Details

Time bar (total: 19.7s)

sample120.0ms

Algorithm
intervals
Results
50.0ms51×body2560valid
21.0ms37×body1280valid
20.0ms45×body640valid
9.0ms81×body80valid
9.0ms26×body320valid
3.0ms16×body160valid

simplify49.0ms

Calls
1 calls:
Slowest
49.0ms
(/ (- 1 (cos x)) (* x x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize11.0ms

Local error

Found 2 expressions with local error:

14.1b
(/ (- 1 (cos x)) (* x x))
2.2b
(- 1 (cos x))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×times-frac associate-/l*
2×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip-- add-log-exp associate-/l/
1×cbrt-undiv clear-num associate-/r* sub-neg frac-2neg div-sub div-exp div-inv
Calls
2 calls:
Slowest
4.0ms
(/ (- 1 (cos x)) (* x x))
1.0ms
(- 1 (cos x))

series86.0ms

Calls
2 calls:
Slowest
50.0ms
(/ (- 1 (cos x)) (* x x))
36.0ms
(- 1 (cos x))

simplify1.2s

Calls
19 calls:
Slowest
507.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
143.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
118.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
88.0ms
(- (log (- 1 (cos x))) (log (* x x)))
61.0ms
(/ (- 1 (cos x)) (pow x 2))

prune365.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

13.9b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
11×pow1
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-*r* prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp associate-*l* associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×pow-prod-down associate-/r/ *-commutative sqr-sin sin-mult
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-prod-up div-inv associate-/l* associate-/l/
Calls
4 calls:
Slowest
17.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
6.0ms
(* (sin x) (sin x))
4.0ms
(* (* x x) (+ 1 (cos x)))
2.0ms
(+ 1 (cos x))

series101.0ms

Calls
4 calls:
Slowest
48.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
25.0ms
(* (* x x) (+ 1 (cos x)))
16.0ms
(* (sin x) (sin x))
12.0ms
(+ 1 (cos x))

simplify7.2s

Calls
51 calls:
Slowest
968.0ms
(/ (* (* (* (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)))))
930.0ms
(/ (* (* (* (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)))))
911.0ms
(/ (* (* (* (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)))))
877.0ms
(/ (* (* (* (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)))))
461.0ms
(- (log (* (sin x) (sin x))) (+ (log (* x x)) (log (+ 1 (cos x)))))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
7×associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num associate-/r* fma-def frac-2neg times-frac div-inv associate-/l/
2×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
1×frac-times +-commutative associate-*l/ prod-exp associate-*r/ cbrt-unprod
Calls
4 calls:
Slowest
18.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
5.0ms
(+ (cos x) 1)
3.0ms
(/ (sin x) x)
3.0ms
(/ (sin x) x)

series137.0ms

Calls
4 calls:
Slowest
63.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
31.0ms
(/ (sin x) x)
30.0ms
(/ (sin x) x)
13.0ms
(+ (cos x) 1)

simplify2.7s

Calls
37 calls:
Slowest
467.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
344.0ms
(- (+ (log (/ (sin x) x)) (log (/ (sin x) x))) (log (+ (cos x) 1)))
301.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
250.0ms
(/ (* (* (* (/ (sin x) x) (/ (sin x) x)) (* (/ (sin x) x) (/ (sin x) x))) (* (/ (sin x) x) (/ (sin x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
227.0ms
(- (log (* (/ (sin x) x) (/ (sin x) x))) (log (+ (cos x) 1)))

prune802.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-/l*
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×clear-num associate-/r* fma-def frac-2neg div-inv
2×flip3-+ associate-/r/ flip-+
1×+-commutative rec-exp pow-flip inv-pow
Calls
4 calls:
Slowest
6.0ms
(+ (cos x) 1)
5.0ms
(/ (sin x) x)
5.0ms
(/ (sin x) x)
5.0ms
(/ 1 (+ (cos x) 1))

series85.0ms

Calls
4 calls:
Slowest
31.0ms
(/ (sin x) x)
21.0ms
(/ 1 (+ (cos x) 1))
19.0ms
(/ (sin x) x)
13.0ms
(+ (cos x) 1)

simplify623.0ms

Calls
24 calls:
Slowest
130.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))
110.0ms
(+ (* (cos x) (cos x)) (- (* 1 1) (* (cos x) 1)))
109.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
100.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
42.0ms
(+ (* 1/8 (pow x 2)) (+ (* 1/48 (pow x 4)) 1/2))

prune662.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.5b remaining)

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

bsearch2.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.6s1592×body2560valid
1.2s1272×body1280valid
736.0ms1443×body640valid
349.0ms938×body320valid
285.0ms2288×body80valid
93.0ms467×body160valid