Details

Time bar (total: 25.2s)

sample110.0ms

Algorithm
intervals
Results
47.0ms278×body80valid
21.0ms29×body1280valid
17.0ms30×body640valid
8.0ms17×body320valid
2.0ms9×body160valid

simplify197.0ms

Calls
1 calls:
Slowest
196.0ms
(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

localize16.0ms

Local error

Found 4 expressions with local error:

5.0b
(* sin (* x cos))
5.0b
(* sin (* x cos))
0.4b
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.3b
(* (* sin (* x cos)) (* sin (* x cos)))

rewrite27.0ms

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
(* (* sin (* x cos)) (* sin (* x cos)))
11.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))

series146.0ms

Calls
4 calls:
Slowest
58.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
45.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
22.0ms
(* sin (* x cos))
21.0ms
(* sin (* x cos))

simplify4.0s

Calls
33 calls:
Slowest
583.0ms
(/ (* (cos x) (cos x)) (* (* sin (* x cos)) (* sin (* x cos))))
490.0ms
(/ (* (* (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)))))
447.0ms
(/ (* (* (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)))))
217.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))
210.0ms
(* (* sin (* x cos)) (* sin (* x cos)))

prune693.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b
(* sin (* x cos))
5.0b
(* sin (* x cos))
0.7b
(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
0.7b
(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-cube-cbrt
7×times-frac associate-/l*
6×cbrt-prod
4×pow1 insert-posit16 add-log-exp
3×cbrt-undiv div-exp
2×clear-num associate-/r* frac-2neg associate-*r* *-commutative div-inv
1×prod-exp cbrt-unprod
Calls
4 calls:
Slowest
15.0ms
(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))
7.0ms
(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
2.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series213.0ms

Calls
4 calls:
Slowest
86.0ms
(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))
85.0ms
(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
22.0ms
(* sin (* x cos))
20.0ms
(* sin (* x cos))

simplify2.5s

Calls
40 calls:
Slowest
594.0ms
(/ (* (* (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
388.0ms
(/ (cos (* 2 x)) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
243.0ms
(- (/ 1 (* x (* cos sin))) (* 2/3 (/ x (* cos sin))))
221.0ms
(- (log (cbrt (cos (* 2 x)))) (log (* sin (* x cos))))
207.0ms
(- (+ (log (cbrt (cos (* 2 x)))) (log (cbrt (cos (* 2 x))))) (log (* sin (* x cos))))

prune759.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

5.0b
(* sin (* x cos))
4.7b
(* (/ (cbrt (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) sin) (/ (cbrt (cbrt (cos (* 2 x)))) (* x cos)))
0.7b
(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))
0.7b
(/ (cbrt (cbrt (cos (* 2 x)))) (* x cos))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
19×times-frac
16×add-exp-log
15×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×associate-*r*
12×add-cbrt-cube
10×associate-/l*
6×pow1
4×cbrt-undiv div-exp associate-*l* insert-posit16 div-inv add-log-exp
3×prod-exp cbrt-unprod
2×clear-num associate-/r* frac-2neg *-commutative
1×frac-times pow-prod-down associate-*l/ associate-*r/
Calls
4 calls:
Slowest
15.0ms
(* (/ (cbrt (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) sin) (/ (cbrt (cbrt (cos (* 2 x)))) (* x cos)))
14.0ms
(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))
5.0ms
(/ (cbrt (cbrt (cos (* 2 x)))) (* x cos))
2.0ms
(* sin (* x cos))

series317.0ms

Calls
4 calls:
Slowest
117.0ms
(/ (cbrt (cbrt (cos (* 2 x)))) (* x cos))
98.0ms
(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))
85.0ms
(* (/ (cbrt (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) sin) (/ (cbrt (cbrt (cos (* 2 x)))) (* x cos)))
18.0ms
(* sin (* x cos))

simplify5.1s

Calls
73 calls:
Slowest
641.0ms
(/ (* (* (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
513.0ms
(+ (log (/ (cbrt (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) sin)) (- (log (cbrt (cbrt (cos (* 2 x))))) (log (* x cos))))
419.0ms
(- (/ 1 (* x cos)) (+ (* 10/81 (/ (pow x 3) cos)) (* 2/9 (/ x cos))))
385.0ms
(* (/ (cbrt (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) sin) (/ (cbrt (cbrt (cos (* 2 x)))) (* x cos)))
323.0ms
(+ (log (/ (cbrt (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))) sin)) (log (/ (cbrt (cbrt (cos (* 2 x)))) (* x cos))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

5.0b
(* sin (* x cos))
5.0b
(* sin (* x cos))
0.3b
(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
0.3b
(* (* sin (* x cos)) (* sin (* x cos)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×add-exp-log
10×pow1
7×associate-/r*
6×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-cube-cbrt
4×insert-posit16 add-log-exp
3×rec-exp times-frac associate-*r* *-commutative
2×div-exp prod-exp div-inv
1×pow2 clear-num frac-2neg pow-plus associate-*l* pow-prod-down associate-/r/ pow-prod-up cbrt-unprod pow-flip inv-pow
Calls
4 calls:
Slowest
13.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
6.0ms
(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))

series202.0ms

Calls
4 calls:
Slowest
104.0ms
(/ 1 (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))
44.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
27.0ms
(* sin (* x cos))
27.0ms
(* sin (* x cos))

simplify2.8s

Calls
28 calls:
Slowest
273.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
232.0ms
(* (pow x 2) (* (pow cos 2) (pow sin 2)))
228.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))
196.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))
185.0ms
(cbrt (/ (* (* sin (* x cos)) (* sin (* x cos))) (cos (* 2 x))))

prune737.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes274.0ms

Accuracy

0% (2.6b remaining)

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

bsearch2.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.5s9074×body80valid
1.1s947×body640valid
907.0ms824×body1280valid
411.0ms552×body320valid
116.0ms298×body160valid