Details

Time bar (total: 21.2s)

sample136.0ms

Algorithm
intervals
Results
45.0ms51×body2560valid
40.0ms45×body640valid
21.0ms38×body1280valid
9.0ms31×body320valid
9.0ms78×body80valid
2.0ms13×body160valid

simplify50.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize25.0ms

Local error

Found 2 expressions with local error:

14.9b
(/ (- 1 (cos x)) (* x x))
1.2b
(- 1 (cos x))

rewrite12.0ms

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×pow1 flip3-- insert-posit16 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
9.0ms
(/ (- 1 (cos x)) (* x x))
2.0ms
(- 1 (cos x))

series76.0ms

Calls
2 calls:
Slowest
58.0ms
(/ (- 1 (cos x)) (* x x))
18.0ms
(- 1 (cos x))

simplify1.2s

Calls
19 calls:
Slowest
619.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
113.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
72.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
69.0ms
(/ (- 1 (cos x)) (pow x 2))
63.0ms
(/ (- 1 (cos x)) (pow x 2))

prune332.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

14.9b
(/ (* (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)))

rewrite29.0ms

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×cbrt-undiv div-exp associate-*l* associate-*r/ insert-posit16 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
16.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
6.0ms
(* (sin x) (sin x))
5.0ms
(* (* x x) (+ 1 (cos x)))
2.0ms
(+ 1 (cos x))

series460.0ms

Calls
4 calls:
Slowest
353.0ms
(+ 1 (cos x))
49.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
33.0ms
(* (* x x) (+ 1 (cos x)))
25.0ms
(* (sin x) (sin x))

simplify7.8s

Calls
51 calls:
Slowest
932.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x))))
916.0ms
(/ (* (* (* (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)))))
834.0ms
(/ (* (* (* (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)))))
829.0ms
(/ (* (* (* (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)))))
783.0ms
(/ (* (* (* (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)))))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

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)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log associate-/l*
4×associate-*r* associate-*l* insert-posit16 div-inv add-log-exp
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
13.0ms
(* (/ (sin x) x) (/ (sin x) x))
7.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)
6.0ms
(/ (sin x) x)

series121.0ms

Calls
4 calls:
Slowest
44.0ms
(* (/ (sin x) x) (/ (sin x) x))
32.0ms
(/ (sin x) x)
31.0ms
(/ (sin x) x)
14.0ms
(+ (cos x) 1)

simplify1.0s

Calls
32 calls:
Slowest
192.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
144.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
143.0ms
(- (+ (* 2/45 (pow x 4)) 1) (* 1/3 (pow x 2)))
134.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
103.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))

prune781.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

17.7b
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
17.7b
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
17.7b
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
0.4b
(+ (cos x) 1)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-div
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×cbrt-prod frac-times pow1/3 associate-*l/ associate-*r/
1×+-commutative flip3-+ flip-+
Calls
4 calls:
Slowest
4.0ms
(+ (cos x) 1)
3.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
3.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
3.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))

series567.0ms

Calls
4 calls:
Slowest
196.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
184.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
173.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
13.0ms
(+ (cos x) 1)

simplify2.1s

Calls
24 calls:
Slowest
277.0ms
(exp (* 1/3 (+ (log (pow (sin x) 2)) (* 2 (log (/ -1 x))))))
275.0ms
(exp (* 1/3 (+ (log (pow (sin x) 2)) (* 2 (log (/ -1 x))))))
262.0ms
(exp (* 1/3 (+ (log (pow (sin x) 2)) (* 2 (log (/ -1 x))))))
249.0ms
(exp (* 1/3 (+ (* 2 (log (/ 1 x))) (log (pow (sin x) 2)))))
242.0ms
(exp (* 1/3 (+ (* 2 (log (/ 1 x))) (log (pow (sin x) 2)))))

prune713.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s1666×body2560valid
1.1s1473×body640valid
839.0ms1284×body1280valid
347.0ms2202×body80valid
289.0ms908×body320valid
103.0ms467×body160valid