Details

analyze234.0ms (6.5%)

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)

sample36.0ms (1%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
1.0ms	14×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`div-sub_binary64`
4×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	26	23
2	40	23
3	48	23
4	52	23
5	55	23
6	66	23
7	65	23
8	54	23

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.0b	(.f64 2 (cos.f64 (+.f64 (.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 48 to 42 computations (12.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0b	(+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
1.0b	(cos.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
1.0b	(*.f64 PI.f64 2/3)

rewrite68.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 70

Calls

4 calls:

6.0ms	(cos.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
5.0ms	(+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
4.0ms	(*.f64 PI.f64 2/3)
3.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

Compiler

Compiled 1549 to 910 computations (41.3% saved)

series62.0ms (1.7%)

Error

1.0b

Counts

4 → 18

Calls

4 calls:

28.0ms	(cos.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
18.0ms	(+.f64 (*.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)
0.0ms	(*.f64 PI.f64 2/3)

Compiler

Compiled 644 to 566 computations (12.1% saved)

simplify140.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

722×	`div-sub_binary64`
361×	`associate-/r/_binary64`
313×	`*-commutative_binary64`
278×	`associate-/r*_binary64`
219×	`cancel-sign-sub-inv_binary64`

Counts

88 → 75

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	150	1689
1	271	1611
2	550	1608
3	1146	1564
4	2498	1558
5	3644	1544
6	4453	1544
7	5130	1544

prune49.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	2	76

Error

0.9b

Counts

76 → 2

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 2/3 PI.f64)) (cos.f64 (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))))) (.f64 (sin.f64 (.f64 2/3 PI.f64)) (sin.f64 (*.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))))))))
▶	0.9b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) 0))

Status

Error

Program

1.0b

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

▶

0.9b

(*.f64 2 (+.f64 (neg.f64 (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) 0))

Compiler

Compiled 1232 to 731 computations (40.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))
0.9b	(/.f64 (acos.f64 (/.f64 g h)) 3)

rewrite43.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 36

Calls

2 calls:

3.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)
2.0ms	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))

Compiler

Compiled 715 to 455 computations (36.4% saved)

series34.0ms (0.9%)

Error

0.9b

Counts

2 → 12

Calls

2 calls:

20.0ms	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))
12.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)

Compiler

Compiled 350 to 300 computations (14.3% saved)

simplify187.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

611×	`*-commutative_binary64`
595×	`sqr-pow_binary64`
469×	`associate-/l/_binary64`
393×	`associate-/r/_binary64`
390×	`associate-/l*_binary64`

Counts

48 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	769
1	118	701
2	189	701
3	285	701
4	506	701
5	729	701
6	1151	701
7	2447	701
8	2900	701
9	2904	701
10	3140	701
11	3507	701
12	4074	701
13	4908	701
14	4999	701
15	5000	701
16	4799	701

prune27.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	17	3	20
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	19	3	22

Error

Counts

22 → 3

Alt Table

Status	Error	Program
	0.9b	(.f64 2 (+.f64 (neg.f64 (cos.f64 (.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) (/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3)))) 0))
▶	0.0b	(.f64 2 (+.f64 (neg.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))) (*.f64 1/2 (sin.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))))) 0))
	0.9b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (/.f64 g h))))))) 0))

Compiler

Compiled 458 to 316 computations (31% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3)))
0.0b	(+.f64 (.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))) (.f64 1/2 (sin.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))))
0.2b	(/.f64 (asin.f64 (/.f64 g h)) 3)
0.2b	(/.f64 (asin.f64 (/.f64 g h)) 3)

rewrite137.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
22×	`associate-l_binary64`

Counts

4 → 113

Calls

4 calls:

10.0ms	(*.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3)))
10.0ms	(+.f64 (.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))) (.f64 1/2 (sin.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))))
3.0ms	(/.f64 (asin.f64 (/.f64 g h)) 3)
3.0ms	(/.f64 (asin.f64 (/.f64 g h)) 3)

Compiler

Compiled 4005 to 2806 computations (29.9% saved)

series115.0ms (3.2%)

Error

Counts

4 → 24

Calls

4 calls:

51.0ms	(+.f64 (.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))) (.f64 1/2 (sin.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))))
31.0ms	(*.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3)))
15.0ms	(/.f64 (asin.f64 (/.f64 g h)) 3)
14.0ms	(/.f64 (asin.f64 (/.f64 g h)) 3)

Compiler

Compiled 1502 to 1184 computations (21.2% saved)

simplify188.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-/l*_binary64`
390×	`associate-l_binary64`
303×	`associate-r_binary64`
281×	`distribute-rgt-in_binary64`
258×	`distribute-lft-in_binary64`

Counts

137 → 85

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	176	3183
1	387	2957
2	921	2942
3	2211	2915
4	4434	2915
5	4916	2913
6	4988	2913
7	4857	2913

prune67.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Error

Counts

88 → 3

Alt Table

Status	Error	Program
▶	0.9b	(.f64 2 (+.f64 (neg.f64 (cos.f64 (.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) (/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3)))) 0))
✓	0.0b	(.f64 2 (+.f64 (neg.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))) (*.f64 1/2 (sin.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))))) 0))
	0.9b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (/.f64 g h))))))) 0))

Compiler

Compiled 2462 to 1753 computations (28.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) (/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3))
0.0b	(/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3)
0.9b	(sqrt.f64 (acos.f64 (/.f64 g h)))
0.9b	(sqrt.f64 (acos.f64 (/.f64 g h)))

rewrite78.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

54×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
35×	`sqrt-prod_binary64`

Counts

4 → 113

Calls

4 calls:

10.0ms	(*.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) (/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3))
5.0ms	(/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3)
1.0ms	(sqrt.f64 (acos.f64 (/.f64 g h)))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 g h)))

Compiler

Compiled 2733 to 1236 computations (54.8% saved)

series61.0ms (1.7%)

Error

Counts

4 → 24

Calls

4 calls:

17.0ms	(/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3)
17.0ms	(sqrt.f64 (acos.f64 (/.f64 g h)))
14.0ms	(*.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) (/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3))
11.0ms	(sqrt.f64 (acos.f64 (/.f64 g h)))

Compiler

Compiled 976 to 679 computations (30.4% saved)

simplify203.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

428×	`sqr-pow_binary64`
321×	`div-sub_binary64`
289×	`associate-/l*_binary64`
288×	`fabs-mul_binary64`
270×	`sub-neg_binary64`

Counts

137 → 83

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	107	2293
1	200	2203
2	613	2147
3	1534	2147
4	1743	2147
5	2269	2147
6	3335	2147
7	3988	2131
8	4657	2131
9	4735	2131

prune32.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	83	3	86

Error

Counts

86 → 3

Alt Table

Status	Error	Program
	0.9b	(.f64 2 (+.f64 (neg.f64 (cos.f64 (.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) (/.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3)))) 0))
	0.0b	(.f64 2 (+.f64 (neg.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))) (*.f64 1/2 (sin.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))))) 0))
	0.0b	(.f64 2 (+.f64 (neg.f64 (cos.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 (acos.f64 (/.f64 g h))) 3/2) (sqrt.f64 3)) (/.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 g h)))) (sqrt.f64 3))))) 0))

Compiler

Compiled 1293 to 675 computations (47.8% saved)

regimes609.0ms (16.8%)

Accuracy

Total 0.0b remaining (52.1%)

Threshold costs 0.0b (52.1%)

Compiler

Compiled 13481 to 10647 computations (21% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`
2×	`+-commutative_binary64`
1×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	21	28
2	26	26
3	31	26
4	33	26
5	34	26
6	33	26

end1.0ms (0%)

Compiler: Compiled 18 to 16 computations (11.1% saved)

sample1.2s (32.7%)

Algorithm

1×

intervals

Results

804.0ms	8000×	body	128	valid
48.0ms	554×	body	128	nan

Compiler

Compiled 117 to 93 computations (20.5% saved)

Details

analyze234.0ms (6.5%)

sample36.0ms (1%)

simplify12.0ms (0.3%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

rewrite68.0ms (1.9%)

series62.0ms (1.7%)

simplify140.0ms (3.9%)

prune49.0ms (1.4%)

localize9.0ms (0.2%)

rewrite43.0ms (1.2%)

series34.0ms (0.9%)

simplify187.0ms (5.1%)

prune27.0ms (0.7%)

localize18.0ms (0.5%)

rewrite137.0ms (3.8%)

series115.0ms (3.2%)

simplify188.0ms (5.2%)

prune67.0ms (1.9%)

localize12.0ms (0.3%)

rewrite78.0ms (2.2%)

series61.0ms (1.7%)

simplify203.0ms (5.6%)

prune32.0ms (0.9%)

regimes609.0ms (16.8%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.2s (32.7%)

Profiling