Details

Time bar (total: 15.0s)

sample102.0ms

Algorithm
intervals
Results
33.0ms135×body80valid
32.0ms50×body1280valid
17.0ms42×body640valid
6.0ms20×body320valid
2.0ms9×body160valid

simplify602.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01116
12016
24316
39316
417316
527716
631416
done31416

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b
(* (/ 8.0 3.0) (sin (* x 0.5)))
12.8b
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log add-cbrt-cube
19×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*l*
13×times-frac
12×prod-exp cbrt-unprod
10×pow1
7×cbrt-undiv div-exp
6×associate-*r*
5×associate-*l/
4×pow-prod-down
3×associate-/r* add-log-exp
2×*-commutative div-inv unswap-sqr
1×frac-2neg clear-num associate-/l/ associate-/l*
Counts
3 → 79
Calls
3 calls:
82.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
85.0ms
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series227.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
60.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
108.0ms
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.8s

Counts
88 → 88
Iterations

Useful iterations: 2 (357.0ms)

IterNodesCost
01631474
14131285
227151064
done50011064

prune284.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin (* x 0.5)) (sin x))
0.2b
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
0.4b
(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log add-sqr-sqrt add-cbrt-cube
28×times-frac
26×add-cube-cbrt *-un-lft-identity
16×associate-*r*
14×associate-*l*
12×prod-exp cbrt-unprod
10×pow1
7×cbrt-undiv div-exp
4×pow-prod-down associate-*l/
3×associate-/r* div-inv associate-/l* add-log-exp
2×*-commutative unswap-sqr
1×frac-times frac-2neg associate-*r/ clear-num
Counts
3 → 98
Calls
3 calls:
20.0ms
(/ (sin (* x 0.5)) (sin x))
65.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
42.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))

series185.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(/ (sin (* x 0.5)) (sin x))
87.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
48.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.5s

Counts
107 → 107
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01831718
14921676
232321342
done50001292

prune316.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 8.0 (sin (* 0.5 x))) 3.0)
0.2b
(/ (sin (* x 0.5)) (sin x))
0.2b
(* (* (/ 1 1) (/ (* 8.0 (sin (* 0.5 x))) 3.0)) (/ (sin (* x 0.5)) (sin x)))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
198×add-exp-log
101×prod-exp
77×div-exp
75×add-cbrt-cube
31×cbrt-unprod
30×1-exp
24×cbrt-undiv
21×times-frac
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×rec-exp
8×pow1
6×associate-/r*
5×frac-times associate-*l/
4×associate-/l*
3×associate-*r/ pow-prod-down div-inv add-log-exp
2×frac-2neg clear-num
1×associate-*l* *-commutative
Counts
3 → 137
Calls
3 calls:
33.0ms
(/ (* 8.0 (sin (* 0.5 x))) 3.0)
19.0ms
(/ (sin (* x 0.5)) (sin x))
106.0ms
(* (* (/ 1 1) (/ (* 8.0 (sin (* 0.5 x))) 3.0)) (/ (sin (* x 0.5)) (sin x)))

series170.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ (* 8.0 (sin (* 0.5 x))) 3.0)
40.0ms
(/ (sin (* x 0.5)) (sin x))
82.0ms
(* (* (/ 1 1) (/ (* 8.0 (sin (* 0.5 x))) 3.0)) (/ (sin (* x 0.5)) (sin x)))

simplify634.0ms

Counts
146 → 146
Iterations

Useful iterations: done (627.0ms)

IterNodesCost
02723299
19292643
done50002187

prune433.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))) (/ (sin (* x 0.5)) (sin x)))
0.2b
(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0))))
0.4b
(* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))
1.0b
(/ (cbrt 8.0) (cbrt 3.0))

rewrite630.0ms

Algorithm
rewrite-expression-head
Rules
268×add-exp-log
162×add-cbrt-cube
145×prod-exp cbrt-unprod
86×times-frac
82×cbrt-prod
80×add-sqr-sqrt
69×cbrt-undiv div-exp
66×add-cube-cbrt *-un-lft-identity
54×associate-*r*
20×pow1
11×associate-*r/
10×pow-prod-down
9×associate-*l*
6×frac-times associate-*l/ associate-/r* associate-/l*
5×unswap-sqr
4×div-inv add-log-exp
3×*-commutative
1×frac-2neg clear-num
Counts
4 → 267
Calls
4 calls:
448.0ms
(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))) (/ (sin (* x 0.5)) (sin x)))
102.0ms
(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0))))
52.0ms
(* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))
9.0ms
(/ (cbrt 8.0) (cbrt 3.0))

series668.0ms

Counts
4 → 10
Calls
4 calls:
288.0ms
(* (* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))) (/ (sin (* x 0.5)) (sin x)))
242.0ms
(* (/ (* (cbrt 8.0) (cbrt 8.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0))))
138.0ms
(* (sin (* 0.5 x)) (/ (cbrt 8.0) (cbrt 3.0)))
0.0ms
(/ (cbrt 8.0) (cbrt 3.0))

simplify613.0ms

Counts
277 → 277
Iterations

Useful iterations: done (603.0ms)

IterNodesCost
03957989
112827534
done50014852

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
01620
12118
22316
done2316

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.8s1543×body1280valid
743.0ms1255×body640valid
660.0ms621×body320valid
542.0ms4291×body80valid
107.0ms290×body160valid