Details

analyze1.0s (20.5%)

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
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

sample86.0ms (1.7%)

Algorithm

1×

intervals

Results

50.0ms	108×	body	1280	valid
15.0ms	56×	body	640	valid
4.0ms	64×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	640	invalid

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune6.0ms (0.1%)

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: 15.7b

Counts

2 → 1

localize10.0ms (0.2%)

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)))
3.1b	(cos.f64 (+.f64 a b))

rewrite21.0ms (0.4%)

Algorithm

1×	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`
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 → 47

Calls

3 calls:

10.0ms	(cos.f64 (+.f64 a b))
6.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0ms	(*.f64 r (sin.f64 b))

series44.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

28.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
8.0ms	(*.f64 r (sin.f64 b))
7.0ms	(cos.f64 (+.f64 a b))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5357	439

prune88.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

localize16.0ms (0.3%)

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)))
0.1b	(*.f64 r (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))

rewrite27.0ms (0.5%)

Algorithm

1×	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`
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 → 75

Calls

4 calls:

10.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms	(*.f64 r (sin.f64 b))

series99.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
19.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
10.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
8.0ms	(*.f64 r (sin.f64 b))

simplify42.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4979	974
1	4979	974

prune139.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	83	13	96

Merged error: 0.0b

Counts

96 → 13

localize15.0ms (0.3%)

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))

rewrite37.0ms (0.7%)

Algorithm

1×	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`
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 → 99

Calls

4 calls:

12.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series124.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
33.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
19.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
11.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5901	1692

prune142.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Merged error: 0.0b

Counts

124 → 12

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (.f64 (sin.f64 a) (sin.f64 b))))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
4.0b	(log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/r/_binary64`
3×	`associate-/r_binary64` `cbrt-unprod_binary64` `log-prod_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`rem-log-exp_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 96

Calls

4 calls:

12.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (.f64 (sin.f64 a) (sin.f64 b))))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

series119.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
37.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (.f64 (sin.f64 a) (sin.f64 b))))))
11.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))
10.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5378	1501

prune96.0ms (1.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	108	12	120

Merged error: 0.0b

Counts

120 → 12

regimes222.0ms (4.3%)

Accuracy

Total 0.3b remaining (85.8%)

Threshold costs 0.3b (85.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18

end0.0ms (0%)

sample2.5s (48.9%)

Algorithm

1×

intervals

Results

1.4s	2923×	body	1280	valid
517.0ms	1803×	body	640	valid
169.0ms	792×	body	320	valid
147.0ms	2136×	body	80	valid
50.0ms	346×	body	160	valid
1.0ms	2×	body	640	invalid
0.0ms	1×	body	1280	invalid

Details

analyze1.0s (20.5%)

sample86.0ms (1.7%)

simplify5.0ms (0.1%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite21.0ms (0.4%)

series44.0ms (0.9%)

simplify66.0ms (1.3%)

prune88.0ms (1.7%)

localize16.0ms (0.3%)

rewrite27.0ms (0.5%)

series99.0ms (1.9%)

simplify42.0ms (0.8%)

prune139.0ms (2.7%)

localize15.0ms (0.3%)

rewrite37.0ms (0.7%)

series124.0ms (2.4%)

simplify57.0ms (1.1%)

prune142.0ms (2.8%)

localize19.0ms (0.4%)

rewrite31.0ms (0.6%)

series119.0ms (2.3%)

simplify51.0ms (1%)

prune96.0ms (1.9%)

regimes222.0ms (4.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.5s (48.9%)

Profiling