Details

analyze1.1s

Algorithm

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample87.0ms

Algorithm

intervals

Results

48.0ms	92×	body	1280	valid
17.0ms	58×	body	640	valid
6.0ms	29×	body	320	valid
4.0ms	67×	body	80	valid
1.0ms	10×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune2.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 13.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
3.4b	(cos.f64 (+.f64 a b))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64` `insert-posit16`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `cos-sum_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

3 → 50

Calls

3 calls:

5.0ms	(*.f64 r (sin.f64 b))
7.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))

series1.4s

Counts

3 → 9

Calls

3 calls:

390.0ms	(*.f64 r (sin.f64 b))
672.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
378.0ms	(cos.f64 (+.f64 a b))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	335	455
1	335	455
0	90	272
1	90	272
0	335	455
1	335	455
0	90	272
1	90	272
0	5140	12
0	1187	1701
1	1187	1701
0	5134	1096
0	1187	1701
1	1187	1701
0	5134	1096
0	1	3
1	1	3
0	382	550
1	382	550
0	80	339
1	80	339
0	382	550
1	382	550
0	80	339
1	80	339
0	5140	12

simplify170.0ms

Counts

59 → 59

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	4630	663
1	4630	663

prune52.0ms

Filtered

47 candidates to 59 candidates (-25.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	50	9	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	9	60

Merged error: 0.2b

Counts

60 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`sin-mult_binary64`
4×	`cos-mult_binary64` `associate-/r/_binary64` `insert-posit16`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(*.f64 r (sin.f64 b))
7.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
12.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series2.1s

Counts

4 → 12

Calls

4 calls:

399.0ms	(*.f64 r (sin.f64 b))
564.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
757.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
410.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	427	663
1	427	663
0	103	432
1	103	432
0	427	663
1	427	663
0	103	432
1	103	432
0	5140	12
0	1500	2341
1	1500	2341
0	5160	1523
0	1500	2341
1	1500	2341
0	5160	1523
0	1	3
1	1	3
0	643	1233
1	643	1233
0	24	9
1	24	9
0	643	1233
1	643	1233
0	24	9
1	24	9
0	5095	36
0	382	550
1	382	550
0	80	339
1	80	339
0	382	550
1	382	550
0	80	339
1	80	339
0	5140	12

simplify162.0ms

Counts

91 → 91

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4917	1528
1	4917	1528

prune92.0ms

Filtered

73 candidates to 91 candidates (-24.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	89	11	100

Merged error: 0.0b

Counts

100 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`associate-r_binary64`
19×	`times-frac_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-/r/_binary64`
7×	`sin-mult_binary64`
6×	`add-log-exp_binary64` `cos-mult_binary64` `associate-l_binary64`
4×	`insert-posit16`
3×	`associate-/r_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 103

Calls

4 calls:

7.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
15.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
11.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series2.2s

Counts

4 → 12

Calls

4 calls:

563.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
752.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
504.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
408.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	427	663
1	427	663
0	103	432
1	103	432
0	427	663
1	427	663
0	103	432
1	103	432
0	5140	12
0	919	2031
1	919	2031
0	221	741
1	221	741
0	919	2031
1	919	2031
0	221	741
1	221	741
0	1	3
1	1	3
0	1510	2370
1	1510	2370
0	1120	995
1	1120	995
0	1510	2370
1	1510	2370
0	1120	995
1	1120	995
0	1	3
1	1	3
0	643	1233
1	643	1233
0	24	9
1	24	9
0	643	1233
1	643	1233
0	24	9
1	24	9
0	5095	36

simplify129.0ms

Counts

115 → 115

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5578	2682

prune100.0ms

Filtered

92 candidates to 115 candidates (-25.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	114	12	126

Merged error: 0.0b

Counts

126 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.2b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
0.2b	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
4×	`associate-/l*_binary64` `insert-posit16`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `cos-mult_binary64` `associate-/r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

12.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
6.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
11.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
7.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))

series671.0ms

Calls

1 calls:

348.0ms

(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	769	1516
1	769	1516
0	515	1021
1	515	1021
0	769	1516
1	769	1516
0	515	1021
1	515	1021
0	1	3
1	1	3
0	1771	2515
1	1771	2515

Details

analyze1.1s

sample87.0ms

simplify19.0ms

prune2.0ms

localize10.0ms

rewrite19.0ms

series1.4s

simplify170.0ms

prune52.0ms

localize15.0ms

rewrite32.0ms

series2.1s

simplify162.0ms

prune92.0ms

localize15.0ms

rewrite43.0ms

series2.2s

simplify129.0ms

prune100.0ms

localize14.0ms

rewrite38.0ms

series671.0ms

Profiling