Details

Time bar (total: 22.7s)

sample149.0ms

Algorithm
intervals
Results
65.0ms59×body2560valid
30.0ms26×body1280valid
21.0ms47×body640valid
13.0ms35×body320valid
8.0ms75×body80valid
3.0ms14×body160valid

simplify40.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

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
27.0ms
(/ (- 1 (cos x)) (* x x))
2.0ms
(- 1 (cos x))

series88.0ms

Calls
2 calls:
Slowest
63.0ms
(/ (- 1 (cos x)) (* x x))
24.0ms
(- 1 (cos x))

simplify1.3s

Calls
19 calls:
Slowest
622.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
167.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
137.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
65.0ms
(/ (- 1 (cos x)) (pow x 2))
63.0ms
(/ (- 1 (cos x)) (pow x 2))

prune364.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite31.0ms

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
19.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
6.0ms
(* (* x x) (+ 1 (cos x)))
5.0ms
(* (sin x) (sin x))
1.0ms
(+ 1 (cos x))

series182.0ms

Calls
4 calls:
Slowest
88.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
45.0ms
(* (* x x) (+ 1 (cos x)))
33.0ms
(* (sin x) (sin x))
16.0ms
(+ 1 (cos x))

simplify6.9s

Calls
51 calls:
Slowest
912.0ms
(/ (* (* (* (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)))))
908.0ms
(/ (* (* (* (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)))))
872.0ms
(/ (* (* (* (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)))))
807.0ms
(/ (* (* (* (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)))))
463.0ms
(- (+ (log (sin x)) (log (sin x))) (+ (log (* x x)) (log (+ 1 (cos x)))))

prune755.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize12.0ms

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)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log associate-/l*
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u div-inv add-log-exp
3×fma-def
2×clear-num frac-2neg
1×pow2 frac-times +-commutative flip3-+ pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip-+
Calls
4 calls:
Slowest
7.0ms
(* (/ (sin x) x) (/ (sin x) x))
3.0ms
(+ (cos x) 1)
3.0ms
(/ (sin x) x)
3.0ms
(/ (sin x) x)

series154.0ms

Calls
4 calls:
Slowest
54.0ms
(/ (sin x) x)
47.0ms
(* (/ (sin x) x) (/ (sin x) x))
42.0ms
(/ (sin x) x)
11.0ms
(+ (cos x) 1)

simplify870.0ms

Calls
34 calls:
Slowest
173.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
133.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
95.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))
94.0ms
(- (+ (* 2/45 (pow x 4)) 1) (* 1/3 (pow x 2)))
84.0ms
(+ (log (/ (sin x) x)) (log (/ (sin x) x)))

prune747.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize15.0ms

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))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
8×add-cbrt-cube add-exp-log
7×div-inv associate-/l*
6×pow1
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* fma-def associate-*l*
2×clear-num frac-2neg flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative div-exp pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod associate-/l/
Calls
4 calls:
Slowest
27.0ms
(/ (/ (* (sin x) (/ (sin x) x)) x) (+ (cos x) 1))
10.0ms
(* (sin x) (/ (sin x) x))
6.0ms
(+ (cos x) 1)
5.0ms
(/ (sin x) x)

series232.0ms

Calls
4 calls:
Slowest
79.0ms
(* (sin x) (/ (sin x) x))
79.0ms
(/ (/ (* (sin x) (/ (sin x) x)) x) (+ (cos x) 1))
55.0ms
(/ (sin x) x)
18.0ms
(+ (cos x) 1)

simplify4.4s

Calls
60 calls:
Slowest
474.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
459.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
393.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
306.0ms
(- (log (/ (* (sin x) (/ (sin x) x)) x)) (log (+ (cos x) 1)))
243.0ms
(/ (* (* (/ (* (sin x) (/ (sin x) x)) x) (/ (* (sin x) (/ (sin x) x)) x)) (/ (* (sin x) (/ (sin x) x)) x)) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))

prune936.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.0s1702×body2560valid
1.7s1159×body1280valid
809.0ms1540×body640valid
386.0ms942×body320valid
274.0ms2214×body80valid
164.0ms443×body160valid