Details

analyze230.0ms (5.8%)

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)

sample38.0ms (1%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
1.0ms	19×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify11.0ms (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

prune5.0ms (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)

localize10.0ms (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 (1.7%)

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

series53.0ms (1.3%)

Error

1.0b

Counts

4 → 18

Calls

4 calls:

23.0ms	(cos.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
15.0ms	(+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
13.0ms	(/.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)

simplify136.0ms (3.4%)

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

prune67.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	3	76

Error

0.9b

Counts

76 → 3

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (+.f64 (.f64 (cos.f64 (.f64 PI.f64 5/6)) (cos.f64 (/.f64 (asin.f64 (neg.f64 (/.f64 g h))) 3))) (.f64 (sin.f64 (*.f64 PI.f64 5/6)) (sin.f64 (/.f64 (asin.f64 (neg.f64 (/.f64 g h))) 3)))))
▶	1.0b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) 0))
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (+.f64 (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))) (*.f64 2/3 PI.f64))) 3)))

Compiler

Compiled 1270 to 765 computations (39.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(acos.f64 (/.f64 g h))
0.0b	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))
1.0b	(/.f64 (acos.f64 (/.f64 g h)) 3)

rewrite57.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

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 → 44

Calls

3 calls:

3.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)
2.0ms	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))
1.0ms	(acos.f64 (/.f64 g h))

Compiler

Compiled 854 to 532 computations (37.7% saved)

series39.0ms (1%)

Error

0.9b

Counts

3 → 18

Calls

3 calls:

18.0ms	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))
12.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)
7.0ms	(acos.f64 (/.f64 g h))

Compiler

Compiled 530 to 452 computations (14.7% saved)

simplify200.0ms (5%)

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

62 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	896
1	118	815
2	189	815
3	285	815
4	506	815
5	729	815
6	1151	815
7	2447	815
8	2900	815
9	2904	815
10	3140	815
11	3507	815
12	4074	815
13	4908	815
14	4999	815
15	5000	815
16	4799	815

prune29.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	21	3	24

Error

Counts

24 → 3

Alt Table

Status	Error	Program
	1.0b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (/.f64 g h))))))) 0))
▶	0.0b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 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))

Compiler

Compiled 465 to 329 computations (29.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 (/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 3))
1.0b	(/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 3)
1.0b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3))
1.0b	(pow.f64 (acos.f64 (/.f64 g h)) 3)

rewrite122.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

60×	`cbrt-prod_binary64`
45×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
42×	`add-cube-cbrt_binary64`

Counts

4 → 126

Calls

4 calls:

5.0ms	(/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 3)
4.0ms	(cos.f64 (/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 3))
4.0ms	(pow.f64 (acos.f64 (/.f64 g h)) 3)
2.0ms	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3))

Compiler

Compiled 2615 to 1766 computations (32.5% saved)

series61.0ms (1.5%)

Error

Counts

4 → 24

Calls

4 calls:

19.0ms	(pow.f64 (acos.f64 (/.f64 g h)) 3)
17.0ms	(cos.f64 (/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 3))
12.0ms	(/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 3)
10.0ms	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3))

Compiler

Compiled 749 to 643 computations (14.2% saved)

simplify126.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-/r/_binary64`
520×	`log-prod_binary64`
309×	`associate-l_binary64`
275×	`associate-r_binary64`
217×	`exp-prod_binary64`

Counts

150 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	2448
1	177	2229
2	530	2213
3	2082	2213
4	4587	2213
5	4929	2213

prune39.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	123	3	126

Error

Counts

126 → 3

Alt Table

Status	Error	Program
	1.0b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (/.f64 g h))))))) 0))
✓	0.0b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 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))

Compiler

Compiled 1128 to 749 computations (33.6% saved)

localize15.0ms (0.4%)

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	(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)

rewrite130.0ms (3.3%)

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 → 108

Calls

4 calls:

7.0ms	(*.f64 (/.f64 (sqrt.f64 3) 2) (cos.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)
2.0ms	(sin.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))

Compiler

Compiled 3641 to 2548 computations (30% saved)

series77.0ms (1.9%)

Error

Counts

4 → 24

Calls

4 calls:

28.0ms	(*.f64 (/.f64 (sqrt.f64 3) 2) (cos.f64 (/.f64 (asin.f64 (/.f64 g h)) 3)))
20.0ms	(sin.f64 (/.f64 (asin.f64 (/.f64 g h)) 3))
14.0ms	(/.f64 (asin.f64 (/.f64 g h)) 3)
12.0ms	(/.f64 (asin.f64 (/.f64 g h)) 3)

Compiler

Compiled 1475 to 1165 computations (21% saved)

simplify229.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

672×	`fabs-mul_binary64`
525×	`associate-/l*_binary64`
474×	`prod-exp_binary64`
411×	`pow-sqr_binary64`
374×	`associate-*l/_binary64`

Counts

132 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	2611
1	303	2347
2	632	2341
3	1187	2341
4	2284	2341
5	2531	2341
6	3077	2341
7	4056	2341
8	4473	2341
9	4633	2341
10	4988	2341
11	5710	2341

prune72.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
	1.0b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (/.f64 g h))))))) 0))
	0.0b	(*.f64 2 (+.f64 (neg.f64 (cos.f64 (/.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 g h)) 3)) 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))

Compiler

Compiled 2174 to 1565 computations (28% saved)

regimes982.0ms (24.7%)

Accuracy

Total 0.0b remaining (86.7%)

Threshold costs 0.0b (86.7%)

Compiler

Compiled 21979 to 18256 computations (16.9% saved)

simplify5.0ms (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 (29.1%)

Algorithm

1×

intervals

Results

775.0ms	8000×	body	128	valid
47.0ms	561×	body	128	nan

Compiler

Compiled 100 to 86 computations (14% saved)

Details

analyze230.0ms (5.8%)

sample38.0ms (1%)

simplify11.0ms (0.3%)

prune5.0ms (0.1%)

localize10.0ms (0.3%)

rewrite68.0ms (1.7%)

series53.0ms (1.3%)

simplify136.0ms (3.4%)

prune67.0ms (1.7%)

localize9.0ms (0.2%)

rewrite57.0ms (1.4%)

series39.0ms (1%)

simplify200.0ms (5%)

prune29.0ms (0.7%)

localize12.0ms (0.3%)

rewrite122.0ms (3.1%)

series61.0ms (1.5%)

simplify126.0ms (3.2%)

prune39.0ms (1%)

localize15.0ms (0.4%)

rewrite130.0ms (3.3%)

series77.0ms (1.9%)

simplify229.0ms (5.8%)

prune72.0ms (1.8%)

regimes982.0ms (24.7%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.2s (29.1%)

Profiling