Details

Time bar (total: 20.0s)

sample135.0ms

Algorithm
intervals
Results
58.0ms51×body2560valid
24.0ms38×body1280valid
22.0ms45×body640valid
10.0ms78×body80valid
10.0ms31×body320valid
2.0ms13×body160valid

simplify87.0ms

Calls
1 calls:
Slowest
87.0ms
(/ (- 1 (cos x)) (* x x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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
5.0ms
(/ (- 1 (cos x)) (* x x))
1.0ms
(- 1 (cos x))

series67.0ms

Calls
2 calls:
Slowest
39.0ms
(/ (- 1 (cos x)) (* x x))
28.0ms
(- 1 (cos x))

simplify1.2s

Calls
19 calls:
Slowest
552.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
144.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
107.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
63.0ms
(- (log (- 1 (cos x))) (log (* x x)))
56.0ms
(/ (- 1 (cos x)) (pow x 2))

prune802.0ms

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)))

rewrite34.0ms

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
14.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
9.0ms
(* (* x x) (+ 1 (cos x)))
8.0ms
(* (sin x) (sin x))
1.0ms
(+ 1 (cos x))

series119.0ms

Calls
4 calls:
Slowest
50.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
35.0ms
(* (* x x) (+ 1 (cos x)))
18.0ms
(* (sin x) (sin x))
16.0ms
(+ 1 (cos x))

simplify7.0s

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)))))
910.0ms
(/ (* (* (* (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)))))
908.0ms
(/ (* (* (* (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)))))
829.0ms
(/ (* (* (* (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)))))
422.0ms
(- (+ (log (sin x)) (log (sin x))) (+ (log (* x x)) (log (+ 1 (cos x)))))

prune964.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize11.0ms

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)

series110.0ms

Calls
4 calls:
Slowest
40.0ms
(* (/ (sin x) x) (/ (sin x) x))
32.0ms
(/ (sin x) x)
30.0ms
(/ (sin x) x)
9.0ms
(+ (cos x) 1)

simplify926.0ms

Calls
34 calls:
Slowest
165.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
137.0ms
(- (+ (* 2/45 (pow x 4)) 1) (* 1/3 (pow x 2)))
122.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
110.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))
96.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))

prune652.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

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)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-div
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod frac-times fma-def pow1/3 associate-*l/ associate-*r/
1×+-commutative flip3-+ flip-+
Calls
4 calls:
Slowest
6.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
3.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
3.0ms
(+ (cos x) 1)
3.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))

series598.0ms

Calls
4 calls:
Slowest
214.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
194.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
182.0ms
(cbrt (* (/ (sin x) x) (/ (sin x) x)))
8.0ms
(+ (cos x) 1)

simplify2.0s

Calls
26 calls:
Slowest
314.0ms
(exp (* 1/3 (+ (log (pow (sin x) 2)) (* 2 (log (/ -1 x))))))
252.0ms
(exp (* 1/3 (+ (log (pow (sin x) 2)) (* 2 (log (/ -1 x))))))
245.0ms
(exp (* 1/3 (+ (* 2 (log (/ 1 x))) (log (pow (sin x) 2)))))
221.0ms
(exp (* 1/3 (+ (log (pow (sin x) 2)) (* 2 (log (/ -1 x))))))
187.0ms
(exp (* 1/3 (+ (* 2 (log (/ 1 x))) (log (pow (sin x) 2)))))

prune833.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.7s1666×body2560valid
921.0ms1473×body640valid
856.0ms1284×body1280valid
319.0ms908×body320valid
206.0ms2202×body80valid
172.0ms467×body160valid