Details

sample129.0ms

Algorithm

intervals

Results

56.0ms	45×	body	2560	valid
45.0ms	95×	body	1280	valid
13.0ms	57×	body	640	valid
6.0ms	38×	body	320	valid
1.0ms	14×	body	160	valid
0.0ms	7×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 31.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

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

series56.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify80.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune142.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	46	12	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	12	59

Merged error: 0.2b

Counts

59 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (log (exp (- 1.0 (cos x)))) (sin x))
0.2b	(exp (- 1.0 (cos x)))
1.8b	(- 1.0 (cos x))
1.9b	(log (exp (- 1.0 (cos x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`exp-prod` `log-pow`
27×	`times-frac`
25×	`add-cube-cbrt`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod`
4×	`exp-sum`
3×	`sub-neg` `exp-diff` `associate-/r*`
2×	`log-div` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 103

Calls

4 calls:

8.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
5.0ms	(exp (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
37.0ms	(exp (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
22.0ms	(log (exp (- 1.0 (cos x))))

simplify105.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	295	766
1	890	686
2	3427	674
3	5001	672

prune199.0ms

Filtered

115 candidates to 73 candidates (63.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	114	13	127

Merged error: 0.1b

Counts

127 → 13

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.8b	(- 1.0 (cos x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`flip3--` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

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

series67.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1 (sin x))
37.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
18.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	320	548
1	1393	482
2	5001	456

prune142.0ms

Filtered

96 candidates to 58 candidates (60.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	96	13	109

Merged error: 0.1b

Counts

109 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (log (exp (- 1.0 (cos x))))) (/ (sin x) (sqrt (- 1.0 (cos x)))))
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))
1.9b	(log (exp (- 1.0 (cos x))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

672×	`times-frac`
474×	`sqrt-prod`
440×	`add-sqr-sqrt` `*-un-lft-identity`
294×	`add-cube-cbrt`
192×	`log-pow`
160×	`exp-prod`
73×	`distribute-lft-out--` `difference-of-squares`
36×	`pow1`
30×	`associate-/r*`
27×	`associate-/r/`
26×	`sqrt-div`
15×	`flip3--` `flip--`
14×	`div-inv`
12×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`log-prod`
3×	`cbrt-undiv` `sub-neg` `div-exp`
2×	`diff-log` `exp-sum`
1×	`log-div` `frac-2neg` `exp-diff` `rem-log-exp` `clear-num`

Counts

4 → 465

Calls

4 calls:

25.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) (/ (sin x) (sqrt (- 1.0 (cos x)))))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) (/ (sin x) (sqrt (- 1.0 (cos x)))))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
25.0ms	(log (exp (- 1.0 (cos x))))

simplify98.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1169	9500
1	5001	7842

prune678.0ms

Filtered

477 candidates to 211 candidates (44.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	472	5	477
Fresh	3	7	10
Picked	0	1	1
Done	1	1	2
Total	476	14	490

Merged error: 0.1b

Counts

490 → 14

regimes66.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 29.5b

bsearch93.0ms

Steps

Iters	Range		Point
10	8.416769919470913e-17	1.2368608357549227	0.022497800307323425
11	-55383.34621353126	-7.66540900750845e-16	-0.02011364234498406

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1560×	body	2560	valid
1.2s	2769×	body	1280	valid
437.0ms	1840×	body	640	valid
148.0ms	942×	body	320	valid
58.0ms	519×	body	160	valid
24.0ms	367×	body	80	valid
11.0ms	3×	body	5120	valid