Details

sample139.0ms

Algorithm

intervals

Results

66.0ms	52×	body	2560	valid
34.0ms	73×	body	1280	valid
20.0ms	64×	body	640	valid
7.0ms	43×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	12×	body	80	valid

simplify5.0ms

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

prune3.0ms

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: 33.4b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

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

series11.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify79.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2640	373
3	5002	373

prune199.0ms

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: 0.1b

Counts

59 → 14

localize10.0ms

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))
0.2b	(* 1/24 (pow x 3))

rewrite27.0ms

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))
10.0ms	(+ (* 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))

series25.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
6.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms	(* 1/240 (pow x 5))
4.0ms	(* 1/24 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	355	458
1	1538	429
2	5002	428

prune329.0ms

Filtered

92 candidates to 59 candidates (35.9%)

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: 0.1b

Counts

106 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
13.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series25.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
5.0ms	(pow (cos x) 3)
2.0ms	(+ (cos x) 1.0)
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	434	688
1	1925	638
2	5001	618

prune427.0ms

Filtered

101 candidates to 61 candidates (39.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	101	14	115

Merged error: 0.1b

Counts

115 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

543×	`times-frac`
517×	`add-sqr-sqrt`
337×	`*-un-lft-identity`
208×	`difference-of-squares`
205×	`add-cube-cbrt`
159×	`unpow-prod-down` `cube-prod`
105×	`sqr-pow`
81×	`associate-/l*`
65×	`distribute-lft-out--`
13×	`difference-cubes`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/r*`
2×	`div-sub`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `unpow3` `pow-exp` `clear-num` `sum-log` `flip--` `associate-/l/` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 412

Calls

4 calls:

36.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series51.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
5.0ms	(pow (cos x) 3)
2.0ms	(+ (cos x) 1.0)
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify109.0ms

Algorithm

egg-herbie

Counts

424 → 424

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1427	9452
1	5002	9346

prune4.1s

Filtered

424 candidates to 241 candidates (43.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	421	3	424
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	424	14	438

Merged error: 0.1b

Counts

438 → 14

regimes196.0ms

Accuracy

98.4% (0.5b remaining)

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

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	36
1	45	36

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	1621×	body	2560	valid
1.2s	2738×	body	1280	valid
447.0ms	1864×	body	640	valid
160.0ms	955×	body	320	valid
52.0ms	463×	body	160	valid
23.0ms	356×	body	80	valid
11.0ms	3×	body	5120	valid

Details

sample139.0ms

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series11.0ms

simplify79.0ms

prune199.0ms

localize10.0ms

rewrite27.0ms

series25.0ms

simplify52.0ms

prune329.0ms

localize15.0ms

rewrite32.0ms

series25.0ms

simplify63.0ms

prune427.0ms

localize15.0ms

rewrite85.0ms

series51.0ms

simplify109.0ms

prune4.1s

regimes196.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample4.3s

Profiling