Details

Time bar (total: 7.7s)

sample70.0ms

Algorithm
intervals
Results
29.0ms294×body80valid
10.0ms24×body1280valid
9.0ms28×body640valid
5.0ms21×body320valid
2.0ms14×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.4b
(* (* x (pow sin 2.0)) x)
7.5b
(* x (pow sin 2.0))
20.0b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite70.0ms

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:
24.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
8.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
28.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series849.0ms

Counts
4 → 12
Calls
4 calls:
297.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
156.0ms
(* (* x (pow sin 2.0)) x)
135.0ms
(* x (pow sin 2.0))
261.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify64.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0448971
12063815
25002815

prune293.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.4b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.0b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
416×add-exp-log
343×prod-exp
84×pow-to-exp pow-exp
52×add-cbrt-cube
43×div-exp
29×cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
9×associate-*l*
6×pow1 unpow-prod-down
5×cbrt-undiv
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 → 194
Calls
4 calls:
11.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
87.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
32.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
89.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series984.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
293.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
289.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
262.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify91.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06032216
128211509
250021497

prune299.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.7b
(/ (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)))))))
5.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite34.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 114
Calls
4 calls:
5.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.0ms
(/ (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)))))))
10.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series557.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
102.0ms
(/ (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)))))))
209.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
210.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03251562
112441292
250011217

prune379.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.8b
(/ (cbrt (cos (* 2.0 x))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.4b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
43×prod-exp
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×times-frac
18×add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
12×cbrt-prod
7×cbrt-unprod associate-/l*
6×unpow-prod-down associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×frac-2neg associate-*r* clear-num *-commutative div-inv sqr-pow
Counts
4 → 128
Calls
4 calls:
6.0ms
(/ (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.0ms
(/ (cbrt (cos (* 2.0 x))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
10.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
10.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series693.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x)))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
132.0ms
(/ (cbrt (cos (* 2.0 x))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
211.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
210.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify59.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03891849
113921657
250011631

prune494.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

regimes349.0ms

Accuracy

18.9% (2.3b remaining)

Error of 2.4b against oracle of 0.1b and baseline of 3.0b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03848
13848

end0.0ms

sample2.0s

Algorithm
intervals
Results
860.0ms9056×body80valid
366.0ms827×body1280valid
316.0ms995×body640valid
139.0ms569×body320valid
54.0ms308×body160valid