Details

analyze220.0ms (5%)

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 (1.3%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
2.0ms	25×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify9.0ms (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

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)

localize12.0ms (0.3%)

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))
✓	1.0b	(/.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)))

series37.0ms (0.8%)

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)))
8.0ms	(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)))
1.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))

simplify130.0ms (3%)

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

prune130.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Error

0.9b

Counts

98 → 4

Alt Table

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

Compiler

Compiled 2183 to 1243 computations (43.1% saved)

localize13.0ms (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 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))
✓	1.0b	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.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 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
✓	1.0b	(/.f64 1 (sqrt.f64 3))

series230.0ms (5.2%)

Counts

4 → 72

Calls

4 calls:

97.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
69.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))
64.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
0.0ms	(/.f64 1 (sqrt.f64 3))

rewrite31.0ms (0.7%)

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:

14.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.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 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
0.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))

simplify198.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

224 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	4593
1	330	3862
2	933	3699
3	2132	3651
4	2660	3651
5	4263	3651
6	4937	3651
7	5174	3651

prune271.0ms (6.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	207	3	210

Error

0.9b

Counts

210 → 3

Alt Table

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

Compiler

Compiled 5615 to 3907 computations (30.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series182.0ms (4.2%)

Counts

3 → 72

Calls

3 calls:

97.0ms

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

69.0ms

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

16.0ms

(*.f64 (/.f64 1 (sqrt.f64 3)) (acos.f64 (/.f64 (neg.f64 g) h)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`associate-l_binary64`
22×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

3 → 68

Calls

3 calls:

9.0ms

(*.f64 (/.f64 1 (sqrt.f64 3)) (acos.f64 (/.f64 (neg.f64 g) h)))

1.0ms

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

0.0ms

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

simplify100.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

524×	`distribute-rgt-in_binary64`
515×	`distribute-lft-in_binary64`
457×	`times-frac_binary64`
383×	`associate-l_binary64`
324×	`associate-r_binary64`

Counts

140 → 115

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	108	2736
1	177	2373
2	375	2373
3	736	2373
4	2718	2373
5	4995	2373

prune185.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	164	3	167

Error

0.9b

Counts

167 → 3

Alt Table

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

Compiler

Compiled 4316 to 3083 computations (28.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(/.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)))))

series51.0ms (1.2%)

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))))
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:

1.0ms	(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)))))

simplify249.0ms (5.7%)

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

prune123.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	119	3	122

Error

0.9b

Counts

122 → 3

Alt Table

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

Compiler

Compiled 2722 to 1644 computations (39.6% saved)

regimes889.0ms (20.3%)

Accuracy

Total 0.0b remaining (1.3%)

Threshold costs 0.0b (1.3%)

Counts

99 → 1

Compiler

Compiled 19091 to 15778 computations (17.4% saved)

simplify3.0ms (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	20	35
1	29	35
2	33	35
3	36	35
4	37	35
5	36	35

end1.0ms (0%)

Compiler: Compiled 23 to 21 computations (8.7% saved)

sample1.2s (27.6%)

Algorithm

1×

intervals

Results

816.0ms	8000×	body	128	valid
47.0ms	579×	body	128	nan

Compiler

Compiled 113 to 97 computations (14.2% saved)

Details

analyze220.0ms (5%)

sample56.0ms (1.3%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize12.0ms (0.3%)

series37.0ms (0.8%)

rewrite6.0ms (0.1%)

simplify130.0ms (3%)

prune130.0ms (3%)

localize13.0ms (0.3%)

series230.0ms (5.2%)

rewrite31.0ms (0.7%)

simplify198.0ms (4.5%)

prune271.0ms (6.2%)

localize13.0ms (0.3%)

series182.0ms (4.2%)

rewrite15.0ms (0.3%)

simplify100.0ms (2.3%)

prune185.0ms (4.2%)

localize12.0ms (0.3%)

series51.0ms (1.2%)

rewrite2.0ms (0%)

simplify249.0ms (5.7%)

prune123.0ms (2.8%)

regimes889.0ms (20.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.2s (27.6%)

Profiling