Details

Time bar (total: 41.8s)

sample149.0ms

Algorithm
intervals
Results
66.0ms59×body2560valid
31.0ms47×body640valid
18.0ms26×body1280valid
12.0ms35×body320valid
9.0ms75×body80valid
3.0ms14×body160valid

simplify65.0ms

Calls
1 calls:
Slowest
64.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-log-exp
3×fma-neg distribute-lft-out--
2×expm1-log1p-u pow1 cbrt-undiv flip3-- div-exp insert-posit16 log1p-expm1-u 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
29.0ms
(/ (- 1 (cos x)) (* x x))
11.0ms
(- 1 (cos x))

series138.0ms

Calls
2 calls:
Slowest
104.0ms
(/ (- 1 (cos x)) (* x x))
33.0ms
(- 1 (cos x))

simplify3.6s

Calls
55 calls:
Slowest
706.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
571.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
315.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
161.0ms
(fma (sqrt 1) (sqrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
152.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

prune482.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×pow1
14×*-un-lft-identity
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt
7×associate-*r*
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u
3×fma-def 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
36.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
29.0ms
(* (* x x) (+ 1 (cos x)))
11.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series204.0ms

Calls
4 calls:
Slowest
82.0ms
(* (* x x) (+ 1 (cos x)))
78.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
32.0ms
(* (sin x) (sin x))
11.0ms
(+ 1 (cos x))

simplify12.2s

Calls
75 calls:
Slowest
1.3s
(/ (* (* (* (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) (+ 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)))))
898.0ms
(/ (* (* (* (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

localize31.0ms

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)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
58×times-frac
51×*-un-lft-identity
49×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×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×fma-def
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
16.0ms
(* (/ (sin x) x) (/ (sin x) x))
11.0ms
(+ (cos x) 1)
10.0ms
(/ (sin x) x)
7.0ms
(/ (sin x) x)

series146.0ms

Calls
4 calls:
Slowest
46.0ms
(* (/ (sin x) x) (/ (sin x) x))
43.0ms
(/ (sin x) x)
37.0ms
(/ (sin x) x)
20.0ms
(+ (cos x) 1)

simplify5.2s

Calls
140 calls:
Slowest
461.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
453.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
379.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
232.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
212.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
57×*-un-lft-identity
44×add-sqr-sqrt
39×add-cube-cbrt
25×add-cbrt-cube add-exp-log
13×associate-*l*
10×cbrt-undiv div-exp associate-/l*
9×distribute-lft-out
8×div-inv
7×associate-/r*
6×pow1 add-log-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×fma-def associate-*r*
2×clear-num frac-2neg flip3-+ associate-/r/ flip-+ unswap-sqr
1×+-commutative sum-log pow-prod-down associate-*l/ *-commutative associate-/l/
Calls
4 calls:
Slowest
38.0ms
(/ (/ (* (/ (sin x) x) (sin x)) x) (+ (cos x) 1))
13.0ms
(* (/ (sin x) x) (sin x))
7.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series214.0ms

Calls
4 calls:
Slowest
90.0ms
(/ (/ (* (/ (sin x) x) (sin x)) x) (+ (cos x) 1))
65.0ms
(* (/ (sin x) x) (sin x))
42.0ms
(/ (sin x) x)
17.0ms
(+ (cos x) 1)

simplify10.2s

Calls
142 calls:
Slowest
570.0ms
(/ (/ (* (* (* (/ (sin x) x) (sin x)) (* (/ (sin x) x) (sin x))) (* (/ (sin x) x) (sin x))) (* (* x x) x)) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
531.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
530.0ms
(/ (/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (sin x) (sin x)) (sin x))) (* (* x x) x)) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
488.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
488.0ms
(/ (/ (* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (sin x) (sin x)) (sin x))) (* (* x x) x)) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.4s1702×body2560valid
875.0ms1159×body1280valid
797.0ms1540×body640valid
356.0ms942×body320valid
318.0ms2214×body80valid
102.0ms443×body160valid