Details

Time bar (total: 46.4s)

sample115.0ms

Algorithm
intervals
Results
39.0ms46×body2560valid
29.0ms30×body1280valid
17.0ms53×body640valid
9.0ms37×body320valid
8.0ms79×body80valid
2.0ms11×body160valid

simplify36.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
36.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize24.0ms

Local error

Found 2 expressions with local error:

12.5b
(/ (- 1 (cos x)) (* x x))
2.1b
(- 1 (cos x))

rewrite31.0ms

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
18.0ms
(/ (- 1 (cos x)) (* x x))
11.0ms
(- 1 (cos x))

series112.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
80.0ms
(/ (- 1 (cos x)) (* x x))
32.0ms
(- 1 (cos x))

simplify2.4s

Counts
35 → 53
Calls
35 calls:
Slowest
679.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
677.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
260.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
114.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
80.0ms
(- (log (- 1 (cos x))) (log (* x x)))

prune414.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

12.3b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.5b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite118.0ms

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
45.0ms
(* (* x x) (+ 1 (cos x)))
39.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
22.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series203.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
53.0ms
(* (* x x) (+ 1 (cos x)))
31.0ms
(* (sin x) (sin x))
18.0ms
(+ 1 (cos x))

simplify12.1s

Counts
73 → 108
Calls
73 calls:
Slowest
1.4s
(/ (* (* (* (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)))))
1.1s
(/ (* (* (* (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) (* 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) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))
982.0ms
(/ (* (* (* (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)))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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
23.0ms
(* (/ (sin x) x) (/ (sin x) x))
17.0ms
(/ (sin x) x)
14.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series154.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
49.0ms
(* (/ (sin x) x) (/ (sin x) x))
49.0ms
(/ (sin x) x)
38.0ms
(/ (sin x) x)
17.0ms
(+ (cos x) 1)

simplify4.9s

Counts
138 → 149
Calls
138 calls:
Slowest
424.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
408.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
349.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
255.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
246.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
176×times-frac
129×add-sqr-sqrt
102×*-un-lft-identity
96×add-cube-cbrt
62×add-exp-log
44×associate-*l*
32×add-cbrt-cube
29×div-exp
16×associate-/r*
14×prod-exp
13×cbrt-undiv associate-*r*
11×div-inv
10×unswap-sqr
7×pow1
6×rec-exp 1-exp cbrt-unprod associate-/l* add-log-exp
4×insert-posit16
2×clear-num frac-2neg associate-/r/
1×frac-times +-commutative sum-log flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+ pow-flip distribute-lft-out inv-pow
Counts
4 → 218
Calls
4 calls:
Slowest
38.0ms
(* (/ 1 (/ x (sin x))) (/ (sin x) x))
15.0ms
(/ (sin x) x)
15.0ms
(/ 1 (/ x (sin x)))
6.0ms
(+ (cos x) 1)

series173.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(* (/ 1 (/ x (sin x))) (/ (sin x) x))
50.0ms
(/ (sin x) x)
40.0ms
(/ 1 (/ x (sin x)))
18.0ms
(+ (cos x) 1)

simplify15.5s

Counts
238 → 230
Calls
238 calls:
Slowest
586.0ms
(* (* (* (/ 1 (/ x (sin x))) (/ 1 (/ x (sin x)))) (/ 1 (/ x (sin x)))) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
464.0ms
(+ (- 0 (- (log x) (log (sin x)))) (log (/ (sin x) x)))
458.0ms
(+ (- 0 (- (log x) (log (sin x)))) (- (log (sin x)) (log x)))
441.0ms
(/ (* (* 1 1) 1) (* (* (/ x (sin x)) (/ x (sin x))) (/ x (sin x))))
393.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.5b remaining)

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

bsearch3.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.7s1647×body2560valid
1.3s1443×body640valid
877.0ms1246×body1280valid
349.0ms912×body320valid
257.0ms2271×body80valid
104.0ms481×body160valid