Details

Time bar (total: 23.6s)

sample139.0ms

Algorithm
intervals
Results
60.0ms288×body80valid
25.0ms33×body640valid
23.0ms25×body1280valid
13.0ms21×body320valid
3.0ms9×body160valid

simplify259.0ms

Calls
1 calls:
Slowest
258.0ms
(/ (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: 2.9b

localize21.0ms

Local error

Found 4 expressions with local error:

6.8b
(* sin (* x cos))
6.8b
(* sin (* x cos))
0.9b
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.3b
(* (* sin (* x cos)) (* sin (* x cos)))

rewrite28.0ms

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
11.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
10.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
5.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series226.0ms

Calls
4 calls:
Slowest
89.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
62.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
39.0ms
(* sin (* x cos))
36.0ms
(* sin (* x cos))

simplify3.7s

Calls
33 calls:
Slowest
569.0ms
(/ (* (* (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)))))
544.0ms
(/ (* (cos x) (cos x)) (* (* sin (* x cos)) (* sin (* x cos))))
406.0ms
(/ (* (* (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)))))
202.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))
185.0ms
(/ (cos (* 2 x)) (* (pow sin 2) (* (pow x 2) (pow cos 2))))

prune738.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

6.8b
(* sin (* x cos))
6.8b
(* sin (* x cos))
0.4b
(/ (cos (* 2 x)) (* sin (* x cos)))
0.2b
(cos (* 2 x))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×associate-*r* *-commutative cos-2
1×cbrt-undiv clear-num associate-/r* frac-2neg div-sub div-exp div-inv
Calls
4 calls:
Slowest
12.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
4.0ms
(cos (* 2 x))
2.0ms
(* sin (* x cos))
2.0ms
(* sin (* x cos))

series128.0ms

Calls
4 calls:
Slowest
43.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
43.0ms
(* sin (* x cos))
33.0ms
(* sin (* x cos))
9.0ms
(cos (* 2 x))

simplify1.4s

Calls
25 calls:
Slowest
536.0ms
(- (/ 1 (* x (* cos sin))) (* 2 (/ x (* cos sin))))
273.0ms
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
189.0ms
(- (log (cos (* 2 x))) (log (* sin (* x cos))))
178.0ms
(/ (* (cos x) (cos x)) (* sin (* x cos)))
97.0ms
(- (+ (* 2/3 (pow x 4)) 1) (* 2 (pow x 2)))

prune740.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

6.8b
(* sin (* x cos))
6.8b
(* sin (* x cos))
0.4b
(/ (- (* (cos x) (cos x)) (* (sin x) (sin x))) (* sin (* x cos)))
0.4b
(- (* (cos x) (cos x)) (* (sin x) (sin x)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
4×expm1-log1p-u pow1 times-frac cos-mult insert-posit16 log1p-expm1-u sin-mult associate-/l* associate-/l/
3×difference-of-squares
2×flip3-- associate-*r* *-commutative frac-sub flip-- sub-div
1×cbrt-undiv sqr-cos clear-num associate-/r* sub-neg frac-2neg fma-neg 2-cos diff-log div-sub div-exp prod-diff associate--l+ sqr-sin div-inv associate--r-
Calls
4 calls:
Slowest
21.0ms
(/ (- (* (cos x) (cos x)) (* (sin x) (sin x))) (* sin (* x cos)))
13.0ms
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
1.0ms
(* sin (* x cos))
1.0ms
(* sin (* x cos))

series238.0ms

Calls
4 calls:
Slowest
101.0ms
(/ (- (* (cos x) (cos x)) (* (sin x) (sin x))) (* sin (* x cos)))
56.0ms
(- (* (cos x) (cos x)) (* (sin x) (sin x)))
48.0ms
(* sin (* x cos))
33.0ms
(* sin (* x cos))

simplify4.8s

Calls
42 calls:
Slowest
671.0ms
(/ (* (* (- (* (cos x) (cos x)) (* (sin x) (sin x))) (- (* (cos x) (cos x)) (* (sin x) (sin x)))) (- (* (cos x) (cos x)) (* (sin x) (sin x)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
420.0ms
(- (* (+ (cos (+ x x)) (cos (- x x))) 2) (* 2 (- (cos (- x x)) (cos (+ x x)))))
364.0ms
(- (+ (cos (+ x x)) (cos (- x x))) (- (cos (- x x)) (cos (+ x x))))
337.0ms
(- (* (+ (cos (+ x x)) (cos (- x x))) 2) (* 2 (- (cos (- x x)) (cos (+ x x)))))
299.0ms
(- (log (- (* (cos x) (cos x)) (* (sin x) (sin x)))) (log (* sin (* x cos))))

prune910.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

6.8b
(* sin (* x cos))
6.5b
(* (/ (+ (cos x) (sin x)) sin) (/ (- (cos x) (sin x)) (* x cos)))
1.1b
(/ (- (cos x) (sin x)) (* x cos))
0.4b
(+ (cos x) (sin x))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×add-sqr-sqrt
11×add-cbrt-cube add-exp-log
10×times-frac associate-*r* add-cube-cbrt
6×pow1 add-log-exp
5×associate-/l*
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×fma-def div-inv distribute-lft-out-- difference-of-squares
2×cbrt-undiv div-exp prod-exp *-commutative cbrt-unprod associate-/l/
1×frac-times +-commutative clear-num associate-/r* sum-log frac-2neg flip3-+ flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ flip-+ flip-- distribute-lft-out
Calls
4 calls:
Slowest
24.0ms
(* (/ (+ (cos x) (sin x)) sin) (/ (- (cos x) (sin x)) (* x cos)))
17.0ms
(/ (- (cos x) (sin x)) (* x cos))
4.0ms
(+ (cos x) (sin x))
2.0ms
(* sin (* x cos))

series246.0ms

Calls
4 calls:
Slowest
128.0ms
(* (/ (+ (cos x) (sin x)) sin) (/ (- (cos x) (sin x)) (* x cos)))
77.0ms
(/ (- (cos x) (sin x)) (* x cos))
27.0ms
(* sin (* x cos))
14.0ms
(+ (cos x) (sin x))

simplify3.2s

Calls
55 calls:
Slowest
449.0ms
(* (* (* (/ (+ (cos x) (sin x)) sin) (/ (+ (cos x) (sin x)) sin)) (/ (+ (cos x) (sin x)) sin)) (/ (* (* (- (cos x) (sin x)) (- (cos x) (sin x))) (- (cos x) (sin x))) (* (* (* x cos) (* x cos)) (* x cos))))
403.0ms
(+ (log (/ (+ (cos x) (sin x)) sin)) (- (log (- (cos x) (sin x))) (log (* x cos))))
327.0ms
(* (* (* (/ (+ (cos x) (sin x)) sin) (/ (+ (cos x) (sin x)) sin)) (/ (+ (cos x) (sin x)) sin)) (* (* (/ (- (cos x) (sin x)) (* x cos)) (/ (- (cos x) (sin x)) (* x cos))) (/ (- (cos x) (sin x)) (* x cos))))
234.0ms
(- (/ 1 (* x (* cos sin))) (* 2 (/ x (* cos sin))))
231.0ms
(+ (log (/ (+ (cos x) (sin x)) sin)) (log (/ (- (cos x) (sin x)) (* x cos))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes239.0ms

Accuracy

0% (2.2b remaining)

Error of 2.3b against oracle of 0.1b and baseline of 2.3b

bsearch3.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.5s9109×body80valid
953.0ms755×body1280valid
897.0ms1040×body640valid
320.0ms577×body320valid
126.0ms339×body160valid