Details

Time bar (total: 43.7s)

sample129.0ms

Algorithm
intervals
Results
56.0ms313×body80valid
22.0ms31×body640valid
18.0ms19×body1280valid
11.0ms20×body320valid
4.0ms11×body160valid

simplify259.0ms

Calls
1 calls:
Slowest
259.0ms
(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize22.0ms

Local error

Found 4 expressions with local error:

3.2b
(* sin (* x cos))
3.2b
(* sin (* x cos))
0.3b
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.2b
(* (* sin (* x cos)) (* sin (* x cos)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube add-exp-log
9×pow1
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×insert-posit16 add-log-exp
3×times-frac associate-*r* *-commutative associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×pow2 clear-num associate-/r* frac-2neg pow-plus div-sub associate-*l* pow-prod-down pow-prod-up cos-2 div-inv
Calls
4 calls:
Slowest
12.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
6.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))

series233.0ms

Calls
4 calls:
Slowest
90.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
70.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
38.0ms
(* sin (* x cos))
35.0ms
(* sin (* x cos))

simplify4.0s

Calls
33 calls:
Slowest
866.0ms
(/ (* (cos x) (cos x)) (* (* sin (* x cos)) (* sin (* x cos))))
507.0ms
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))))
438.0ms
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin (* x cos)) (* sin (* x cos))) (* (* sin (* x cos)) (* sin (* x cos)))) (* (* sin (* x cos)) (* sin (* x cos)))))
200.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))
195.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))

prune690.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

3.2b
(* sin (* x cos))
3.2b
(* sin (* x cos))
0.8b
(/ (cos (* 2 x)) (* sin (* x cos)))
0.2b
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
16×times-frac
11×add-cbrt-cube add-exp-log
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt associate-/l*
4×pow1 cbrt-undiv div-exp insert-posit16 div-inv add-log-exp
3×div-sub
2×clear-num associate-/r* frac-2neg associate-*r* *-commutative cos-2
1×associate-/l/
Calls
4 calls:
Slowest
9.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
7.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
1.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series186.0ms

Calls
4 calls:
Slowest
76.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
49.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
32.0ms
(* sin (* x cos))
29.0ms
(* sin (* x cos))

simplify4.1s

Calls
51 calls:
Slowest
853.0ms
(/ (* (* (/ (cos (* 2 x)) (* sin (* x cos))) (/ (cos (* 2 x)) (* sin (* x cos)))) (/ (cos (* 2 x)) (* sin (* x cos)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
600.0ms
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
218.0ms
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
204.0ms
(- (/ 1 (* x (* cos sin))) (* 2 (/ x (* cos sin))))
203.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))

prune764.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))
3.2b
(* sin (* x cos))
0.3b
(/ (cos (* 2 x)) (* x cos))
0.2b
(/ (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* sin (* x cos)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×associate-*r*
7×times-frac
6×pow1 cbrt-undiv div-exp
4×associate-*l* prod-exp cbrt-unprod insert-posit16 div-inv associate-/l* add-log-exp
3×associate-/l/
2×frac-times clear-num associate-/r* frac-2neg associate-*l/ associate-*r/ *-commutative
1×div-sub pow-prod-down cos-2
Calls
4 calls:
Slowest
12.0ms
(/ (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* sin (* x cos)))
9.0ms
(* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))
6.0ms
(/ (cos (* 2 x)) (* x cos))
2.0ms
(* sin (* x cos))

series256.0ms

Calls
4 calls:
Slowest
113.0ms
(/ (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* sin (* x cos)))
55.0ms
(* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))
50.0ms
(/ (cos (* 2 x)) (* x cos))
38.0ms
(* sin (* x cos))

simplify11.4s

Calls
54 calls:
Slowest
2.6s
(/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x cos) (* x cos)) (* x cos)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
2.1s
(/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (* (* (/ (cos (* 2 x)) (* x cos)) (/ (cos (* 2 x)) (* x cos))) (/ (cos (* 2 x)) (* x cos)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
1.8s
(/ (* (* (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))) (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
467.0ms
(- (+ (log (/ 1 sin)) (- (log (cos (* 2 x))) (log (* x cos)))) (log (* sin (* x cos))))
461.0ms
(* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x cos) (* x cos)) (* x cos))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (* (/ 1 sin) (cos (* 2 x))) (* x cos))
3.2b
(* sin (* x cos))
0.2b
(* (/ 1 sin) (cos (* 2 x)))
0.2b
(/ (/ (* (/ 1 sin) (cos (* 2 x))) (* x cos)) (* sin (* x cos)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
8×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
7×cbrt-undiv div-exp
6×pow1 associate-/l*
5×div-inv
4×associate-*r* associate-*l* insert-posit16 add-log-exp
3×prod-exp cbrt-unprod
2×clear-num associate-/r* frac-2neg associate-*l/ *-commutative associate-/l/
1×pow-prod-down
Calls
4 calls:
Slowest
23.0ms
(/ (/ (* (/ 1 sin) (cos (* 2 x))) (* x cos)) (* sin (* x cos)))
21.0ms
(/ (* (/ 1 sin) (cos (* 2 x))) (* x cos))
13.0ms
(* (/ 1 sin) (cos (* 2 x)))
3.0ms
(* sin (* x cos))

series269.0ms

Calls
4 calls:
Slowest
91.0ms
(/ (* (/ 1 sin) (cos (* 2 x))) (* x cos))
90.0ms
(/ (/ (* (/ 1 sin) (cos (* 2 x))) (* x cos)) (* sin (* x cos)))
55.0ms
(* (/ 1 sin) (cos (* 2 x)))
34.0ms
(* sin (* x cos))

simplify13.6s

Calls
51 calls:
Slowest
2.3s
(/ (/ (* (* (* (/ 1 sin) (cos (* 2 x))) (* (/ 1 sin) (cos (* 2 x)))) (* (/ 1 sin) (cos (* 2 x)))) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
2.2s
(/ (/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
1.6s
(/ (* (* (/ (* (/ 1 sin) (cos (* 2 x))) (* x cos)) (/ (* (/ 1 sin) (cos (* 2 x))) (* x cos))) (/ (* (/ 1 sin) (cos (* 2 x))) (* x cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
685.0ms
(/ (* (* (* (/ 1 sin) (cos (* 2 x))) (* (/ 1 sin) (cos (* 2 x)))) (* (/ 1 sin) (cos (* 2 x)))) (* (* (* x cos) (* x cos)) (* x cos)))
674.0ms
(/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))) (* (* (* x cos) (* x cos)) (* x cos)))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes454.0ms

Accuracy

0% (2.6b remaining)

Error of 2.7b against oracle of 0.1b and baseline of 2.7b

bsearch4.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.3s9071×body80valid
944.0ms794×body1280valid
810.0ms893×body640valid
351.0ms598×body320valid
159.0ms338×body160valid