Details

Time bar (total: 35.5s)

sample138.0ms

Algorithm
intervals
Results
64.0ms48×body2560valid
21.0ms51×body640valid
21.0ms37×body1280valid
10.0ms31×body320valid
7.0ms77×body80valid
2.0ms12×body160valid

simplify61.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
60.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize23.0ms

Local error

Found 2 expressions with local error:

13.8b
(/ (- 1 (cos x)) (* x x))
1.8b
(- 1 (cos x))

rewrite48.0ms

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))
5.0ms
(- 1 (cos x))

series113.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
79.0ms
(/ (- 1 (cos x)) (* x x))
34.0ms
(- 1 (cos x))

simplify3.7s

Counts
55 → 69
Calls
55 calls:
Slowest
760.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
645.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
288.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
152.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
141.0ms
(fma (- (cbrt (cos x))) (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x)))))

prune580.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

13.7b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite131.0ms

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
53.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
40.0ms
(* (* x x) (+ 1 (cos x)))
20.0ms
(* (sin x) (sin x))
15.0ms
(+ 1 (cos x))

series201.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
67.0ms
(* (* x x) (+ 1 (cos x)))
21.0ms
(* (sin x) (sin x))
16.0ms
(+ 1 (cos x))

simplify12.8s

Counts
75 → 119
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)))))
1.3s
(/ (* (* (* (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)))))
1.2s
(/ (* (* (* (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) (* 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

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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
14.0ms
(* (/ (sin x) x) (/ (sin x) x))
7.0ms
(+ (cos x) 1)
7.0ms
(/ (sin x) x)
7.0ms
(/ (sin x) x)

series165.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
58.0ms
(* (/ (sin x) x) (/ (sin x) x))
49.0ms
(/ (sin x) x)
35.0ms
(/ (sin x) x)
23.0ms
(+ (cos x) 1)

simplify5.2s

Counts
140 → 160
Calls
140 calls:
Slowest
449.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
430.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
412.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
224.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))
193.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (/ (sin x) x))
0.4b
(+ (cos x) 1)
0.1b
(* (/ (sin x) x) (log1p (expm1 (/ (sin x) x))))
0.1b
(/ (sin x) x)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
19×times-frac
13×associate-*l*
11×add-cbrt-cube add-exp-log
6×pow1 add-log-exp
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16
3×associate-/r* fma-def associate-*r* associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×+-commutative expm1-log1p clear-num sum-log frac-2neg flip3-+ pow-prod-down associate-*l/ *-commutative flip-+ distribute-lft-out expm1-udef
Counts
4 → 95
Calls
4 calls:
Slowest
13.0ms
(/ (sin x) x)
11.0ms
(* (/ (sin x) x) (log1p (expm1 (/ (sin x) x))))
5.0ms
(+ (cos x) 1)
0.0ms
(expm1 (/ (sin x) x))

series566.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
439.0ms
(* (/ (sin x) x) (log1p (expm1 (/ (sin x) x))))
55.0ms
(expm1 (/ (sin x) x))
54.0ms
(/ (sin x) x)
18.0ms
(+ (cos x) 1)

simplify3.0s

Counts
66 → 107
Calls
66 calls:
Slowest
805.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (log1p (expm1 (/ (sin x) x))) (log1p (expm1 (/ (sin x) x)))) (log1p (expm1 (/ (sin x) x)))))
383.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
164.0ms
(- (+ (* 1/45 (* (pow x 4) E)) E) (+ (* 1/6 (* (pow x 2) E)) 1))
153.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (log1p (expm1 (/ (sin x) x))) (log1p (expm1 (/ (sin x) x)))) (log1p (expm1 (/ (sin x) x)))))
152.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes56.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.3s1548×body2560valid
954.0ms1289×body1280valid
868.0ms1505×body640valid
304.0ms936×body320valid
238.0ms2265×body80valid
130.0ms457×body160valid