Details

Time bar (total: 10.5s)

sample78.0ms

Algorithm
intervals
Results
22.0ms297×body80valid
21.0ms25×body1280valid
12.0ms37×body640valid
4.0ms21×body320valid
1.0ms5×body160valid

simplify35.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.5b
(* (* x (pow sin 2.0)) x)
8.6b
(* x (pow sin 2.0))
20.0b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
122×add-exp-log
82×prod-exp
34×add-cbrt-cube
18×pow-to-exp pow-exp
17×add-sqr-sqrt
16×div-exp cbrt-unprod
12×add-cube-cbrt *-un-lft-identity
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×cbrt-undiv add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 115
Calls
4 calls:
62.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
24.0ms
(* (* x (pow sin 2.0)) x)
11.0ms
(* x (pow sin 2.0))
67.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series944.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
169.0ms
(* (* x (pow sin 2.0)) x)
144.0ms
(* x (pow sin 2.0))
293.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify55.0ms

Counts
127 → 127

prune294.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.9b

localize20.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (* x (pow sin 2.0)) x)
4.4b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
8.3b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
8.6b
(* x (pow sin 2.0))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
226×add-exp-log
202×prod-exp
50×pow-to-exp pow-exp
34×add-cbrt-cube
20×cbrt-unprod
18×associate-*l*
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity associate-*r*
10×unpow-prod-down
6×pow1
4×*-commutative add-log-exp sqr-pow
3×unswap-sqr
1×pow-prod-down
Counts
4 → 146
Calls
4 calls:
21.0ms
(* (* x (pow sin 2.0)) x)
151.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
64.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
12.0ms
(* x (pow sin 2.0))

series902.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(* (* x (pow sin 2.0)) x)
308.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
285.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
148.0ms
(* x (pow sin 2.0))

simplify64.0ms

Counts
158 → 158

prune308.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
3.5b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
4.4b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
8.3b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
1410×add-exp-log
1300×prod-exp
338×pow-to-exp pow-exp
130×div-exp
74×add-cbrt-cube
46×cbrt-unprod
15×associate-*l*
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-undiv unpow-prod-down
5×associate-*r*
4×add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 394
Calls
4 calls:
508.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
73.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
538.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
202.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
170.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
305.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
305.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify127.0ms

Counts
406 → 406

prune310.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.8b
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
3.3b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.3b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
44×prod-exp
21×add-cbrt-cube
17×associate-*l*
16×add-sqr-sqrt
14×pow-to-exp add-cube-cbrt *-un-lft-identity pow-exp
11×pow1
8×cbrt-unprod
6×unpow-prod-down
5×associate-*r*
4×add-log-exp
3×times-frac swap-sqr *-commutative associate-/l*
2×cbrt-undiv div-exp sqr-pow
1×pow2 frac-2neg pow-plus pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up div-inv unswap-sqr
Counts
4 → 106
Calls
4 calls:
7.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
16.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
31.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
29.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series648.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
125.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
250.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
236.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify44.0ms

Counts
118 → 118

prune343.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes295.0ms

Accuracy

0% (2.3b remaining)

Error of 2.5b against oracle of 0.2b and baseline of 2.5b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.6s9024×body80valid
462.0ms808×body1280valid
322.0ms931×body640valid
154.0ms560×body320valid
47.0ms310×body160valid