Details

sample158.0ms

Algorithm

intervals

Results

57.0ms	36×	body	1280	valid
54.0ms	265×	body	80	valid
17.0ms	22×	body	640	valid
10.0ms	17×	body	320	valid
5.0ms	11×	body	160	valid

simplify315.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

314.0ms

(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize32.0ms

Local error

Found 4 expressions with local error:

4.0b	(* sin (* x cos))
4.0b	(* sin (* x cos))
0.7b	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.3b	(* (* sin (* x cos)) (* sin (* x cos)))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

128×	`pow1`
97×	`add-cbrt-cube` `add-exp-log`
72×	`pow-prod-down`
60×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`pow-sqr` `pow-prod-up`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-plus` `associate-r` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `div-sub` `swap-sqr` `cos-2` `div-inv`

Counts

4 → 146

Calls

4 calls:

Slowest

104.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
103.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
27.0ms	(* sin (* x cos))
18.0ms	(* sin (* x cos))

series266.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

106.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
72.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
49.0ms	(* sin (* x cos))
38.0ms	(* sin (* x cos))

simplify27.8s

Counts

127 → 158

Calls

127 calls:

Slowest

1.8s	(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))))
1.3s	(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))
1.3s	(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))
1.2s	(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))))
1.2s	(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

4.0b	(* sin (* x cos))
4.0b	(* sin (* x cos))
0.4b	(cbrt (cos (* 2 x)))
0.4b	(cbrt (cos (* 2 x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `associate-r` `*-commutative`

Counts

4 → 70

Calls

4 calls:

Slowest

20.0ms	(* sin (* x cos))
15.0ms	(* sin (* x cos))
3.0ms	(cbrt (cos (* 2 x)))
3.0ms	(cbrt (cos (* 2 x)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(cbrt (cos (* 2 x)))
137.0ms	(cbrt (cos (* 2 x)))
45.0ms	(* sin (* x cos))
45.0ms	(* sin (* x cos))

simplify2.7s

Counts

34 → 82

Calls

34 calls:

Slowest

593.0ms	(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
537.0ms	(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
396.0ms	(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
380.0ms	(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
209.0ms	(- 1 (+ (* 2/3 (pow x 2)) (* 2/9 (pow x 4))))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

4.0b	(* sin (* x cos))
4.0b	(* sin (* x cos))
0.4b	(cbrt (cos (* 2 x)))
0.4b	(cbrt (cos (* 2 x)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `associate-r` `*-commutative`

Counts

4 → 70

Calls

4 calls:

Slowest

29.0ms	(* sin (* x cos))
27.0ms	(* sin (* x cos))
3.0ms	(cbrt (cos (* 2 x)))
3.0ms	(cbrt (cos (* 2 x)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(cbrt (cos (* 2 x)))
139.0ms	(cbrt (cos (* 2 x)))
45.0ms	(* sin (* x cos))
37.0ms	(* sin (* x cos))

simplify3.1s

Counts

34 → 82

Calls

34 calls:

Slowest

838.0ms	(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
590.0ms	(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
404.0ms	(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
357.0ms	(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
205.0ms	(- 1 (+ (* 2/3 (pow x 2)) (* 2/9 (pow x 4))))

prune1.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

4.0b	(* sin (* x cos))
4.0b	(* sin (* x cos))
0.4b	(cbrt (cos (* 2 x)))
0.4b	(cbrt (cos (* 2 x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `associate-r` `*-commutative`

Counts

4 → 70

Calls

4 calls:

Slowest

28.0ms	(* sin (* x cos))
23.0ms	(* sin (* x cos))
7.0ms	(cbrt (cos (* 2 x)))
6.0ms	(cbrt (cos (* 2 x)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(cbrt (cos (* 2 x)))
124.0ms	(cbrt (cos (* 2 x)))
41.0ms	(* sin (* x cos))
32.0ms	(* sin (* x cos))

simplify2.8s

Counts

34 → 82

Calls

34 calls:

Slowest

503.0ms	(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
498.0ms	(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
451.0ms	(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
386.0ms	(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
255.0ms	(- 1 (+ (* 2/3 (pow x 2)) (* 2/9 (pow x 4))))

prune1.3s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

regimes671.0ms

Accuracy

21.3% (2.2b remaining)

Error of 2.4b against oracle of 0.2b and baseline of 3.0b

bsearch8.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.1s	9064×	body	80	valid
1.5s	801×	body	1280	valid
817.0ms	917×	body	640	valid
507.0ms	625×	body	320	valid
131.0ms	310×	body	160	valid