Details

sample132.0ms

Algorithm

intervals

Results

57.0ms	45×	body	2560	valid
42.0ms	95×	body	1280	valid
13.0ms	57×	body	640	valid
10.0ms	38×	body	320	valid
2.0ms	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))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune162.0ms

Filtered

74 candidates to 51 candidates (68.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	12	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	12	75

Merged error: 0.2b

Counts

75 → 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))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
30×	`exp-prod` `log-pow`
27×	`times-frac` `prod-diff`
22×	`exp-sum`
14×	`log-prod`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `exp-diff` `fma-neg` `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 → 141

Calls

4 calls:

9.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
5.0ms	(exp (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))
6.0ms	(log (exp (- 1.0 (cos x))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
43.0ms	(exp (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))

simplify48.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	385	1279
1	1183	956
2	5001	809

prune243.0ms

Filtered

153 candidates to 90 candidates (58.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	152	13	165

Merged error: 0.1b

Counts

165 → 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))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
9×	`prod-diff`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-/r` `flip--` `log1p-expm1-u` `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 → 105

Calls

3 calls:

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

series69.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ 1 (sin x))
34.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
22.0ms	(- 1.0 (cos x))

simplify50.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	381	728
1	1613	574
2	5002	548

prune171.0ms

Filtered

114 candidates to 69 candidates (60.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	114	13	127

Merged error: 0.1b

Counts

127 → 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))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

672×	`times-frac`
474×	`sqrt-prod`
460×	`add-sqr-sqrt` `*-un-lft-identity`
314×	`add-cube-cbrt`
192×	`log-pow`
160×	`exp-prod`
73×	`distribute-lft-out--` `difference-of-squares`
36×	`pow1`
30×	`associate-/r*`
27×	`prod-diff` `associate-/r/`
26×	`sqrt-div`
15×	`flip3--` `flip--`
14×	`log-prod` `div-inv`
12×	`associate-/l*`
11×	`exp-sum`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `sub-neg` `div-exp`
2×	`diff-log`
1×	`log-div` `frac-2neg` `exp-diff` `rem-log-exp` `clear-num`

Counts

4 → 506

Calls

4 calls:

25.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) (/ (sin x) (sqrt (- 1.0 (cos x)))))
5.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
6.0ms	(log (exp (- 1.0 (cos x))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) (/ (sin x) (sqrt (- 1.0 (cos x)))))
18.0ms	(- 1.0 (cos x))
25.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify106.0ms

Algorithm

egg-herbie

Counts

518 → 518

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1255	10011
1	5002	8105

prune756.0ms

Filtered

518 candidates to 231 candidates (44.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	514	4	518
Fresh	2	8	10
Picked	0	1	1
Done	1	1	2
Total	517	14	531

Merged error: 0.1b

Counts

531 → 14

regimes133.0ms

Accuracy

97.9% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 29.5b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	24
1	31	24

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1560×	body	2560	valid
1.3s	2769×	body	1280	valid
462.0ms	1840×	body	640	valid
153.0ms	942×	body	320	valid
63.0ms	519×	body	160	valid
25.0ms	367×	body	80	valid
10.0ms	3×	body	5120	valid