Details

Time bar (total: 39.2s)

sample98.0ms

Algorithm
intervals
Results
42.0ms59×body2560valid
14.0ms75×body80valid
14.0ms47×body640valid
11.0ms26×body1280valid
8.0ms35×body320valid
2.0ms14×body160valid

simplify36.0ms

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: 30.3b

localize22.0ms

Local error

Found 2 expressions with local error:

16.4b
(/ (- 1 (cos x)) (* x x))
1.0b
(- 1 (cos x))

rewrite46.0ms

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
Calls
2 calls:
Slowest
40.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series96.0ms

Calls
2 calls:
Slowest
71.0ms
(/ (- 1 (cos x)) (* x x))
25.0ms
(- 1 (cos x))

simplify2.4s

Calls
35 calls:
Slowest
681.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
638.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
226.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
139.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
64.0ms
(- (log (- 1 (cos x))) (log (* x x)))

prune430.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

16.4b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite74.0ms

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/
Calls
4 calls:
Slowest
27.0ms
(* (* x x) (+ 1 (cos x)))
27.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
10.0ms
(* (sin x) (sin x))
7.0ms
(+ 1 (cos x))

series177.0ms

Calls
4 calls:
Slowest
92.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
49.0ms
(* (* x x) (+ 1 (cos x)))
20.0ms
(* (sin x) (sin x))
16.0ms
(+ 1 (cos x))

simplify10.9s

Calls
73 calls:
Slowest
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)))))
1.1s
(/ (* (* (* (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)))))
961.0ms
(/ (* (* (* (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)))))
939.0ms
(/ (* (* (* (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)))))
858.0ms
(/ (* (* (* (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)))))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1)
0.1b
(* (/ (sin x) x) (/ (sin x) x))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite52.0ms

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
Calls
4 calls:
Slowest
20.0ms
(* (/ (sin x) x) (/ (sin x) x))
11.0ms
(+ (cos x) 1)
11.0ms
(/ (sin x) x)
7.0ms
(/ (sin x) x)

series192.0ms

Calls
4 calls:
Slowest
61.0ms
(* (/ (sin x) x) (/ (sin x) x))
57.0ms
(/ (sin x) x)
56.0ms
(/ (sin x) x)
19.0ms
(+ (cos x) 1)

simplify5.1s

Calls
138 calls:
Slowest
476.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
432.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
420.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
266.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
180.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1)
0.2b
(* (sin x) (/ (sin x) x))
0.1b
(/ (sin x) x)
0.1b
(/ (/ (* (sin x) (/ (sin x) x)) x) (+ (cos x) 1))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
56×*-un-lft-identity
43×add-sqr-sqrt
38×add-cube-cbrt
25×add-cbrt-cube add-exp-log
13×associate-*r*
10×cbrt-undiv div-exp associate-/l*
9×distribute-lft-out
8×div-inv
7×associate-/r*
6×pow1 add-log-exp
4×prod-exp cbrt-unprod insert-posit16
3×associate-*l*
2×clear-num frac-2neg flip3-+ associate-/r/ flip-+ unswap-sqr
1×+-commutative sum-log pow-prod-down associate-*r/ *-commutative associate-/l/
Calls
4 calls:
Slowest
31.0ms
(* (sin x) (/ (sin x) x))
18.0ms
(/ (/ (* (sin x) (/ (sin x) x)) x) (+ (cos x) 1))
10.0ms
(+ (cos x) 1)
9.0ms
(/ (sin x) x)

series222.0ms

Calls
4 calls:
Slowest
89.0ms
(/ (/ (* (sin x) (/ (sin x) x)) x) (+ (cos x) 1))
68.0ms
(* (sin x) (/ (sin x) x))
50.0ms
(/ (sin x) x)
15.0ms
(+ (cos x) 1)

simplify10.4s

Calls
139 calls:
Slowest
1.0s
(/ (/ (* (* (* (sin x) (sin x)) (sin x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* x x) x)) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
570.0ms
(/ (/ (* (* (* (sin x) (/ (sin x) x)) (* (sin x) (/ (sin x) x))) (* (sin x) (/ (sin x) x))) (* (* x x) x)) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
470.0ms
(/ (/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x))) (* (* x x) x)) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
448.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
440.0ms
(* (* (* (sin x) (sin x)) (sin x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes49.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.0s1702×body2560valid
1.3s1159×body1280valid
875.0ms1540×body640valid
379.0ms942×body320valid
293.0ms2214×body80valid
102.0ms443×body160valid