Details

analyze447.0ms (6.7%)

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)

sample73.0ms (1.1%)

Algorithm

1×

intervals

Results

53.0ms	256×	body	128	valid
3.0ms	16×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify18.0ms (0.3%)

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

prune7.0ms (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)

localize21.0ms (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)))

series76.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

46.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
18.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
11.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite12.0ms (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:

5.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
2.0ms	(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))

simplify213.0ms (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

prune241.0ms (3.6%)

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 (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)))))

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 (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)))))

Compiler

Compiled 2089 to 1181 computations (43.5% saved)

localize29.0ms (0.4%)

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	(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 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
✓	1.0b	(/.f64 1 (sqrt.f64 3))

series395.0ms (5.9%)

Counts

4 → 72

Calls

4 calls:

175.0ms	(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)))))
110.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
109.0ms	(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	(/.f64 1 (sqrt.f64 3))

rewrite57.0ms (0.9%)

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:

27.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
5.0ms	(/.f64 1 (sqrt.f64 3))
2.0ms	(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)))))
1.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))

simplify339.0ms (5.1%)

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

prune427.0ms (6.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	206	2	208

Error

1.0b

Counts

208 → 2

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))))))

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))))))

Compiler

Compiled 5584 to 3882 computations (30.5% saved)

localize49.0ms (0.7%)

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)

rewrite13.0ms (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:

5.0ms	(*.f64 (PI.f64) 2/3)
4.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))
2.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))

simplify105.0ms (1.6%)

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

prune371.0ms (5.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	162	2	164

Error

Counts

164 → 2

Alt Table

Status	Error	Program
▶	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 (log1p.f64 (expm1.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))))))

Status

Error

Program

▶

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

Compiler

Compiled 7577 to 5553 computations (26.7% saved)

localize46.0ms (0.7%)

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	(expm1.f64 (sin.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

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`log1p-expm1-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

1.0ms

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

simplify152.0ms (2.3%)

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

11 → 12

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	137
1	18	118
2	20	118
3	25	118
4	30	118
5	39	118
6	59	118
7	113	118
8	290	118
9	595	118
10	599	118
11	729	118
12	883	118
13	1051	118
14	1280	118
15	1581	118
16	1929	118
17	2404	118
18	3022	118
19	3218	118
20	3392	118
21	3506	118
22	3553	118
23	3605	118
24	4483	118
25	4788	118

prune411.0ms (6.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	164	2	166

Error

Counts

166 → 2

Alt Table

Status	Error	Program
✓	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 (log1p.f64 (expm1.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))))))

Status

Error

Program

✓

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

Compiler

Compiled 7949 to 5909 computations (25.7% saved)

regimes1.9s (28.2%)

Accuracy

Total 0.0b remaining (63.6%)

Threshold costs 0.0b (63.6%)

Counts

113 → 1

Compiler

Compiled 31889 to 26087 computations (18.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	27	93
1	45	93
2	57	93
3	66	93
4	71	93
5	72	93
6	71	93

end1.0ms (0%)

Compiler: Compiled 56 to 46 computations (17.9% saved)

sample1.3s (19.1%)

Algorithm

1×

intervals

Results

849.0ms	8000×	body	128	valid
46.0ms	520×	body	128	nan

Compiler

Compiled 143 to 121 computations (15.4% saved)

Details

analyze447.0ms (6.7%)

sample73.0ms (1.1%)

simplify18.0ms (0.3%)

prune7.0ms (0.1%)

localize21.0ms (0.3%)

series76.0ms (1.1%)

rewrite12.0ms (0.2%)

simplify213.0ms (3.2%)

prune241.0ms (3.6%)

localize29.0ms (0.4%)

series395.0ms (5.9%)

rewrite57.0ms (0.9%)

simplify339.0ms (5.1%)

prune427.0ms (6.4%)

localize49.0ms (0.7%)

series0.0ms (0%)

rewrite13.0ms (0.2%)

simplify105.0ms (1.6%)

prune371.0ms (5.6%)

localize46.0ms (0.7%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify152.0ms (2.3%)

prune411.0ms (6.2%)

regimes1.9s (28.2%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.3s (19.1%)

Profiling