Details

Time bar (total: 44.6s)

sample147.0ms

Algorithm
intervals
Results
62.0ms313×body80valid
26.0ms31×body640valid
21.0ms19×body1280valid
12.0ms20×body320valid
5.0ms11×body160valid

simplify204.0ms

Calls
1 calls:
Slowest
203.0ms
(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize29.0ms

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)))

rewrite29.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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
14.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
10.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))

series259.0ms

Calls
4 calls:
Slowest
96.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
81.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
43.0ms
(* sin (* x cos))
38.0ms
(* sin (* x cos))

simplify3.5s

Calls
33 calls:
Slowest
609.0ms
(/ (* (cos x) (cos x)) (* (* sin (* x cos)) (* sin (* x cos))))
462.0ms
(/ (* (* (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)))))
361.0ms
(/ (* (* (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)))))
186.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
175.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))

prune677.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

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)))

rewrite21.0ms

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×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u 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
11.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
6.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
1.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series181.0ms

Calls
4 calls:
Slowest
85.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
40.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
28.0ms
(* sin (* x cos))
28.0ms
(* sin (* x cos))

simplify4.3s

Calls
51 calls:
Slowest
755.0ms
(/ (* (* (/ (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))))
667.0ms
(/ (/ (* (* (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))))
228.0ms
(/ (/ 1 (* sin (* x cos))) (* x cos))
225.0ms
(- (/ 1 (* x (* cos sin))) (* 2 (/ x (* cos sin))))
197.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))

prune808.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))

rewrite26.0ms

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×expm1-log1p-u associate-*l* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u 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)))
6.0ms
(* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))
6.0ms
(/ (cos (* 2 x)) (* x cos))
1.0ms
(* sin (* x cos))

series245.0ms

Calls
4 calls:
Slowest
94.0ms
(/ (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* sin (* x cos)))
70.0ms
(* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))
45.0ms
(/ (cos (* 2 x)) (* x cos))
36.0ms
(* sin (* x cos))

simplify12.1s

Calls
54 calls:
Slowest
3.0s
(/ (* (* (* (/ 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))))
2.6s
(/ (* (* (* (/ 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))))
1.7s
(/ (* (* (* (/ 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))))
434.0ms
(* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x cos) (* x cos)) (* x cos))))
413.0ms
(- (+ (log (/ 1 sin)) (- (log (cos (* 2 x))) (log (* x cos)))) (log (* sin (* x cos))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite49.0ms

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×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u 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
21.0ms
(/ (* (/ 1 sin) (cos (* 2 x))) (* x cos))
12.0ms
(/ (/ (* (/ 1 sin) (cos (* 2 x))) (* x cos)) (* sin (* x cos)))
12.0ms
(* (/ 1 sin) (cos (* 2 x)))
2.0ms
(* sin (* x cos))

series298.0ms

Calls
4 calls:
Slowest
125.0ms
(/ (/ (* (/ 1 sin) (cos (* 2 x))) (* x cos)) (* sin (* x cos)))
76.0ms
(/ (* (/ 1 sin) (cos (* 2 x))) (* x cos))
60.0ms
(* (/ 1 sin) (cos (* 2 x)))
37.0ms
(* sin (* x cos))

simplify13.7s

Calls
51 calls:
Slowest
2.4s
(/ (/ (* (* (* (/ 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))))
2.0s
(/ (/ (* (* (* (/ 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))))
1.7s
(/ (* (* (/ (* (/ 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))))
655.0ms
(/ (* (* (* (/ 1 sin) (cos (* 2 x))) (* (/ 1 sin) (cos (* 2 x)))) (* (/ 1 sin) (cos (* 2 x)))) (* (* (* x cos) (* x cos)) (* x cos)))
624.0ms
(/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))) (* (* (* x cos) (* x cos)) (* x cos)))

prune963.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes369.0ms

Accuracy

0% (2.6b remaining)

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

bsearch3.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.9s9071×body80valid
1.3s794×body1280valid
896.0ms893×body640valid
823.0ms598×body320valid
187.0ms338×body160valid