Details

Time bar (total: 7.6s)

sample58.0ms

Algorithm
intervals
Results
21.0ms47×body1280valid
15.0ms51×body640valid
7.0ms126×body80valid
4.0ms22×body320valid
1.0ms10×body160valid

simplify124.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01116
12016
24216
39016
416816
523716
625516
done25516

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize11.0ms

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)))
15.4b
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite55.0ms

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:
20.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
21.0ms
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series178.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
40.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
80.0ms
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify760.0ms

Counts
94 → 94
Iterations

Useful iterations: 2 (199.0ms)

IterNodesCost
01691554
14131349
216641080
done50011080

prune243.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

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:
5.0ms
(/ (* 8.0 (sin (* x 0.5))) 3.0)
4.0ms
(/ (sin (* x 0.5)) (sin x))
18.0ms
(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series159.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(/ (* 8.0 (sin (* x 0.5))) 3.0)
39.0ms
(/ (sin (* x 0.5)) (sin x))
81.0ms
(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify611.0ms

Counts
109 → 109
Iterations

Useful iterations: 2 (173.0ms)

IterNodesCost
01811823
14631671
217801392
done50011392

prune266.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
0.2b
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))
0.2b
(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (sin (* x 0.5)))
15.4b
(/ (* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (sin (* x 0.5))) (sin x))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log add-cbrt-cube
33×associate-*l*
31×add-sqr-sqrt
28×sqrt-prod
24×add-cube-cbrt *-un-lft-identity
22×times-frac
20×pow1
16×associate-*l/ prod-exp cbrt-unprod
13×sqrt-div
10×pow-prod-down
7×associate-*r*
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-times associate-*r/ associate-/r* *-commutative div-inv associate-/l/ unswap-sqr
1×frac-2neg clear-num associate-/l*
Counts
4 → 128
Calls
4 calls:
13.0ms
(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
31.0ms
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))
81.0ms
(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (sin (* x 0.5)))
79.0ms
(/ (* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (sin (* x 0.5))) (sin x))

series428.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
94.0ms
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))
105.0ms
(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (sin (* x 0.5)))
161.0ms
(/ (* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (sin (* x 0.5))) (sin x))

simplify837.0ms

Counts
140 → 140
Iterations

Useful iterations: 2 (214.0ms)

IterNodesCost
02212790
15432038
221991648
done50001648

prune380.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (sin x))
0.2b
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b
(* (/ 8.0 3.0) (sin (* x 0.5)))
15.5b
(* (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (/ 1 (sin x)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
82×add-exp-log
52×add-cbrt-cube
43×prod-exp
33×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity times-frac
25×cbrt-unprod
21×pow1
19×associate-*r*
16×div-exp
15×associate-*l*
10×pow-prod-down
9×cbrt-undiv
8×associate-*l/
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative div-inv associate-/l*
2×unswap-sqr
1×frac-times pow-flip frac-2neg associate-*r/ clear-num un-div-inv inv-pow
Counts
4 → 145
Calls
4 calls:
3.0ms
(/ 1 (sin x))
21.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
68.0ms
(* (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (/ 1 (sin x)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ 1 (sin x))
55.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
43.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
83.0ms
(* (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (/ 1 (sin x)))

simplify871.0ms

Counts
157 → 157
Iterations

Useful iterations: 2 (283.0ms)

IterNodesCost
02342577
16042064
220421635
done50011635

prune299.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01116
11416
done1416

end0.0ms

sample1.7s

Algorithm
intervals
Results
727.0ms1519×body1280valid
381.0ms1285×body640valid
268.0ms4288×body80valid
129.0ms607×body320valid
41.0ms301×body160valid