Details

Time bar (total: 4.5m)

sample142.0ms

Algorithm
intervals
Results
66.0ms287×body80valid
26.0ms30×body1280valid
23.0ms36×body640valid
6.0ms13×body320valid
2.0ms5×body160valid

simplify250.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
250.0ms
(/ (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: 2.6b

localize18.0ms

Local error

Found 4 expressions with local error:

4.6b
(* sin (* x cos))
4.6b
(* sin (* x cos))
0.4b
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.3b
(* (* sin (* x cos)) (* sin (* x cos)))

rewrite260.0ms

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
107.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
91.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
32.0ms
(* sin (* x cos))
27.0ms
(* sin (* x cos))

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
63.0ms
(* (* sin (* x cos)) (* sin (* x cos)))
36.0ms
(* sin (* x cos))
36.0ms
(* sin (* x cos))

simplify27.8s

Counts
127 → 158
Calls
127 calls:
Slowest
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)))))
1.4s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* 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)))))
1.3s
(/ (* (* (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)))))
1.2s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

4.6b
(* sin (* x cos))
4.6b
(* sin (* x cos))
0.8b
(/ (cos (* 2 x)) (* sin (* x cos)))
0.2b
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))

rewrite143.0ms

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
45.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
37.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
31.0ms
(* sin (* x cos))
28.0ms
(* sin (* x cos))

series236.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(/ (/ (cos (* 2 x)) (* sin (* x cos))) (* sin (* x cos)))
63.0ms
(/ (cos (* 2 x)) (* sin (* x cos)))
35.0ms
(* sin (* x cos))
31.0ms
(* sin (* x cos))

simplify26.7s

Counts
91 → 135
Calls
91 calls:
Slowest
1.9s
(/ (/ (* (* (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))))
1.6s
(/ (/ (* (* (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))))
1.5s
(/ (* (* (/ (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 (* 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 x) x) (* (* cos cos) cos))))

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

4.6b
(* sin (* x cos))
4.6b
(* sin (* x cos))
0.7b
(/ 1 (/ (* sin (* x cos)) (cos (* 2 x))))
0.2b
(/ (/ 1 (/ (* sin (* x cos)) (cos (* 2 x)))) (* sin (* x cos)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
231×add-exp-log
119×times-frac
107×div-exp
103×add-cbrt-cube
81×prod-exp
50×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
43×cbrt-undiv
33×cbrt-unprod
29×associate-/l*
16×rec-exp 1-exp
15×pow1
14×div-inv
8×associate-/r*
6×associate-*l* pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/
2×clear-num frac-2neg associate-*r* *-commutative
1×pow-flip inv-pow associate-/l/
Counts
4 → 226
Calls
4 calls:
Slowest
60.0ms
(/ (/ 1 (/ (* sin (* x cos)) (cos (* 2 x)))) (* sin (* x cos)))
46.0ms
(/ 1 (/ (* sin (* x cos)) (cos (* 2 x))))
18.0ms
(* sin (* x cos))
18.0ms
(* sin (* x cos))

series249.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ (/ 1 (/ (* sin (* x cos)) (cos (* 2 x)))) (* sin (* x cos)))
63.0ms
(/ 1 (/ (* sin (* x cos)) (cos (* 2 x))))
41.0ms
(* sin (* x cos))
29.0ms
(* sin (* x cos))

simplify56.0s

Counts
224 → 238
Calls
224 calls:
Slowest
1.6s
(/ (/ (* (* 1 1) 1) (/ (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))
1.5s
(/ (/ (* (* 1 1) 1) (/ (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
1.4s
(/ (* (* (/ 1 (/ (* sin (* x cos)) (cos (* 2 x)))) (/ 1 (/ (* sin (* x cos)) (cos (* 2 x))))) (/ 1 (/ (* sin (* x cos)) (cos (* 2 x))))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
1.4s
(/ (/ (* (* 1 1) 1) (/ (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
1.3s
(/ (/ (* (* 1 1) 1) (/ (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))

prune2.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (/ 1 (/ sin (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))))) (/ (* x cos) (cbrt (cos (* 2 x)))))
4.6b
(* sin (* x cos))
0.4b
(cbrt (cos (* 2 x)))
0.4b
(cbrt (cos (* 2 x)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
752×times-frac
242×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
135×add-exp-log
87×cbrt-prod
86×div-exp
72×div-inv
49×add-cbrt-cube
35×cbrt-undiv
26×associate-/l*
22×prod-exp
12×associate-/r/
10×associate-/r* cbrt-unprod
9×pow1 rec-exp 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* pow-prod-down
2×pow1/3
1×clear-num frac-2neg associate-*r* *-commutative associate-/l/
Counts
4 → 402
Calls
4 calls:
Slowest
73.0ms
(/ (/ 1 (/ sin (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))))) (/ (* x cos) (cbrt (cos (* 2 x)))))
18.0ms
(* sin (* x cos))
3.0ms
(cbrt (cos (* 2 x)))
3.0ms
(cbrt (cos (* 2 x)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(cbrt (cos (* 2 x)))
124.0ms
(cbrt (cos (* 2 x)))
67.0ms
(/ (/ 1 (/ sin (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))))) (/ (* x cos) (cbrt (cos (* 2 x)))))
53.0ms
(* sin (* x cos))

simplify2.3m

Counts
623 → 414
Calls
623 calls:
Slowest
839.0ms
(- (- (log (/ sin (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x))))))) (- (log (* x cos)) (log (cbrt (cos (* 2 x))))))
832.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt sin) (cbrt (cos (* 2 x))))) (/ x (cbrt (sqrt (cos (* 2 x))))))
801.0ms
(/ (/ 1 (/ (sqrt sin) (cbrt (cos (* 2 x))))) (/ cos (cbrt (cbrt (cos (* 2 x))))))
749.0ms
(/ (/ (sqrt 1) (/ (sqrt sin) (cbrt (cos (* 2 x))))) (/ cos (cbrt (cos (* 2 x)))))
697.0ms
(/ (/ (sqrt 1) (/ 1 (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))))) (/ cos (cbrt (cbrt (cos (* 2 x))))))

prune6.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes731.0ms

Accuracy

0% (2.9b remaining)

Error of 3.1b against oracle of 0.2b and baseline of 3.1b

bsearch4.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.9s9053×body80valid
1.0s952×body640valid
1.0s819×body1280valid
918.0ms602×body320valid
159.0ms329×body160valid