-*l/_binary64`
378×	`associate-*r/_binary64`
293×	`log-div_binary64`
277×	`*-commutative_binary64`

Counts

38 → 46

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	383
1	83	337
2	169	337
3	229	337
4	293	337
5	442	337
6	806	337
7	1343	337
8	3492	337
9	4632	337
10	4833	337
11	4757	337

prune55.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	73	4	77

Error

0.0b

Counts

77 → 4

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 PI.f64 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (.f64 (log1p.f64 (expm1.f64 (sin.f64 (*.f64 PI.f64 2/3)))) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 1 (/.f64 3 (acos.f64 (/.f64 (neg.f64 g) h)))))))
	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 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2222 to 1378 computations (38% saved)

regimes444.0ms (8.5%)

Accuracy

Total 0.0b remaining (68.1%)

Threshold costs 0.0b (68.1%)

Compiler

Compiled 10188 to 7953 computations (21.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	37	53
2	49	53
3	58	53
4	63	53
5	64	53
6	64	53

end1.0ms (0%)

Compiler: Compiled 33 to 25 computations (24.2% saved)

sample1.4s (26.4%)

Algorithm

1×

intervals

Results

964.0ms	8000×	body	128	valid
54.0ms	576×	body	128	nan

Compiler

Compiled 163 to 127 computations (22.1% saved)

Details

analyze249.0ms (4.8%)

sample40.0ms (0.8%)

simplify41.0ms (0.8%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite6.0ms (0.1%)

series102.0ms (2%)

simplify161.0ms (3.1%)

prune134.0ms (2.6%)

localize12.0ms (0.2%)

rewrite17.0ms (0.3%)

series147.0ms (2.8%)

simplify265.0ms (5.1%)

prune276.0ms (5.3%)

localize14.0ms (0.3%)

rewrite2.0ms (0%)

series1.3s (25.2%)

simplify280.0ms (5.4%)

prune141.0ms (2.7%)

localize18.0ms (0.3%)

rewrite6.0ms (0.1%)

series0.0ms (0%)

simplify95.0ms (1.8%)

prune55.0ms (1.1%)

regimes444.0ms (8.5%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.4s (26.4%)

Profiling