Details

sample129.0ms

Algorithm

intervals

Results

61.0ms	48×	body	2560	valid
37.0ms	86×	body	1280	valid
14.0ms	64×	body	640	valid
6.0ms	36×	body	320	valid
2.0ms	14×	body	80	valid
1.0ms	8×	body	160	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

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 33.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 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))

series55.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify79.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	230	396
1	662	373
2	2605	373
3	5002	373

prune132.0ms

Filtered

58 candidates to 42 candidates (27.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	44	14	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	14	59

Merged error: 0.2b

Counts

59 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
23×	`associate-l`
22×	`distribute-lft-out`
20×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`pow1` `unpow-prod-down` `add-cbrt-cube`
6×	`prod-exp` `unswap-sqr`
4×	`sum-log` `sqr-pow`
3×	`+-commutative`
2×	`pow-to-exp` `associate-+r+` `flip3-+` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`unpow3`

Counts

4 → 92

Calls

4 calls:

17.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
32.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
6.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series275.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
59.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
50.0ms	(* 1/240 (pow x 5))
36.0ms	(* 1/24 (pow x 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	340	535
1	1419	513
2	5002	512

prune180.0ms

Filtered

104 candidates to 59 candidates (43.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	104	14	118

Merged error: 0.2b

Counts

118 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `rem-log-exp` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `clear-num` `rem-exp-log`

Counts

4 → 113

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
47.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify95.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	300	818
1	788	768
2	2918	766
3	5002	766

prune249.0ms

Filtered

125 candidates to 89 candidates (28.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	124	15	139

Merged error: 0.2b

Counts

139 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
1.1b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
1.5b	(- 1.0 (cos x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

339×	`times-frac`
236×	`*-un-lft-identity`
235×	`add-sqr-sqrt`
167×	`add-cube-cbrt`
156×	`exp-prod`
79×	`log-pow`
53×	`associate-/r/`
36×	`associate-/r*`
34×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
13×	`div-inv` `associate-/l*`
11×	`flip3--` `flip--`
9×	`add-cbrt-cube`
7×	`div-exp` `add-log-exp`
6×	`pow1`
5×	`clear-num`
4×	`frac-2neg`
3×	`cbrt-undiv` `log-prod`
2×	`rec-exp` `1-exp` `rem-log-exp` `remove-double-div`
1×	`sub-neg` `pow-flip` `diff-log` `rem-exp-log` `inv-pow`

Counts

4 → 311

Calls

4 calls:

11.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
22.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
17.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
4.0ms	(- 1.0 (cos x))

series148.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
44.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
44.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
19.0ms	(- 1.0 (cos x))

simplify76.0ms

Algorithm

egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	650	2694
1	2657	2439
2	5001	2191

prune524.0ms

Filtered

323 candidates to 203 candidates (37.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	315	8	323
Fresh	8	5	13
Picked	0	1	1
Done	0	1	1
Total	323	15	338

Merged error: 0.2b

Counts

338 → 15

regimes73.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.8b

bsearch60.0ms

Steps

Iters	Range		Point
9	0.0004381094517774334	96283.49646244562	0.01916768720892558
6	-0.04448272872103196	-0.010589856477353462	-0.022467842987435108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	21
1	46	21
2	49	21
3	49	21

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1594×	body	2560	valid
1.2s	2719×	body	1280	valid
455.0ms	1937×	body	640	valid
153.0ms	914×	body	320	valid
52.0ms	489×	body	160	valid
22.0ms	345×	body	80	valid
10.0ms	2×	body	5120	valid