Details

Time bar (total: 19.9s)

sample104.0ms

Algorithm
intervals
Results
43.0ms51×body2560valid
20.0ms37×body1280valid
17.0ms45×body640valid
7.0ms81×body80valid
7.0ms26×body320valid
3.0ms16×body160valid

simplify59.0ms

Calls
1 calls:
Slowest
59.0ms
(/ (- 1 (cos x)) (* x x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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))

series81.0ms

Calls
2 calls:
Slowest
52.0ms
(/ (- 1 (cos x)) (* x x))
29.0ms
(- 1 (cos x))

simplify1.2s

Calls
19 calls:
Slowest
651.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
130.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
82.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
65.0ms
(- (log (- 1 (cos x))) (log (* x x)))
60.0ms
(/ (- 1 (cos x)) (pow x 2))

prune331.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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)))

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
11.0ms
(* (* x x) (+ 1 (cos x)))
9.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
6.0ms
(* (sin x) (sin x))
1.0ms
(+ 1 (cos x))

series108.0ms

Calls
4 calls:
Slowest
50.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
23.0ms
(* (sin x) (sin x))
21.0ms
(* (* x x) (+ 1 (cos x)))
14.0ms
(+ 1 (cos x))

simplify7.3s

Calls
51 calls:
Slowest
979.0ms
(/ (* (* (* (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)))))
841.0ms
(/ (* (* (* (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)))))
840.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x))))
764.0ms
(/ (* (* (* (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)))))
733.0ms
(/ (* (* (* (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)))))

prune773.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize22.0ms

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))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-/l*
4×pow1 insert-posit16 add-log-exp
3×clear-num associate-/r* 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
12.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
5.0ms
(+ (cos x) 1)
3.0ms
(/ (sin x) x)
3.0ms
(/ (sin x) x)

series102.0ms

Calls
4 calls:
Slowest
54.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
20.0ms
(/ (sin x) x)
19.0ms
(/ (sin x) x)
9.0ms
(+ (cos x) 1)

simplify2.6s

Calls
35 calls:
Slowest
333.0ms
(- (log (* (/ (sin x) x) (/ (sin x) x))) (log (+ (cos x) 1)))
315.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
300.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
291.0ms
(/ (* (* (* (/ (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)))
288.0ms
(- (+ (log (/ (sin x) x)) (log (/ (sin x) x))) (log (+ (cos x) 1)))

prune696.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*l*
6×pow1 add-cbrt-cube add-exp-log
4×insert-posit16 add-log-exp
3×associate-*r* associate-*l/ associate-/l*
2×flip3-+ *-commutative flip-+ div-inv
1×+-commutative clear-num frac-2neg pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
14.0ms
(* (+ (cos x) 1) x)
9.0ms
(* (/ (sin x) x) (sin x))
5.0ms
(/ (sin x) x)
3.0ms
(+ (cos x) 1)

series99.0ms

Calls
4 calls:
Slowest
40.0ms
(* (/ (sin x) x) (sin x))
27.0ms
(* (+ (cos x) 1) x)
19.0ms
(/ (sin x) x)
13.0ms
(+ (cos x) 1)

simplify1.2s

Calls
28 calls:
Slowest
438.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (sin x) (sin x)) (sin x)))
161.0ms
(* (- (* (cos x) (cos x)) (* 1 1)) x)
107.0ms
(- (+ x (* 2/45 (pow x 5))) (* 1/3 (pow x 3)))
99.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))
97.0ms
(- (+ (* 2 x) (* 1/24 (pow x 5))) (* 1/2 (pow x 3)))

prune638.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s1592×body2560valid
1.1s1272×body1280valid
768.0ms1443×body640valid
311.0ms938×body320valid
264.0ms2288×body80valid
169.0ms467×body160valid