Details

Time bar (total: 31.9s)

sample188.0ms

Algorithm
intervals
Results
74.0ms57×body2560valid
35.0ms45×body1280valid
28.0ms72×body80valid
23.0ms39×body640valid
15.0ms35×body320valid
2.0ms8×body160valid

simplify59.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
58.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize21.0ms

Local error

Found 2 expressions with local error:

16.8b
(/ (- 1 (cos x)) (* x x))
0.9b
(- 1 (cos x))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-cube-cbrt add-log-exp
3×distribute-lft-out--
2×pow1 cbrt-undiv flip3-- div-exp insert-posit16 flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
2 → 47
Calls
2 calls:
Slowest
46.0ms
(/ (- 1 (cos x)) (* x x))
10.0ms
(- 1 (cos x))

series120.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
91.0ms
(/ (- 1 (cos x)) (* x x))
29.0ms
(- 1 (cos x))

simplify2.4s

Counts
35 → 53
Calls
35 calls:
Slowest
670.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
597.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
283.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
83.0ms
(- (pow 1 3) (pow (cos x) 3))
80.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

prune389.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

16.9b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.5b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×pow1
13×*-un-lft-identity prod-exp cbrt-unprod
12×add-sqr-sqrt
9×add-cube-cbrt
7×associate-*r*
6×cbrt-undiv div-exp add-log-exp
4×associate-*l* pow-prod-down associate-*r/ insert-posit16
3×flip3-+ swap-sqr flip-+
2×associate-/r/ *-commutative sqr-sin sin-mult distribute-lft-out unswap-sqr
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-sqr pow-prod-up div-inv associate-/l* associate-/l/
Counts
4 → 96
Calls
4 calls:
Slowest
41.0ms
(* (* x x) (+ 1 (cos x)))
38.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
20.0ms
(* (sin x) (sin x))
9.0ms
(+ 1 (cos x))

series219.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
72.0ms
(* (* x x) (+ 1 (cos x)))
33.0ms
(* (sin x) (sin x))
17.0ms
(+ 1 (cos x))

simplify12.4s

Counts
73 → 108
Calls
73 calls:
Slowest
1.2s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))
1.2s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.1s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))
1.0s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.0s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) x) (* (* x x) x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))

prune921.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos x) 1)
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)
0.1b
(* (/ (sin x) x) (/ (sin x) x))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
58×times-frac
50×*-un-lft-identity
48×add-cube-cbrt
20×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
6×cbrt-undiv associate-/r* div-exp div-inv associate-/l* add-log-exp
4×prod-exp cbrt-unprod insert-posit16 unswap-sqr
2×clear-num frac-2neg
1×pow2 frac-times +-commutative sum-log flip3-+ pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+ distribute-lft-out
Counts
4 → 137
Calls
4 calls:
Slowest
20.0ms
(* (/ (sin x) x) (/ (sin x) x))
7.0ms
(/ (sin x) x)
7.0ms
(/ (sin x) x)
5.0ms
(+ (cos x) 1)

series162.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
65.0ms
(* (/ (sin x) x) (/ (sin x) x))
44.0ms
(/ (sin x) x)
42.0ms
(/ (sin x) x)
11.0ms
(+ (cos x) 1)

simplify4.7s

Counts
138 → 149
Calls
138 calls:
Slowest
452.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
443.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
390.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
187.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
174.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (exp (cos x)) E)
0.6b
(log (* (exp (cos x)) E))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×times-frac
11×add-exp-log
10×add-cbrt-cube
9×pow1
6×associate-/r* associate-/l*
4×prod-exp insert-posit16 add-log-exp
3×rem-log-exp associate-*r* associate-*l*
2×cbrt-undiv e-exp-1 clear-num frac-2neg div-exp pow-prod-down log-pow div-inv
1×log-prod *-commutative cbrt-unprod unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
29.0ms
(* (exp (cos x)) E)
24.0ms
(log (* (exp (cos x)) E))
8.0ms
(/ (sin x) x)
7.0ms
(/ (sin x) x)

series305.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(log (* (exp (cos x)) E))
60.0ms
(* (exp (cos x)) E)
40.0ms
(/ (sin x) x)
38.0ms
(/ (sin x) x)

simplify2.4s

Counts
74 → 102
Calls
74 calls:
Slowest
462.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
422.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
345.0ms
(* (* (* (exp (cos x)) (exp (cos x))) (exp (cos x))) (* (* E E) E))
188.0ms
(- (+ (pow E 2) (* 1/6 (* (pow x 4) (pow E 2)))) (* 1/2 (* (pow x 2) (pow E 2))))
161.0ms
(- (+ (log (pow E 2)) (* 1/24 (pow x 4))) (* 1/2 (pow x 2)))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.2s1673×body2560valid
1.1s1248×body1280valid
839.0ms1472×body640valid
305.0ms925×body320valid
234.0ms2232×body80valid
126.0ms450×body160valid