Details

analyze213.0ms (5.5%)

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)

sample54.0ms (1.4%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
1.0ms	18×	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

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)

localize13.0ms (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)))

series36.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(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 (0.2%)

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:

3.0ms	(/.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))

simplify123.0ms (3.2%)

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

prune106.0ms (2.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	2	98

Error

1.0b

Counts

98 → 2

Alt Table

Status	Error	Program
▶	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))))))
	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))))))

Status

Error

Program

▶

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))))))

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))))))

Compiler

Compiled 2111 to 1191 computations (43.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.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))

series168.0ms (4.3%)

Counts

4 → 72

Calls

4 calls:

91.0ms	(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)))))
61.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
16.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
0.0ms	(/.f64 1 (sqrt.f64 3))

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`add-sqr-sqrt_binary64`
94×	`times-frac_binary64`
66×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`
53×	`sqrt-prod_binary64`

Counts

4 → 185

Calls

4 calls:

15.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
3.0ms	(/.f64 1 (sqrt.f64 3))
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 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))

simplify218.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-def_binary64`
500×	`times-frac_binary64`
416×	`associate-/l*_binary64`
322×	`*-commutative_binary64`
314×	`fma-neg_binary64`

Counts

257 → 252

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	5264
1	352	4590
2	993	4409
3	2295	4361
4	2691	4361
5	3479	4361
6	4441	4361
7	4886	4361

prune332.0ms (8.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	251	3	254

Error

1.0b

Counts

254 → 3

Alt Table

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

Compiler

Compiled 7050 to 4807 computations (31.8% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(sin.f64 (*.f64 (PI.f64) 2/3))
	1.0b	(/.f64 1 (sqrt.f64 3))
✓	1.0b	(*.f64 (PI.f64) 2/3)
✓	1.6b	(cos.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	(sin.f64 (*.f64 (PI.f64) 2/3))
0.0ms	(*.f64 (PI.f64) 2/3)

rewrite6.0ms (0.2%)

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))

simplify85.0ms (2.2%)

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 → 42

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

prune160.0ms (4.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	163	2	165

Error

Counts

165 → 2

Alt Table

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

Status

Error

Program

✓

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))))))

▶

0.0b

(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (*.f64 (sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3)))) (sin.f64 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))))

Compiler

Compiled 7577 to 5553 computations (26.7% saved)

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(/.f64 1 (sqrt.f64 3))
	1.0b	(*.f64 (PI.f64) 2/3)
✓	1.0b	(sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3))))
	1.6b	(cos.f64 (*.f64 (PI.f64) 2/3))

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

(sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3))))

simplify137.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

10 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	140
1	30	125
2	32	125
3	37	125
4	42	125
5	51	125
6	71	125
7	124	125
8	299	125
9	604	125
10	608	125
11	738	125
12	892	125
13	1060	125
14	1289	125
15	1590	125
16	1938	125
17	2413	125
18	3031	125
19	3227	125
20	3401	125
21	3515	125
22	3562	125
23	3614	125
24	4492	125
25	4797	125

prune206.0ms (5.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	169	2	171

Error

Counts

171 → 2

Alt Table

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

Status

Error

Program

✓

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))))))

✓

0.0b

(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (*.f64 (sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3)))) (sin.f64 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))))

Compiler

Compiled 8194 to 6090 computations (25.7% saved)

regimes698.0ms (18.1%)

Accuracy

Total 0.0b remaining (70.4%)

Threshold costs 0.0b (70.4%)

Counts

77 → 1

Compiler

Compiled 18362 to 15404 computations (16.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-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	26	73
1	43	73
2	55	73
3	64	73
4	69	73
5	70	73
6	69	73

end1.0ms (0%)

Compiler: Compiled 45 to 37 computations (17.8% saved)

sample1.2s (30.7%)

Algorithm

1×

intervals

Results

803.0ms	8000×	body	128	valid
46.0ms	520×	body	128	nan

Compiler

Compiled 132 to 112 computations (15.2% saved)

Details

analyze213.0ms (5.5%)

sample54.0ms (1.4%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

series36.0ms (0.9%)

rewrite6.0ms (0.2%)

simplify123.0ms (3.2%)

prune106.0ms (2.8%)

localize15.0ms (0.4%)

series168.0ms (4.3%)

rewrite37.0ms (1%)

simplify218.0ms (5.6%)

prune332.0ms (8.6%)

localize20.0ms (0.5%)

series0.0ms (0%)

rewrite6.0ms (0.2%)

simplify85.0ms (2.2%)

prune160.0ms (4.1%)

localize25.0ms (0.6%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify137.0ms (3.5%)

prune206.0ms (5.3%)

regimes698.0ms (18.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.2s (30.7%)

Profiling