Details

Time bar (total: 38.8s)

sample161.0ms

Algorithm
intervals
Results
52.0ms46×body2560valid
40.0ms30×body1280valid
27.0ms53×body640valid
15.0ms37×body320valid
13.0ms79×body80valid
3.0ms11×body160valid

simplify32.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(/ (- 1 (cos x)) (* x x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize17.0ms

Local error

Found 2 expressions with local error:

12.5b
(/ (- 1 (cos x)) (* x x))
2.1b
(- 1 (cos x))

rewrite50.0ms

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
Counts
2 → 63
Calls
2 calls:
Slowest
41.0ms
(/ (- 1 (cos x)) (* x x))
8.0ms
(- 1 (cos x))

series83.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
58.0ms
(/ (- 1 (cos x)) (* x x))
25.0ms
(- 1 (cos x))

simplify3.8s

Counts
55 → 69
Calls
55 calls:
Slowest
658.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
641.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
363.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
162.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
148.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

prune567.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

12.3b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.5b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite92.0ms

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/
Counts
4 → 107
Calls
4 calls:
Slowest
31.0ms
(* (* x x) (+ 1 (cos x)))
30.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
25.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series225.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
73.0ms
(* (* x x) (+ 1 (cos x)))
32.0ms
(* (sin x) (sin x))
18.0ms
(+ 1 (cos x))

simplify12.3s

Counts
75 → 119
Calls
75 calls:
Slowest
1.3s
(/ (* (* (* (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) (+ 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)))))
1.1s
(/ (* (* (* (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)))))
1.1s
(/ (* (* (* (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)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos x) 1)
0.2b
(* (/ (sin x) x) (/ (sin x) x))
0.2b
(/ (sin x) x)
0.2b
(/ (sin x) x)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
58×times-frac
51×*-un-lft-identity
49×add-cube-cbrt
20×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
6×cbrt-undiv associate-/r* div-exp div-inv associate-/l* add-log-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×fma-def
2×clear-num frac-2neg
1×pow2 frac-times +-commutative sum-log flip3-+ pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+ distribute-lft-out
Counts
4 → 148
Calls
4 calls:
Slowest
18.0ms
(* (/ (sin x) x) (/ (sin x) x))
16.0ms
(/ (sin x) x)
15.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series165.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
53.0ms
(/ (sin x) x)
52.0ms
(* (/ (sin x) x) (/ (sin x) x))
43.0ms
(/ (sin x) x)
16.0ms
(+ (cos x) 1)

simplify5.1s

Counts
140 → 160
Calls
140 calls:
Slowest
517.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
416.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
358.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
221.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
211.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

12.3b
(/ (* (sin x) (sin x)) (* x (fma (cos x) x x)))
0.5b
(fma (cos x) x x)
0.3b
(* (sin x) (sin x))
0.1b
(* x (fma (cos x) x x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
14×add-sqr-sqrt
13×pow1
10×*-un-lft-identity add-cube-cbrt
6×associate-*r* associate-*l* prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr fma-udef
2×pow-prod-down *-commutative sqr-sin sin-mult unswap-sqr
1×pow2 distribute-rgt-in clear-num associate-/r* frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-sqr pow-prod-up div-inv associate-/l* associate-/l/
Counts
4 → 90
Calls
4 calls:
Slowest
16.0ms
(* (sin x) (sin x))
15.0ms
(/ (* (sin x) (sin x)) (* x (fma (cos x) x x)))
11.0ms
(* x (fma (cos x) x x))
0.0ms
(fma (cos x) x x)

series343.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(/ (* (sin x) (sin x)) (* x (fma (cos x) x x)))
104.0ms
(* x (fma (cos x) x x))
42.0ms
(fma (cos x) x x)
19.0ms
(* (sin x) (sin x))

simplify7.4s

Counts
61 → 102
Calls
61 calls:
Slowest
1.0s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* x (fma (cos x) x x)) (* x (fma (cos x) x x))) (* x (fma (cos x) x x))))
733.0ms
(* (* (* x x) x) (* (* (fma (cos x) x x) (fma (cos x) x x)) (fma (cos x) x x)))
540.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* x (fma (cos x) x x)) (* x (fma (cos x) x x))) (* x (fma (cos x) x x))))
533.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* x x) x) (* (* (fma (cos x) x x) (fma (cos x) x x)) (fma (cos x) x x))))
524.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))

prune909.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.4s1647×body2560valid
837.0ms1246×body1280valid
820.0ms1443×body640valid
348.0ms2271×body80valid
296.0ms912×body320valid
143.0ms481×body160valid