Details

Time bar (total: 37.5s)

sample137.0ms

Algorithm
intervals
Results
74.0ms66×body2560valid
20.0ms47×body640valid
18.0ms39×body1280valid
6.0ms69×body80valid
6.0ms19×body320valid
3.0ms16×body160valid

simplify31.0ms

Calls
1 calls:
Slowest
30.0ms
(/ (- 1 (cos x)) (* x x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize11.0ms

Local error

Found 2 expressions with local error:

18.9b
(/ (- 1 (cos x)) (* x x))
2.1b
(- 1 (cos x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-cube-cbrt add-log-exp
3×distribute-lft-out--
2×pow1 cbrt-undiv flip3-- div-exp insert-posit16 flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Calls
2 calls:
Slowest
22.0ms
(/ (- 1 (cos x)) (* x x))
6.0ms
(- 1 (cos x))

series94.0ms

Calls
2 calls:
Slowest
63.0ms
(/ (- 1 (cos x)) (* x x))
31.0ms
(- 1 (cos x))

simplify2.9s

Calls
35 calls:
Slowest
696.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
660.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
443.0ms
(- (log (- 1 (cos x))) (log (* x x)))
214.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
124.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

prune384.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

18.9b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.3b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.0b
(* (* x x) (+ 1 (cos x)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×pow1
13×*-un-lft-identity prod-exp cbrt-unprod
12×add-sqr-sqrt
9×add-cube-cbrt
7×associate-*r*
6×cbrt-undiv div-exp add-log-exp
4×associate-*l* pow-prod-down associate-*r/ insert-posit16
3×flip3-+ swap-sqr flip-+
2×associate-/r/ *-commutative sqr-sin sin-mult distribute-lft-out unswap-sqr
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-sqr pow-prod-up div-inv associate-/l* associate-/l/
Calls
4 calls:
Slowest
31.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
25.0ms
(* (* x x) (+ 1 (cos x)))
11.0ms
(* (sin x) (sin x))
8.0ms
(+ 1 (cos x))

series176.0ms

Calls
4 calls:
Slowest
79.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
51.0ms
(* (* x x) (+ 1 (cos x)))
34.0ms
(* (sin x) (sin x))
13.0ms
(+ 1 (cos x))

simplify11.4s

Calls
73 calls:
Slowest
1.2s
(/ (* (* (* (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)))))
1.1s
(/ (* (* (* (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)))))
993.0ms
(/ (* (* (* (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)))))
959.0ms
(/ (* (* (* (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)))))
900.0ms
(/ (* (* (* (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)))))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×times-frac
48×*-un-lft-identity
42×add-cube-cbrt
36×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×swap-sqr associate-*r* associate-*l*
11×pow1
8×prod-exp cbrt-unprod
7×associate-/r*
6×div-inv add-log-exp
4×insert-posit16 associate-/l* unswap-sqr
3×distribute-lft-out associate-/l/
2×frac-times clear-num frac-2neg flip3-+ associate-*l/ associate-*r/ associate-/r/ flip-+
1×pow2 +-commutative sum-log pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
Calls
4 calls:
Slowest
35.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
27.0ms
(* (/ (sin x) x) (/ (sin x) x))
17.0ms
(/ (sin x) x)
10.0ms
(+ (cos x) 1)

series223.0ms

Calls
4 calls:
Slowest
90.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
64.0ms
(* (/ (sin x) x) (/ (sin x) x))
47.0ms
(/ (sin x) x)
21.0ms
(+ (cos x) 1)

simplify9.2s

Calls
142 calls:
Slowest
538.0ms
(/ (* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
535.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
517.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
486.0ms
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
485.0ms
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
26×*-un-lft-identity
22×add-cube-cbrt
19×times-frac
17×associate-*l*
13×add-cbrt-cube add-exp-log
8×pow1
6×associate-*r* add-log-exp
4×insert-posit16
3×associate-/r* associate-*l/ prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp pow-prod-down *-commutative flip-+ div-inv distribute-lft-out
1×+-commutative clear-num sum-log frac-2neg
Calls
4 calls:
Slowest
17.0ms
(* (/ (sin x) x) (sin x))
15.0ms
(* (+ (cos x) 1) x)
7.0ms
(/ (sin x) x)
5.0ms
(+ (cos x) 1)

series146.0ms

Calls
4 calls:
Slowest
50.0ms
(* (/ (sin x) x) (sin x))
49.0ms
(* (+ (cos x) 1) x)
33.0ms
(/ (sin x) x)
14.0ms
(+ (cos x) 1)

simplify3.6s

Calls
74 calls:
Slowest
445.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
436.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (sin x) (sin x)) (sin x)))
377.0ms
(- (+ (* 2 x) (* 1/24 (pow x 5))) (* 1/2 (pow x 3)))
369.0ms
(* (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)) (* (* x x) x))
358.0ms
(- (+ x (* 2/45 (pow x 5))) (* 1/3 (pow x 3)))

prune961.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.9s1605×body2560valid
1.4s1507×body640valid
809.0ms963×body320valid
800.0ms1244×body1280valid
331.0ms2234×body80valid
104.0ms447×body160valid