Details

Time bar (total: 48.5s)

sample110.0ms

Algorithm
intervals
Results
48.0ms284×body80valid
17.0ms37×body640valid
14.0ms22×body1280valid
6.0ms22×body320valid
2.0ms9×body160valid

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
14616
239316
done500016

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.7b
(* (* x (pow sin 2.0)) x)
6.5b
(* x (pow sin 2.0))
20.3b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite225.0ms

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 expm1-log1p-u log1p-expm1-u 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 → 123
Calls
4 calls:
90.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
35.0ms
(* (* x (pow sin 2.0)) x)
12.0ms
(* x (pow sin 2.0))
81.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.4s

Counts
4 → 12
Calls
4 calls:
548.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
259.0ms
(* (* x (pow sin 2.0)) x)
239.0ms
(* x (pow sin 2.0))
402.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify7.1s

Counts
135 → 135
Iterations

Useful iterations: done (7.1s)

IterNodesCost
01792045
124391897
done50011627

prune899.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.1b

localize39.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (* x (pow sin 2.0)) x)
5.9b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
6.5b
(* x (pow sin 2.0))
7.8b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite433.0ms

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×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp sqr-pow
3×unswap-sqr
1×pow-prod-down
Counts
4 → 154
Calls
4 calls:
29.0ms
(* (* x (pow sin 2.0)) x)
273.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
25.0ms
(* x (pow sin 2.0))
96.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series1.3s

Counts
4 → 12
Calls
4 calls:
230.0ms
(* (* x (pow sin 2.0)) x)
449.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
212.0ms
(* x (pow sin 2.0))
428.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify2.3s

Counts
166 → 166
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01712944
110552106
done50011854

prune476.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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))))
4.7b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
5.9b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
7.8b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite2.1s

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×expm1-log1p-u log1p-expm1-u 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 → 402
Calls
4 calls:
759.0ms
(/ (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))))
134.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
844.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
350.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.6s

Counts
4 → 12
Calls
4 calls:
516.0ms
(/ (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))))
214.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
470.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
387.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify10.8s

Counts
414 → 414
Iterations

Useful iterations: done (10.8s)

IterNodesCost
026713999
121366519
done50005867

prune556.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)))))
0.2b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
5.9b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
7.8b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite973.0ms

Algorithm
rewrite-expression-head
Rules
1691×add-exp-log
1549×prod-exp
399×pow-to-exp pow-exp
157×div-exp
92×add-cbrt-cube
59×cbrt-unprod
15×associate-*l*
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×cbrt-undiv
6×pow1 unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*r* *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 470
Calls
4 calls:
345.0ms
(/ (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)))))
52.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
334.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
133.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.5s

Counts
4 → 12
Calls
4 calls:
477.0ms
(/ (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)))))
235.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
356.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
407.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify8.8s

Counts
482 → 482
Iterations

Useful iterations: done (8.8s)

IterNodesCost
028316424
121057622
done50006836

prune416.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.6b

regimes607.0ms

Accuracy

0% (1.3b remaining)

Error of 6.4b against oracle of 5.1b and baseline of 6.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01632
12032
done2032

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.3s8983×body80valid
1.0s980×body640valid
976.0ms816×body1280valid
200.0ms586×body320valid
74.0ms331×body160valid