Details

Time bar (total: 28.8s)

sample96.0ms

Algorithm
intervals
Results
35.0ms285×body80valid
19.0ms36×body1280valid
10.0ms24×body640valid
5.0ms18×body320valid
2.0ms9×body160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5000
41263
3241
267
126
012

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.0b
(* (* x (pow sin 2.0)) x)
7.1b
(* x (pow sin 2.0))
18.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite167.0ms

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×*-un-lft-identity add-cube-cbrt
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×expm1-log1p-u cbrt-undiv log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×clear-num associate-/r* frac-2neg pow-prod-down div-inv
Counts
4 → 123
Calls
4 calls:
64.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
18.0ms
(* (* x (pow sin 2.0)) x)
14.0ms
(* x (pow sin 2.0))
65.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
393.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
202.0ms
(* (* x (pow sin 2.0)) x)
178.0ms
(* x (pow sin 2.0))
344.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify2.0s

Counts
135 → 135
Iterations
IterNodes
done5001
22402
1448
0174

prune807.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

localize37.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (* x (pow sin 2.0)) x)
5.8b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
6.4b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
7.1b
(* x (pow sin 2.0))

rewrite264.0ms

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×*-un-lft-identity associate-*r* add-cube-cbrt
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:
21.0ms
(* (* x (pow sin 2.0)) x)
57.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
156.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
14.0ms
(* x (pow sin 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
218.0ms
(* (* x (pow sin 2.0)) x)
416.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
395.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
257.0ms
(* x (pow sin 2.0))

simplify2.1s

Counts
166 → 166
Iterations
IterNodes
done5001
22245
1447
0165

prune861.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (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))))
4.0b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
5.8b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
6.4b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

rewrite1.6s

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 *-un-lft-identity add-cube-cbrt
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×clear-num associate-/r* frac-2neg pow-prod-down div-inv
Counts
4 → 402
Calls
4 calls:
578.0ms
(/ (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))))
105.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
247.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
654.0ms
(* (pow cos (/ 2.0 2)) (* (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:
465.0ms
(/ (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))))
213.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
479.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
459.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

simplify3.0s

Counts
414 → 414
Iterations
IterNodes
done5000
23611
1779
0259

prune718.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt cos)
2.4b
(* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2)))
3.9b
(* (pow (* (cbrt cos) (cbrt cos)) (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2)))))
6.4b
(* (pow cos (/ 2.0 2)) (* (pow (* (cbrt cos) (cbrt cos)) (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2))))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
4520×prod-exp
4299×add-exp-log
1300×pow-exp
1088×pow-to-exp
76×add-cbrt-cube
55×cbrt-unprod
13×associate-*l*
12×associate-*r*
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×unpow-prod-down
6×cbrt-prod
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×*-commutative sqr-pow
1×pow1/3
Counts
4 → 948
Calls
4 calls:
1.0ms
(cbrt cos)
47.0ms
(* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2)))
242.0ms
(* (pow (* (cbrt cos) (cbrt cos)) (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2)))))
658.0ms
(* (pow cos (/ 2.0 2)) (* (pow (* (cbrt cos) (cbrt cos)) (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
265.0ms
(cbrt cos)
564.0ms
(* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2)))
634.0ms
(* (pow (* (cbrt cos) (cbrt cos)) (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2)))))
678.0ms
(* (pow cos (/ 2.0 2)) (* (pow (* (cbrt cos) (cbrt cos)) (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow (cbrt cos) (/ 2.0 2))))))

simplify2.3s

Counts
960 → 960
Iterations
IterNodes
done5000
11435
0431

prune1.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.4b

regimes930.0ms

Accuracy

0% (2.2b remaining)

Error of 6.4b against oracle of 4.2b and baseline of 6.4b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done26
126
020

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.8s9169×body80valid
620.0ms802×body1280valid
578.0ms1033×body640valid
268.0ms578×body320valid
72.0ms329×body160valid