Details

analyze522.0ms (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample150.0ms (2.4%)

Algorithm

1×

intervals

Results

89.0ms	71×	body	2560	valid
29.0ms	62×	body	1280	valid
17.0ms	65×	body	640	valid
5.0ms	30×	body	320	valid
3.0ms	20×	body	160	valid
1.0ms	8×	body	80	valid

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	229	7
1	229	7

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 32.7b

Counts

2 → 1

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
2.3b	(-.f64 1.0 (cos.f64 x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
4.0ms	(-.f64 1.0 (cos.f64 x))

series13.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
4.0ms	(-.f64 1.0 (cos.f64 x))

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5058	605

prune109.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	45	12	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	12	58

Merged error: 0.1b

Counts

58 → 12

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/240 (pow.f64 x 5)) (.f64 x 1/2))
0.0b	(+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 x 1/2)))
0.1b	(*.f64 1/240 (pow.f64 x 5))
0.1b	(*.f64 1/24 (pow.f64 x 3))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-l_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-prod_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+r+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 80

Calls

4 calls:

9.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 x 1/2)))
6.0ms	(*.f64 1/24 (pow.f64 x 3))
5.0ms	(*.f64 1/240 (pow.f64 x 5))
5.0ms	(+.f64 (.f64 1/240 (pow.f64 x 5)) (.f64 x 1/2))

series38.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 (.f64 1/240 (pow.f64 x 5)) (.f64 x 1/2))
7.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 x 1/2)))
6.0ms	(*.f64 1/240 (pow.f64 x 5))
5.0ms	(*.f64 1/24 (pow.f64 x 3))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5066	875

prune144.0ms (2.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 0.1b

Counts

104 → 12

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5))) (*.f64 x 1/2))
0.0b	(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5)))
0.1b	(*.f64 1/240 (pow.f64 x 5))
0.1b	(*.f64 1/24 (pow.f64 x 3))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-l_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-prod_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+l+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+.f64 (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5))) (*.f64 x 1/2))
8.0ms	(*.f64 1/24 (pow.f64 x 3))
5.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5)))
5.0ms	(*.f64 1/240 (pow.f64 x 5))

series35.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5)))
7.0ms	(+.f64 (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5))) (*.f64 x 1/2))
6.0ms	(*.f64 1/240 (pow.f64 x 5))
5.0ms	(*.f64 1/24 (pow.f64 x 3))

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5104	909

prune143.0ms (2.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Merged error: 0.1b

Counts

104 → 12

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sin.f64 x))
0.2b	(*.f64 (-.f64 1.0 (cos.f64 x)) (/.f64 1 (sin.f64 x)))
2.3b	(-.f64 1.0 (cos.f64 x))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
10×	`add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64` `associate-l_binary64`
4×	`prod-exp_binary64` `div-exp_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

3 → 86

Calls

3 calls:

10.0ms	(*.f64 (-.f64 1.0 (cos.f64 x)) (/.f64 1 (sin.f64 x)))
4.0ms	(-.f64 1.0 (cos.f64 x))
4.0ms	(/.f64 1 (sin.f64 x))

series16.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(*.f64 (-.f64 1.0 (cos.f64 x)) (/.f64 1 (sin.f64 x)))
5.0ms	(/.f64 1 (sin.f64 x))
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5161	778

prune92.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	95	12	107

Merged error: 0.1b

Counts

107 → 12

regimes123.0ms (1.9%)

Accuracy

Total 0.4b remaining (64.8%)

Threshold costs 0.4b (64.8%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	67
1	62	67

end0.0ms (0%)

sample4.6s (72.8%)

Algorithm

1×

intervals

Results

2.4s	1692×	body	2560	valid
1.3s	2666×	body	1280	valid
487.0ms	1834×	body	640	valid
184.0ms	982×	body	320	valid
66.0ms	465×	body	160	valid
31.0ms	357×	body	80	valid
19.0ms	4×	body	5120	valid

Details

analyze522.0ms (8.2%)

sample150.0ms (2.4%)

simplify14.0ms (0.2%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite12.0ms (0.2%)

series13.0ms (0.2%)

simplify46.0ms (0.7%)

prune109.0ms (1.7%)

localize10.0ms (0.2%)

rewrite28.0ms (0.4%)

series38.0ms (0.6%)

simplify52.0ms (0.8%)

prune144.0ms (2.3%)

localize10.0ms (0.2%)

rewrite29.0ms (0.5%)

series35.0ms (0.6%)

simplify51.0ms (0.8%)

prune143.0ms (2.3%)

localize8.0ms (0.1%)

rewrite21.0ms (0.3%)

series16.0ms (0.3%)

simplify48.0ms (0.8%)

prune92.0ms (1.4%)

regimes123.0ms (1.9%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.6s (72.8%)

Profiling