Details

Time bar (total: 34.0s)

sample170.0ms

Algorithm
intervals
Results
74.0ms316×body80valid
37.0ms27×body1280valid
24.0ms27×body640valid
11.0ms16×body320valid
4.0ms9×body160valid

simplify374.0ms

Calls
1 calls:
Slowest
374.0ms
(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.3b

localize38.0ms

Local error

Found 4 expressions with local error:

5.1b
(* sin (* x cos))
5.1b
(* sin (* x cos))
0.4b
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.2b
(* (* sin (* x cos)) (* sin (* x cos)))

rewrite41.0ms

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
20.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
15.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))

series192.0ms

Calls
4 calls:
Slowest
95.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
35.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
32.0ms
(* sin (* x cos))
31.0ms
(* sin (* x cos))

simplify5.4s

Calls
33 calls:
Slowest
1.1s
(/ (* (* (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)))))
762.0ms
(/ (* (cos x) (cos x)) (* (* sin (* x cos)) (* sin (* x cos))))
538.0ms
(/ (* (* (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)))))
285.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
279.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

5.1b
(* sin (* x cos))
5.1b
(* sin (* x cos))
0.6b
(/ (cos (* 2 x)) (* sin (* x cos)))
0.2b
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))

rewrite36.0ms

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
18.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
12.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))

series191.0ms

Calls
4 calls:
Slowest
80.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
49.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
33.0ms
(* sin (* x cos))
30.0ms
(* sin (* x cos))

simplify5.3s

Calls
51 calls:
Slowest
969.0ms
(/ (* (* (/ (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))))
864.0ms
(/ (/ (* (* (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))))
308.0ms
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
255.0ms
(- (/ 1 (* x (* cos sin))) (* 2 (/ x (* cos sin))))
241.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

5.1b
(/ (/ (cos (* 2 x)) sin) (* x cos))
5.1b
(* sin (* x cos))
0.2b
(/ (/ (/ (cos (* 2 x)) sin) (* x cos)) (* sin (* x cos)))
0.1b
(/ (cos (* 2 x)) sin)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
20×times-frac
15×associate-/l*
11×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×div-inv
6×div-sub
4×pow1 cbrt-undiv div-exp insert-posit16 add-log-exp
3×clear-num frac-2neg cos-2
2×associate-/r* associate-/l/
1×associate-*r* *-commutative
Calls
4 calls:
Slowest
13.0ms
(/ (/ (/ (cos (* 2 x)) sin) (* x cos)) (* sin (* x cos)))
11.0ms
(/ (/ (cos (* 2 x)) sin) (* x cos))
6.0ms
(/ (cos (* 2 x)) sin)
2.0ms
(* sin (* x cos))

series168.0ms

Calls
4 calls:
Slowest
77.0ms
(/ (/ (/ (cos (* 2 x)) sin) (* x cos)) (* sin (* x cos)))
41.0ms
(/ (/ (cos (* 2 x)) sin) (* x cos))
28.0ms
(/ (cos (* 2 x)) sin)
22.0ms
(* sin (* x cos))

simplify6.3s

Calls
60 calls:
Slowest
922.0ms
(/ (* (* (/ (/ (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))))
773.0ms
(/ (/ (* (* (/ (cos (* 2 x)) sin) (/ (cos (* 2 x)) sin)) (/ (cos (* 2 x)) sin)) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
578.0ms
(/ (/ (/ (* (cos x) (cos x)) sin) (* x cos)) (* sin (* x cos)))
306.0ms
(- (/ 1 (* x (* cos sin))) (* 2 (/ x (* cos sin))))
301.0ms
(- (- (log (/ (cos (* 2 x)) sin)) (log (* x cos))) (log (* sin (* x cos))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

16.8b
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
16.8b
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
16.8b
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
5.1b
(* sin (* x cos))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-div pow1/3 div-inv
1×associate-*r* *-commutative
Calls
4 calls:
Slowest
3.0ms
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
3.0ms
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
3.0ms
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
2.0ms
(* sin (* x cos))

series640.0ms

Calls
4 calls:
Slowest
222.0ms
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
201.0ms
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
199.0ms
(cbrt (/ (cos (* 2 x)) (* sin (* x cos))))
18.0ms
(* sin (* x cos))

simplify3.5s

Calls
36 calls:
Slowest
523.0ms
(exp (* 1/3 (+ (log (/ 1 x)) (+ (log (cos (* 2 x))) (+ (log (/ 1 cos)) (log (/ 1 sin)))))))
517.0ms
(exp (* 1/3 (+ (log (/ 1 x)) (+ (log (cos (* 2 x))) (+ (log (/ 1 cos)) (log (/ 1 sin)))))))
509.0ms
(exp (* 1/3 (+ (log (/ 1 x)) (+ (log (cos (* 2 x))) (+ (log (/ 1 cos)) (log (/ 1 sin)))))))
224.0ms
(- (exp (* -1/3 (+ (log sin) (+ (log cos) (log x))))) (* 2/3 (* (pow x 2) (exp (* -1/3 (+ (log sin) (+ (log cos) (log x))))))))
221.0ms
(- (exp (* -1/3 (+ (log sin) (+ (log cos) (log x))))) (* 2/3 (* (pow x 2) (exp (* -1/3 (+ (log sin) (+ (log cos) (log x))))))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes355.0ms

Accuracy

9.4% (2.4b remaining)

Error of 2.6b against oracle of 0.1b and baseline of 2.8b

bsearch370.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.4s9073×body80valid
1.6s798×body1280valid
1.0s975×body640valid
944.0ms584×body320valid
218.0ms306×body160valid