Details

Time bar (total: 51.4s)

sample125.0ms

Algorithm
intervals
Results
44.0ms36×body1280valid
41.0ms265×body80valid
14.0ms22×body640valid
7.0ms17×body320valid
3.0ms11×body160valid

simplify330.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
330.0ms
(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize18.0ms

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)))

rewrite234.0ms

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×insert-posit16 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 → 138
Calls
4 calls:
Slowest
98.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
82.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
27.0ms
(* sin (* x cos))
23.0ms
(* sin (* x cos))

series279.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
94.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
47.0ms
(* sin (* x cos))
39.0ms
(* sin (* x cos))

simplify28.8s

Counts
127 → 150
Calls
127 calls:
Slowest
1.3s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))
1.3s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x 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)))))
1.3s
(/ (* (* (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 x) x) (* (* cos cos) cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))))

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize60.0ms

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)))

rewrite39.0ms

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×insert-posit16 add-log-exp
2×pow1/3 associate-*r* *-commutative
Counts
4 → 62
Calls
4 calls:
Slowest
17.0ms
(* sin (* x cos))
13.0ms
(* sin (* x cos))
5.0ms
(cbrt (cos (* 2 x)))
3.0ms
(cbrt (cos (* 2 x)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(cbrt (cos (* 2 x)))
105.0ms
(cbrt (cos (* 2 x)))
42.0ms
(* sin (* x cos))
30.0ms
(* sin (* x cos))

simplify2.7s

Counts
34 → 74
Calls
34 calls:
Slowest
497.0ms
(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
491.0ms
(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
473.0ms
(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
437.0ms
(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
150.0ms
(- 1 (+ (* 2/3 (pow x 2)) (* 2/9 (pow x 4))))

prune995.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

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)))

rewrite32.0ms

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×insert-posit16 add-log-exp
2×pow1/3 associate-*r* *-commutative
Counts
4 → 62
Calls
4 calls:
Slowest
13.0ms
(* sin (* x cos))
12.0ms
(* sin (* x cos))
3.0ms
(cbrt (cos (* 2 x)))
3.0ms
(cbrt (cos (* 2 x)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(cbrt (cos (* 2 x)))
158.0ms
(cbrt (cos (* 2 x)))
40.0ms
(* sin (* x cos))
35.0ms
(* sin (* x cos))

simplify2.8s

Counts
34 → 74
Calls
34 calls:
Slowest
567.0ms
(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
562.0ms
(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
434.0ms
(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
377.0ms
(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
178.0ms
(- 1 (+ (* 2/3 (pow x 2)) (* 2/9 (pow x 4))))

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize72.0ms

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)))

rewrite45.0ms

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×insert-posit16 add-log-exp
2×pow1/3 associate-*r* *-commutative
Counts
4 → 62
Calls
4 calls:
Slowest
26.0ms
(* sin (* x cos))
13.0ms
(* sin (* x cos))
3.0ms
(cbrt (cos (* 2 x)))
3.0ms
(cbrt (cos (* 2 x)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(cbrt (cos (* 2 x)))
105.0ms
(cbrt (cos (* 2 x)))
45.0ms
(* sin (* x cos))
44.0ms
(* sin (* x cos))

simplify2.9s

Counts
34 → 74
Calls
34 calls:
Slowest
610.0ms
(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
522.0ms
(* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))
466.0ms
(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
445.0ms
(* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))
182.0ms
(- 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

regimes672.0ms

Accuracy

21.3% (2.2b remaining)

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

bsearch5.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.6s9064×body80valid
1.1s801×body1280valid
899.0ms625×body320valid
846.0ms917×body640valid
169.0ms310×body160valid