Details

Time bar (total: 30.4s)

sample181.0ms

Algorithm
intervals
Results
85.0ms52×body2560valid
30.0ms38×body1280valid
25.0ms43×body640valid
15.0ms37×body320valid
9.0ms69×body80valid
5.0ms17×body160valid

simplify60.0ms

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: 31.5b

localize11.0ms

Local error

Found 2 expressions with local error:

14.3b
(/ (- 1 (cos x)) (* x x))
1.9b
(- 1 (cos x))

rewrite35.0ms

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
Counts
2 → 47
Calls
2 calls:
Slowest
27.0ms
(/ (- 1 (cos x)) (* x x))
6.0ms
(- 1 (cos x))

series84.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
57.0ms
(/ (- 1 (cos x)) (* x x))
27.0ms
(- 1 (cos x))

simplify2.5s

Counts
35 → 53
Calls
35 calls:
Slowest
775.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
656.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
249.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
116.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
86.0ms
(- (log (- 1 (cos x))) (log (* x x)))

prune459.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

14.2b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.3b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite100.0ms

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/
Counts
4 → 96
Calls
4 calls:
Slowest
45.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
36.0ms
(* (* x x) (+ 1 (cos x)))
11.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series176.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
49.0ms
(* (* x x) (+ 1 (cos x)))
30.0ms
(* (sin x) (sin x))
26.0ms
(+ 1 (cos x))

simplify11.1s

Counts
73 → 108
Calls
73 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)))))
1.1s
(/ (* (* (* (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)))))
996.0ms
(/ (* (* (* (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)))))
968.0ms
(/ (* (* (* (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)))))
802.0ms
(/ (* (* (* (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)))))

prune965.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
58×times-frac
50×*-un-lft-identity
48×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×prod-exp cbrt-unprod insert-posit16 unswap-sqr
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 → 137
Calls
4 calls:
Slowest
27.0ms
(* (/ (sin x) x) (/ (sin x) x))
15.0ms
(/ (sin x) x)
9.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series184.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(* (/ (sin x) x) (/ (sin x) x))
51.0ms
(/ (sin x) x)
35.0ms
(/ (sin x) x)
16.0ms
(+ (cos x) 1)

simplify4.5s

Counts
138 → 149
Calls
138 calls:
Slowest
455.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
392.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
374.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
213.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
189.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (cos x) 1)
0.2b
(log (+ (cos x) 1))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
18×times-frac
9×add-exp-log
8×add-cbrt-cube
6×associate-/r* associate-/l* add-log-exp
5×pow1
4×log-prod insert-posit16
2×cbrt-undiv log-div clear-num frac-2neg flip3-+ div-exp flip-+ div-inv distribute-lft-out
1×+-commutative sum-log rem-log-exp log-pow
Counts
4 → 85
Calls
4 calls:
Slowest
15.0ms
(/ (sin x) x)
12.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)
4.0ms
(log (+ (cos x) 1))

series200.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(log (+ (cos x) 1))
49.0ms
(/ (sin x) x)
44.0ms
(/ (sin x) x)
17.0ms
(+ (cos x) 1)

simplify2.0s

Counts
69 → 97
Calls
69 calls:
Slowest
431.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
424.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
143.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (* 1/96 (pow x 4))))
116.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))
104.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes87.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.9s1595×body2560valid
1.3s1263×body1280valid
840.0ms1500×body640valid
352.0ms909×body320valid
328.0ms2241×body80valid
109.0ms492×body160valid