Details

Time bar (total: 23.1s)

sample155.0ms

Algorithm
intervals
Results
52.0ms52×body1280valid
47.0ms45×body2560valid
23.0ms49×body640valid
12.0ms27×body320valid
7.0ms72×body80valid
3.0ms11×body160valid

simplify62.0ms

Calls
1 calls:
Slowest
62.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize22.0ms

Local error

Found 2 expressions with local error:

14.7b
(/ (- 1 (cos x)) (* x x))
2.6b
(- 1 (cos x))

rewrite29.0ms

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
11.0ms
(/ (- 1 (cos x)) (* x x))
2.0ms
(- 1 (cos x))

series75.0ms

Calls
2 calls:
Slowest
58.0ms
(/ (- 1 (cos x)) (* x x))
17.0ms
(- 1 (cos x))

simplify1.3s

Calls
19 calls:
Slowest
652.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
154.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
110.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
87.0ms
(- (log (- 1 (cos x))) (log (* x x)))
39.0ms
(/ (- 1 (cos x)) (pow x 2))

prune317.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

14.4b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.3b
(* (sin x) (sin x))
0.2b
(+ 1 (cos x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite37.0ms

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
18.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
8.0ms
(* (* x x) (+ 1 (cos x)))
8.0ms
(* (sin x) (sin x))
2.0ms
(+ 1 (cos x))

series134.0ms

Calls
4 calls:
Slowest
65.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
31.0ms
(* (* x x) (+ 1 (cos x)))
25.0ms
(* (sin x) (sin x))
13.0ms
(+ 1 (cos x))

simplify7.1s

Calls
51 calls:
Slowest
939.0ms
(/ (* (* (* (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)))))
918.0ms
(/ (* (* (* (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)))))
886.0ms
(/ (* (* (* (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)))))
809.0ms
(/ (* (* (* (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)))))
429.0ms
(- (+ (log (sin x)) (log (sin x))) (+ (log (* x x)) (log (+ 1 (cos x)))))

prune956.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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
23.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
6.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)
6.0ms
(/ (sin x) x)

series102.0ms

Calls
4 calls:
Slowest
45.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
29.0ms
(/ (sin x) x)
19.0ms
(/ (sin x) x)
9.0ms
(+ (cos x) 1)

simplify2.8s

Calls
37 calls:
Slowest
394.0ms
(- (+ (log (/ (sin x) x)) (log (/ (sin x) x))) (log (+ (cos x) 1)))
371.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
311.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
292.0ms
(- (log (* (/ (sin x) x) (/ (sin x) x))) (log (+ (cos x) 1)))
267.0ms
(/ (* (* (* (/ (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)))

prune862.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
9×pow1 add-cbrt-cube
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-*r* prod-exp associate-/l*
5×frac-times associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-def pow-prod-down associate-*r/ cbrt-unprod div-inv
2×rec-exp clear-num frac-2neg flip3-+ associate-/r/ flip-+
1×+-commutative associate-*l* un-div-inv *-commutative
Calls
4 calls:
Slowest
16.0ms
(* (* (/ (sin x) x) (/ (sin x) x)) (/ 1 (+ (cos x) 1)))
3.0ms
(+ (cos x) 1)
3.0ms
(/ (sin x) x)
3.0ms
(/ (sin x) x)

series105.0ms

Calls
4 calls:
Slowest
45.0ms
(* (* (/ (sin x) x) (/ (sin x) x)) (/ 1 (+ (cos x) 1)))
31.0ms
(/ (sin x) x)
19.0ms
(/ (sin x) x)
9.0ms
(+ (cos x) 1)

simplify3.6s

Calls
44 calls:
Slowest
315.0ms
(+ (log (* (/ (sin x) x) (/ (sin x) x))) (- (log (+ (cos x) 1))))
295.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
284.0ms
(+ (+ (log (/ (sin x) x)) (log (/ (sin x) x))) (- (log (+ (cos x) 1))))
277.0ms
(* (* (/ (sin x) x) (/ (sin x) x)) (/ 1 (+ (cos x) 1)))
242.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))

prune680.0ms

Pruning

6 alts after pruning (6 fresh and 0 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

sample4.6s

Algorithm
intervals
Results
1.6s1637×body2560valid
1.3s1227×body1280valid
1.0s1513×body640valid
269.0ms949×body320valid
234.0ms2223×body80valid
126.0ms451×body160valid