Details

Time bar (total: 14.2s)

sample120.0ms

Algorithm
intervals
Results
42.0ms264×body80valid
29.0ms34×body1280valid
17.0ms26×body640valid
11.0ms23×body320valid
5.0ms14×body160valid

simplify227.0ms

Calls
1 calls:
Slowest
227.0ms
(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune16.0ms

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)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
6×add-cbrt-cube add-exp-log
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u 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)))
2.0ms
(cos (* 2 x))
1.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series97.0ms

Calls
4 calls:
Slowest
47.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
22.0ms
(* sin (* x cos))
20.0ms
(* sin (* x cos))
8.0ms
(cos (* 2 x))

simplify1.2s

Calls
20 calls:
Slowest
209.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
177.0ms
(+ (log (* sin (* x cos))) (log (* sin (* x cos))))
159.0ms
(* (pow x 2) (* (pow cos 2) (pow sin 2)))
134.0ms
(* (pow x 2) (* (pow cos 2) (pow sin 2)))
130.0ms
(* (pow x 2) (* (pow cos 2) (pow sin 2)))

prune629.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*l* cos-mult *-commutative
2×sqr-cos sin-mult
1×pow2 sub-neg pow-plus flip3-- fma-neg 2-cos diff-log prod-diff 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
9.0ms
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
5.0ms
(* (cos x) (cos x))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))

series83.0ms

Calls
4 calls:
Slowest
25.0ms
(* sin (* x cos))
25.0ms
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
22.0ms
(* sin (* x cos))
11.0ms
(* (cos x) (cos x))

simplify1.2s

Calls
36 calls:
Slowest
332.0ms
(- (* (+ (cos (+ x x)) (cos (- x x))) 2) (* 2 (- (cos (- x x)) (cos (+ x x)))))
282.0ms
(- (+ (cos (+ x x)) (cos (- x x))) (- (cos (- x x)) (cos (+ x x))))
113.0ms
(/ (exp (* (cos x) (cos x))) (exp (* (sin x) (sin x))))
113.0ms
(- (+ (* 2/3 (pow x 4)) 1) (* 2 (pow x 2)))
78.0ms
(- (+ (* 1/3 (pow x 4)) 1) (pow x 2))

prune854.0ms

Pruning

11 alts after pruning (11 fresh and 0 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))
0.5b
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
0.4b
(log1p (- (* (cos x) (cos x)) (* (sin x) (sin x))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
5×expm1-log1p-u
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u
2×associate-*r* cos-mult *-commutative sin-mult
1×sqr-cos log1p-udef sub-neg flip3-- fma-neg 2-cos diff-log prod-diff associate--l+ log1p-expm1 frac-sub sqr-sin flip-- sub-div associate--r- difference-of-squares
Calls
4 calls:
Slowest
10.0ms
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
1.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))
1.0ms
(log1p (- (* (cos x) (cos x)) (* (sin x) (sin x))))

series177.0ms

Calls
4 calls:
Slowest
100.0ms
(log1p (- (* (cos x) (cos x)) (* (sin x) (sin x))))
35.0ms
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
21.0ms
(* sin (* x cos))
21.0ms
(* sin (* x cos))

simplify1.6s

Calls
24 calls:
Slowest
354.0ms
(- (+ (cos (+ x x)) (cos (- x x))) (- (cos (- x x)) (cos (+ x x))))
340.0ms
(- (* (+ (cos (+ x x)) (cos (- x x))) 2) (* 2 (- (cos (- x x)) (cos (+ x x)))))
166.0ms
(log (- (+ (pow (cos x) 2) 1) (pow (sin x) 2)))
148.0ms
(log (- (+ (pow (cos x) 2) 1) (pow (sin x) 2)))
115.0ms
(/ (exp (* (cos x) (cos x))) (exp (* (sin x) (sin x))))

prune919.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

5.9b
(* sin (* x cos))
5.9b
(* sin (* x cos))
0.6b
(fma (cos x) (cos x) (- (* (sin x) (sin x))))
0.3b
(* (sin x) (sin x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
6×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* *-commutative
1×pow2 pow-plus pow-prod-down prod-exp pow-prod-up cbrt-unprod fma-udef sqr-sin sin-mult
Calls
4 calls:
Slowest
6.0ms
(* (sin x) (sin x))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))
0.0ms
(fma (cos x) (cos x) (- (* (sin x) (sin x))))

series108.0ms

Calls
4 calls:
Slowest
43.0ms
(fma (cos x) (cos x) (- (* (sin x) (sin x))))
23.0ms
(* sin (* x cos))
22.0ms
(* sin (* x cos))
20.0ms
(* (sin x) (sin x))

simplify429.0ms

Calls
25 calls:
Slowest
97.0ms
(- (+ (pow x 2) (* 2/45 (pow x 6))) (* 1/3 (pow x 4)))
94.0ms
(- (+ (* 2/3 (pow x 4)) 1) (* 2 (pow x 2)))
48.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x)))
32.0ms
(- (pow (cos x) 2) (pow (sin x) 2))
27.0ms
(- (pow (cos x) 2) (pow (sin x) 2))

prune757.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

regimes322.0ms

Accuracy

20.5% (2.2b remaining)

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

bsearch625.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.1s8976×body80valid
1.2s856×body1280valid
790.0ms987×body640valid
281.0ms556×body320valid
125.0ms295×body160valid