Details

sample144.0ms

Algorithm

intervals

Results

78.0ms	57×	body	2560	valid
37.0ms	80×	body	1280	valid
14.0ms	58×	body	640	valid
5.0ms	32×	body	320	valid
2.0ms	19×	body	160	valid
1.0ms	10×	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: 32.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.2b	(- 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))
3.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify79.0ms

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

prune148.0ms

Filtered

58 candidates to 42 candidates (72.4%)

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: 0.3b

Counts

59 → 14

localize15.0ms

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

4.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
7.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series272.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
59.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
51.0ms	(* 1/240 (pow x 5))
36.0ms	(* 1/24 (pow x 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	355	458
1	1538	430
2	5002	429

prune183.0ms

Filtered

92 candidates to 59 candidates (64.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	92	14	106

Merged error: 0.3b

Counts

106 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.2b	(- 1.0 (cos x))

rewrite27.0ms

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-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

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

series321.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
43.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
33.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
210.0ms	(- 1.0 (cos x))

simplify90.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune259.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	122	16	138

Merged error: 0.2b

Counts

138 → 16

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
0.4b	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
2.2b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt` `*-un-lft-identity`
75×	`times-frac`
52×	`add-cube-cbrt`
44×	`cbrt-prod`
38×	`unpow-prod-down` `cube-prod`
17×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv` `associate-/l*`
3×	`pow-unpow` `associate-/r*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `clear-num` `rem-cbrt-cube`

Counts

4 → 164

Calls

4 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
7.0ms	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
4.0ms	(- 1.0 (cos x))

series149.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
33.0ms	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
64.0ms	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
18.0ms	(- 1.0 (cos x))

simplify72.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	531	1510
1	2278	1417
2	5002	1401

prune224.0ms

Filtered

176 candidates to 86 candidates (48.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	2	11	13
Picked	1	0	1
Done	0	2	2
Total	176	16	192

Merged error: 0.2b

Counts

192 → 16

regimes156.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 31.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	34
1	44	34

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1543×	body	2560	valid
1.3s	2760×	body	1280	valid
474.0ms	1940×	body	640	valid
146.0ms	897×	body	320	valid
57.0ms	486×	body	160	valid
25.0ms	373×	body	80	valid
3.0ms	1×	body	5120	valid