Details

sample188.0ms

Algorithm

intervals

Results

91.0ms	80×	body	1280	valid
50.0ms	73×	body	640	valid
12.0ms	24×	body	320	valid
10.0ms	64×	body	80	valid
5.0ms	15×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	74	30
1	182	30
2	657	30
3	2727	30
4	5001	30

prune6.0ms

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: 0.5b

Counts

2 → 1

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
31×	`associate-l`
22×	`*-un-lft-identity`
18×	`associate-r`
12×	`add-cube-cbrt`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/` `sqrt-prod`
9×	`flip3--` `flip--` `difference-of-squares` `unswap-sqr`
8×	`add-log-exp`
6×	`sub-neg`
5×	`distribute-lft-out--`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`times-frac` `*-commutative`
2×	`diff-log` `associate-*l/`
1×	`diff-cos`

Counts

4 → 115

Calls

4 calls:

22.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series282.0ms

Counts

4 → 10

Calls

4 calls:

135.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
89.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
58.0ms	(- (cos x) (cos y))

simplify82.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	660	1374
1	2790	1282
2	5001	1282

prune657.0ms

Filtered

125 candidates to 85 candidates (68.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	9	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 0.3b

Counts

126 → 9

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.3b	(- (cos x) (cos y))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
53×	`associate-l`
41×	`*-un-lft-identity`
25×	`add-cube-cbrt`
22×	`times-frac`
21×	`associate-r`
16×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
15×	`difference-of-squares`
13×	`pow1` `sqrt-prod`
11×	`unswap-sqr`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`distribute-lft-out--`
6×	`prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
5×	`sub-neg` `pow-prod-down`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `*-commutative`
3×	`associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv` `diff-cos`

Counts

4 → 154

Calls

4 calls:

12.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
25.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- (cos x) (cos y))

series369.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
136.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
90.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
53.0ms	(- (cos x) (cos y))

simplify106.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	843	1663
1	3946	1549
2	5002	1549

prune990.0ms

Filtered

166 candidates to 113 candidates (68.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	155	11	166
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	162	13	175

Merged error: 0.1b

Counts

175 → 13

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.6b	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
1.3b	(- (cos x) (cos y))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

420×	`sqrt-div`
320×	`add-sqr-sqrt`
226×	`associate-*l/`
200×	`frac-times`
180×	`associate-/l*`
176×	`*-un-lft-identity`
105×	`sqrt-prod`
96×	`add-cube-cbrt`
90×	`associate-/r*`
81×	`associate-l`
79×	`difference-of-squares`
60×	`associate-/l/`
57×	`associate-r`
47×	`times-frac`
40×	`distribute-lft-out--`
38×	`flip3--` `flip--`
33×	`unswap-sqr`
30×	`frac-2neg` `clear-num`
24×	`associate-*r/`
16×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`sub-neg` `*-commutative`
4×	`distribute-rgt-in` `distribute-lft-in`
2×	`div-inv`
1×	`diff-log` `diff-cos`

Counts

4 → 411

Calls

4 calls:

22.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
47.0ms	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
5.0ms	(- (cos x) (cos y))

series432.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
88.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
154.0ms	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
53.0ms	(- (cos x) (cos y))

simplify97.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1711	6514
1	5001	6215

prune1.9s

Filtered

423 candidates to 200 candidates (47.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	416	7	423
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	424	12	436

Merged error: 0.1b

Counts

436 → 12

localize53.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* (sqrt (- (sqrt 5.0) 1.0)) (* (sqrt (- (pow (sqrt 5.0) 3) (pow 1.0 3))) (cos x))) (* (sqrt 2.0) (sqrt (* 2.0 (+ (* (sqrt 5.0) (sqrt 5.0)) (+ (* 1.0 1.0) (* (sqrt 5.0) 1.0)))))))
1.0b	(* (sqrt 5.0) (sqrt 5.0))
1.0b	(pow (sqrt 5.0) 3)
1.3b	(- (cos x) (cos y))

rewrite653.0ms

Algorithm

rewrite-expression-head

Rules

4902×	`associate-r`
4715×	`sqrt-prod`
4608×	`add-sqr-sqrt`
3610×	`associate-l`
3458×	`*-un-lft-identity`
2898×	`times-frac`
1260×	`distribute-lft-out`
1150×	`unswap-sqr`
1119×	`difference-of-squares`
808×	`add-cube-cbrt`
780×	`unpow-prod-down` `cube-prod`
431×	`sqr-pow`
259×	`distribute-lft-out--`
227×	`*-commutative`
175×	`pow-unpow`
172×	`difference-cubes`
69×	`associate-/l*`
42×	`associate-/r*`
28×	`add-exp-log` `add-cbrt-cube`
21×	`pow1`
14×	`sqrt-div`
10×	`prod-exp` `cbrt-unprod`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr` `associate-*l/` `associate-/l/`
7×	`flip3--` `flip--`
6×	`cbrt-undiv` `associate-*r/` `div-exp` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times`
3×	`pow-pow` `pow-prod-down` `pow-sqr`
2×	`associate-/r/`
1×	`pow2` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `pow-exp` `clear-num` `rem-square-sqrt` `sqrt-pow2` `flip-+` `div-inv` `diff-cos` `rem-cube-cbrt`

Counts

4 → 3137

Calls

4 calls:

177.0ms	(/ (* (sqrt (- (sqrt 5.0) 1.0)) (* (sqrt (- (pow (sqrt 5.0) 3) (pow 1.0 3))) (cos x))) (* (sqrt 2.0) (sqrt (* 2.0 (+ (* (sqrt 5.0) (sqrt 5.0)) (+ (* 1.0 1.0) (* (sqrt 5.0) 1.0)))))))
7.0ms	(* (sqrt 5.0) (sqrt 5.0))
6.0ms	(pow (sqrt 5.0) 3)
5.0ms	(- (cos x) (cos y))

series1.0s

Counts

4 → 8

Calls

4 calls:

942.0ms	(/ (* (sqrt (- (sqrt 5.0) 1.0)) (* (sqrt (- (pow (sqrt 5.0) 3) (pow 1.0 3))) (cos x))) (* (sqrt 2.0) (sqrt (* 2.0 (+ (* (sqrt 5.0) (sqrt 5.0)) (+ (* 1.0 1.0) (* (sqrt 5.0) 1.0)))))))
0.0ms	(* (sqrt 5.0) (sqrt 5.0))
0.0ms	(pow (sqrt 5.0) 3)
63.0ms	(- (cos x) (cos y))

simplify974.0ms

Algorithm

egg-herbie

Counts

3145 → 3145

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5002	115283

prune11.2s

Filtered

3145 candidates to 863 candidates (27.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	3140	5	3145
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	3146	11	3157

Merged error: 0.1b

Counts

3157 → 11

regimes257.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	47
1	54	47

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.0s	2682×	body	1280	valid
1.3s	1834×	body	640	valid
392.0ms	776×	body	320	valid
379.0ms	2368×	body	80	valid
112.0ms	340×	body	160	valid