Details

Time bar (total: 39.4s)

sample134.0ms

Algorithm
intervals
Results
62.0ms66×body2560valid
24.0ms39×body1280valid
23.0ms47×body640valid
6.0ms69×body80valid
6.0ms19×body320valid
3.0ms16×body160valid

simplify67.0ms

Calls
1 calls:
Slowest
67.0ms
(/ (- 1 (cos x)) (* x x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-log-exp
3×fma-neg distribute-lft-out--
2×expm1-log1p-u pow1 cbrt-undiv flip3-- div-exp insert-posit16 log1p-expm1-u 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
28.0ms
(/ (- 1 (cos x)) (* x x))
10.0ms
(- 1 (cos x))

series99.0ms

Calls
2 calls:
Slowest
74.0ms
(/ (- 1 (cos x)) (* x x))
25.0ms
(- 1 (cos x))

simplify3.5s

Calls
55 calls:
Slowest
679.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
565.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
263.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
153.0ms
(fma (- (cbrt (cos x))) (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x)))))
135.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

prune497.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×pow1
14×*-un-lft-identity
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt
7×associate-*r*
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u
3×fma-def 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
55.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
35.0ms
(* (* x x) (+ 1 (cos x)))
22.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series192.0ms

Calls
4 calls:
Slowest
89.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
59.0ms
(* (* x x) (+ 1 (cos x)))
32.0ms
(* (sin x) (sin x))
12.0ms
(+ 1 (cos x))

simplify12.7s

Calls
75 calls:
Slowest
1.4s
(/ (* (* (* (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)))))
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)))))
1.2s
(/ (* (* (* (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)))))
1.0s
(/ (* (* (* (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

localize30.0ms

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)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
53×times-frac
49×*-un-lft-identity
43×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×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* unswap-sqr
3×fma-def 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
34.0ms
(* (/ (sin x) x) (/ (sin x) x))
19.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
15.0ms
(/ (sin x) x)
5.0ms
(+ (cos x) 1)

series237.0ms

Calls
4 calls:
Slowest
108.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
70.0ms
(* (/ (sin x) x) (/ (sin x) x))
41.0ms
(/ (sin x) x)
18.0ms
(+ (cos x) 1)

simplify9.4s

Calls
144 calls:
Slowest
518.0ms
(/ (* (/ (* (* (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)))
509.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
508.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
491.0ms
(/ (* (/ (* (* (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)))
482.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
27×*-un-lft-identity
23×add-cube-cbrt
19×times-frac
16×associate-*r*
13×add-cbrt-cube add-exp-log
8×pow1
7×associate-*l*
6×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp pow-prod-down associate-*l/ *-commutative flip-+ div-inv distribute-lft-out
1×+-commutative clear-num sum-log frac-2neg associate-*r/
Calls
4 calls:
Slowest
25.0ms
(* (+ (cos x) 1) x)
13.0ms
(* (sin x) (/ (sin x) x))
10.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series143.0ms

Calls
4 calls:
Slowest
47.0ms
(* (+ (cos x) 1) x)
47.0ms
(* (sin x) (/ (sin x) x))
38.0ms
(/ (sin x) x)
11.0ms
(+ (cos x) 1)

simplify3.1s

Calls
75 calls:
Slowest
428.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
395.0ms
(* (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)) (* (* x x) x))
354.0ms
(* (* (* (sin x) (sin x)) (sin x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))
273.0ms
(* (+ (pow (cos x) 3) (pow 1 3)) x)
216.0ms
(* (- (* (cos x) (cos x)) (* 1 1)) x)

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.3s1605×body2560valid
1.3s1244×body1280valid
856.0ms1507×body640valid
386.0ms963×body320valid
264.0ms2234×body80valid
128.0ms447×body160valid