Details

Time bar (total: 5.5s)

sample66.0ms

Algorithm
intervals
Results
33.0ms61×body1280valid
10.0ms36×body640valid
8.0ms135×body80valid
4.0ms18×body320valid
1.0ms6×body160valid

simplify24.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0209
1439
2939
31749
42699
52889
62889
done2889

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b
(* (/ 8.0 3.0) (sin (* x 0.5)))
16.8b
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite153.0ms

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×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×*-commutative div-inv unswap-sqr
1×frac-2neg clear-num associate-/l/ associate-/l*
Counts
3 → 85
Calls
3 calls:
62.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
25.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
63.0ms
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series201.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
49.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
92.0ms
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify66.0ms

Counts
94 → 94
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0412862
12127656
25001637
done5001637

prune280.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (sin (* 0.5 x)) (sin x))
0.2b
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
0.3b
(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite106.0ms

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×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l* add-log-exp
2×*-commutative unswap-sqr
1×frac-times frac-2neg associate-*r/ clear-num
Counts
3 → 104
Calls
3 calls:
12.0ms
(/ (sin (* 0.5 x)) (sin x))
59.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
30.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))

series180.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ (sin (* 0.5 x)) (sin x))
88.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
42.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify73.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
04741006
12505814
25001799
done5001799

prune343.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log add-cbrt-cube
27×add-sqr-sqrt
25×times-frac
22×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod
7×associate-*l*
6×associate-/r*
5×pow1
4×div-inv associate-/l*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num unswap-sqr
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
3 → 100
Calls
3 calls:
18.0ms
(/ (* 8.0 (sin (* x 0.5))) 3.0)
16.0ms
(/ (sin (* 0.5 x)) (sin x))
32.0ms
(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

series182.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ (* 8.0 (sin (* x 0.5))) 3.0)
46.0ms
(/ (sin (* 0.5 x)) (sin x))
89.0ms
(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))

simplify70.0ms

Counts
109 → 109
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
04691030
12437847
25001823
done5001823

prune345.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin (* 0.5 x)) (sin x))
0.2b
(* (* (/ 8.0 (* (cbrt 3.0) (cbrt 3.0))) (/ (sin (* x 0.5)) (cbrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
0.3b
(* (/ 8.0 (* (cbrt 3.0) (cbrt 3.0))) (/ (sin (* x 0.5)) (cbrt 3.0)))
0.4b
(/ (sin (* x 0.5)) (cbrt 3.0))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
94×add-exp-log
72×add-cbrt-cube
65×add-sqr-sqrt
64×times-frac
49×add-cube-cbrt *-un-lft-identity
38×prod-exp cbrt-unprod
35×associate-*r*
30×cbrt-undiv div-exp
23×cbrt-prod
11×pow1
9×associate-/r*
8×associate-*l*
6×frac-times associate-*l/ associate-/l* unswap-sqr
5×div-inv
4×expm1-log1p-u associate-*r/ pow-prod-down log1p-expm1-u add-log-exp
2×frac-2neg clear-num *-commutative
Counts
4 → 192
Calls
4 calls:
13.0ms
(/ (sin (* 0.5 x)) (sin x))
107.0ms
(* (* (/ 8.0 (* (cbrt 3.0) (cbrt 3.0))) (/ (sin (* x 0.5)) (cbrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
47.0ms
(* (/ 8.0 (* (cbrt 3.0) (cbrt 3.0))) (/ (sin (* x 0.5)) (cbrt 3.0)))
13.0ms
(/ (sin (* x 0.5)) (cbrt 3.0))

series487.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (sin (* 0.5 x)) (sin x))
194.0ms
(* (* (/ 8.0 (* (cbrt 3.0) (cbrt 3.0))) (/ (sin (* x 0.5)) (cbrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
152.0ms
(* (/ 8.0 (* (cbrt 3.0) (cbrt 3.0))) (/ (sin (* x 0.5)) (cbrt 3.0)))
91.0ms
(/ (sin (* x 0.5)) (cbrt 3.0))

simplify129.0ms

Counts
204 → 204
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
08602644
147982131
250022131
done50022131

prune685.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01814
11814
done1814

end0.0ms

sample1.8s

Algorithm
intervals
Results
752.0ms1554×body1280valid
385.0ms1284×body640valid
260.0ms4267×body80valid
150.0ms623×body320valid
38.0ms272×body160valid