Details

Time bar (total: 12.2s)

sample119.0ms

Algorithm
intervals
Results
38.0ms264×body80valid
26.0ms34×body1280valid
15.0ms26×body640valid
14.0ms14×body160valid
11.0ms23×body320valid

simplify240.0ms

Calls
1 calls:
Slowest
239.0ms
(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize25.0ms

Local error

Found 4 expressions with local error:

5.9b
(* sin (* x cos))
5.9b
(* sin (* x cos))
0.5b
(cos (* 2 x))
0.3b
(* (* sin (* x cos)) (* sin (* x cos)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
6×add-cbrt-cube add-exp-log
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt insert-posit16 add-log-exp
3×associate-*r* *-commutative
1×pow2 pow-plus associate-*l* pow-prod-down prod-exp pow-prod-up cbrt-unprod cos-2
Calls
4 calls:
Slowest
9.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
5.0ms
(* sin (* x cos))
3.0ms
(cos (* 2 x))
1.0ms
(* sin (* x cos))

series84.0ms

Calls
4 calls:
Slowest
41.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
20.0ms
(* sin (* x cos))
16.0ms
(* sin (* x cos))
7.0ms
(cos (* 2 x))

simplify1.0s

Calls
20 calls:
Slowest
176.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
161.0ms
(* (pow x 2) (* (pow cos 2) (pow sin 2)))
145.0ms
(* (pow x 2) (* (pow cos 2) (pow sin 2)))
131.0ms
(* (pow x 2) (* (pow cos 2) (pow sin 2)))
125.0ms
(+ (log (* sin (* x cos))) (log (* sin (* x cos))))

prune598.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

5.9b
(* sin (* x cos))
5.9b
(* sin (* x cos))
0.5b
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
0.3b
(* (cos x) (cos x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
6×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
5×associate-*r*
4×insert-posit16
3×associate-*l* cos-mult *-commutative
2×sqr-cos sin-mult
1×pow2 sub-neg pow-plus flip3-- 2-cos diff-log pow-prod-down prod-exp associate--l+ pow-prod-up frac-sub cbrt-unprod sqr-sin flip-- sub-div associate--r- difference-of-squares
Calls
4 calls:
Slowest
11.0ms
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
4.0ms
(* (cos x) (cos x))
2.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series76.0ms

Calls
4 calls:
Slowest
24.0ms
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
21.0ms
(* sin (* x cos))
20.0ms
(* sin (* x cos))
11.0ms
(* (cos x) (cos x))

simplify1.1s

Calls
33 calls:
Slowest
347.0ms
(- (* (+ (cos (+ x x)) (cos (- x x))) 2) (* 2 (- (cos (- x x)) (cos (+ x x)))))
277.0ms
(- (+ (cos (+ x x)) (cos (- x x))) (- (cos (- x x)) (cos (+ x x))))
86.0ms
(- (+ (* 2/3 (pow x 4)) 1) (* 2 (pow x 2)))
77.0ms
(/ (exp (* (cos x) (cos x))) (exp (* (sin x) (sin x))))
70.0ms
(- (+ (* 1/3 (pow x 4)) 1) (pow x 2))

prune719.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

5.9b
(* sin (* x cos))
5.9b
(* sin (* x cos))
0.3b
(- (cos x) (sin x))
0.3b
(+ (cos x) (sin x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity add-log-exp
6×add-sqr-sqrt
4×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
2×associate-*r* *-commutative
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
4.0ms
(- (cos x) (sin x))
4.0ms
(+ (cos x) (sin x))
1.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series49.0ms

Calls
4 calls:
Slowest
16.0ms
(* sin (* x cos))
16.0ms
(* sin (* x cos))
9.0ms
(- (cos x) (sin x))
7.0ms
(+ (cos x) (sin x))

simplify252.0ms

Calls
18 calls:
Slowest
92.0ms
(- 1 (+ x (* 1/2 (pow x 2))))
47.0ms
(- (+ x 1) (* 1/2 (pow x 2)))
13.0ms
(/ (exp (cos x)) (exp (sin x)))
13.0ms
(* x (* cos sin))
12.0ms
(* x (* cos sin))

prune491.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

5.9b
(* sin (* x cos))
5.9b
(* sin (* x cos))
0.5b
(pow (* (sin x) (sin x)) 3)
0.5b
(pow (* (cos x) (cos x)) 3)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
10×pow-pow add-cbrt-cube add-exp-log
4×add-sqr-sqrt *-un-lft-identity pow-exp add-cube-cbrt insert-posit16 add-log-exp rem-cube-cbrt
2×cube-div pow2 cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod associate-*r* pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod
1×cos-mult sin-mult
Calls
4 calls:
Slowest
7.0ms
(pow (* (cos x) (cos x)) 3)
4.0ms
(pow (* (sin x) (sin x)) 3)
1.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series81.0ms

Calls
4 calls:
Slowest
26.0ms
(pow (* (sin x) (sin x)) 3)
22.0ms
(pow (* (cos x) (cos x)) 3)
17.0ms
(* sin (* x cos))
16.0ms
(* sin (* x cos))

simplify1.1s

Calls
36 calls:
Slowest
332.0ms
(pow (+ (cos (+ x x)) (cos (- x x))) 3)
311.0ms
(pow (- (cos (- x x)) (cos (+ x x))) 3)
101.0ms
(- (+ (* 4 (pow x 4)) 1) (* 3 (pow x 2)))
71.0ms
(- (+ (* 7/15 (pow x 10)) (pow x 6)) (pow x 8))
24.0ms
(* (log (* (cos x) (cos x))) 3)

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

regimes200.0ms

Accuracy

20.6% (2.1b remaining)

Error of 2.6b against oracle of 0.4b and baseline of 3.1b

bsearch582.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.0s8976×body80valid
881.0ms856×body1280valid
754.0ms987×body640valid
320.0ms556×body320valid
96.0ms295×body160valid