Details

Time bar (total: 3.3m)

sample186.0ms

Algorithm
intervals
Results
70.0ms308×body80valid
30.0ms24×body1280valid
29.0ms31×body640valid
10.0ms15×body320valid
3.0ms7×body160valid

simplify247.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
247.0ms
(/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize19.0ms

Local error

Found 4 expressions with local error:

3.1b
(* sin (* x cos))
3.1b
(* sin (* x cos))
0.5b
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.3b
(* (* sin (* x cos)) (* sin (* x cos)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
128×pow1
97×add-cbrt-cube add-exp-log
72×pow-prod-down
60×prod-exp cbrt-unprod
10×cbrt-undiv div-exp
9×pow-sqr pow-prod-up
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×times-frac pow-plus associate-*r* *-commutative associate-/l*
1×pow2 clear-num associate-/r* frac-2neg div-sub swap-sqr cos-2 div-inv
Counts
4 → 146
Calls
4 calls:
Slowest
125.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
99.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
21.0ms
(* sin (* x cos))
13.0ms
(* sin (* x cos))

series261.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
77.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
44.0ms
(* sin (* x cos))
33.0ms
(* sin (* x cos))

simplify27.8s

Counts
127 → 158
Calls
127 calls:
Slowest
1.6s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))
1.5s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))))
1.3s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))))
1.3s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))
1.3s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

3.1b
(* sin (* x cos))
3.1b
(* sin (* x cos))
0.4b
(/ (cos (* 2 x)) (* sin (* x cos)))
0.2b
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
77×add-cbrt-cube add-exp-log
30×prod-exp cbrt-unprod
24×cbrt-undiv div-exp
16×times-frac
14×pow1
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×associate-/l*
6×associate-*l* pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×div-sub
2×clear-num associate-/r* frac-2neg associate-*r* *-commutative cos-2
1×associate-/l/
Counts
4 → 123
Calls
4 calls:
Slowest
40.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
29.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
17.0ms
(* sin (* x cos))
14.0ms
(* sin (* x cos))

series233.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
54.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
42.0ms
(* sin (* x cos))
38.0ms
(* sin (* x cos))

simplify26.3s

Counts
91 → 135
Calls
91 calls:
Slowest
1.7s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
1.6s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))
1.6s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))
1.4s
(/ (* (* (/ (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))))
1.3s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))
3.1b
(* sin (* x cos))
0.6b
(/ (cos (* 2 x)) (* x cos))
0.2b
(/ (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* sin (* x cos)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
251×add-exp-log
143×add-cbrt-cube
107×prod-exp
97×div-exp
57×cbrt-unprod
51×cbrt-undiv
23×add-sqr-sqrt
18×times-frac
17×*-un-lft-identity
16×associate-*l* add-cube-cbrt
12×rec-exp 1-exp
11×pow1
8×associate-*r*
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
3×unswap-sqr associate-/l/
2×frac-times clear-num associate-/r* frac-2neg associate-*l/ associate-*r/ *-commutative
1×div-sub cos-2
Counts
4 → 181
Calls
4 calls:
Slowest
45.0ms
(/ (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* sin (* x cos)))
38.0ms
(* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))
15.0ms
(/ (cos (* 2 x)) (* x cos))
13.0ms
(* sin (* x cos))

series300.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(/ (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* sin (* x cos)))
76.0ms
(* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))
66.0ms
(/ (cos (* 2 x)) (* x cos))
41.0ms
(* sin (* x cos))

simplify1.0m

Counts
147 → 193
Calls
147 calls:
Slowest
3.3s
(/ (* (/ (* (* 1 1) 1) (* (* sin sin) sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x cos) (* x cos)) (* x cos)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
3.1s
(/ (* (* (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))) (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
3.0s
(/ (* (/ (* (* 1 1) 1) (* (* sin sin) sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x x) x) (* (* cos cos) cos)))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))
2.8s
(/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (* (* (/ (cos (* 2 x)) (* x cos)) (/ (cos (* 2 x)) (* x cos))) (/ (cos (* 2 x)) (* x cos)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
2.7s
(/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x x) x) (* (* cos cos) cos)))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (/ 1 sin) (* (/ 1 x) (/ (cos (* 2 x)) cos)))
3.1b
(* sin (* x cos))
0.3b
(* (/ 1 x) (/ (cos (* 2 x)) cos))
0.2b
(/ (* (/ 1 sin) (* (/ 1 x) (/ (cos (* 2 x)) cos))) (* sin (* x cos)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
804×add-exp-log
394×prod-exp
319×div-exp
254×add-cbrt-cube
112×cbrt-unprod
89×cbrt-undiv
70×rec-exp 1-exp
43×add-sqr-sqrt
35×times-frac
29×associate-*l*
28×*-un-lft-identity
26×add-cube-cbrt
16×pow1
15×associate-*r*
11×frac-times associate-*r/
7×pow-prod-down associate-*l/ associate-/l/
6×unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×*-commutative
1×clear-num associate-/r* frac-2neg associate-/l*
Counts
4 → 327
Calls
4 calls:
Slowest
50.0ms
(/ (* (/ 1 sin) (* (/ 1 x) (/ (cos (* 2 x)) cos))) (* sin (* x cos)))
39.0ms
(* (/ 1 sin) (* (/ 1 x) (/ (cos (* 2 x)) cos)))
31.0ms
(* sin (* x cos))
20.0ms
(* (/ 1 x) (/ (cos (* 2 x)) cos))

series316.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(/ (* (/ 1 sin) (* (/ 1 x) (/ (cos (* 2 x)) cos))) (* sin (* x cos)))
77.0ms
(* (/ 1 sin) (* (/ 1 x) (/ (cos (* 2 x)) cos)))
69.0ms
(* (/ 1 x) (/ (cos (* 2 x)) cos))
35.0ms
(* sin (* x cos))

simplify1.1m

Counts
295 → 339
Calls
295 calls:
Slowest
1.0s
(- (+ (log (/ 1 sin)) (+ (log (/ 1 x)) (log (/ (cos (* 2 x)) cos)))) (+ (log sin) (log (* x cos))))
947.0ms
(- (+ (- (log 1) (log sin)) (+ (log (/ 1 x)) (log (/ (cos (* 2 x)) cos)))) (log (* sin (* x cos))))
912.0ms
(- (+ (- (log sin)) (+ (- (log x)) (log (/ (cos (* 2 x)) cos)))) (+ (log sin) (+ (log x) (log cos))))
885.0ms
(- (+ (log (/ 1 sin)) (+ (- (log 1) (log x)) (log (/ (cos (* 2 x)) cos)))) (log (* sin (* x cos))))
869.0ms
(- (+ (log (/ 1 sin)) (log (* (/ 1 x) (/ (cos (* 2 x)) cos)))) (+ (log sin) (+ (log x) (log cos))))

prune4.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes212.0ms

Accuracy

0% (2.3b remaining)

Error of 2.4b against oracle of 0.1b and baseline of 2.4b

bsearch3.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.9s9086×body80valid
1.3s790×body1280valid
894.0ms957×body640valid
429.0ms580×body320valid
104.0ms285×body160valid