Details

Time bar (total: 34.7s)

sample172.0ms

Algorithm
intervals
Results
55.0ms43×body2560valid
41.0ms51×body1280valid
40.0ms54×body640valid
12.0ms71×body80valid
8.0ms21×body320valid
5.0ms16×body160valid

simplify30.0ms

Counts
1 → 1
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: 32.6b

localize26.0ms

Local error

Found 2 expressions with local error:

14.7b
(/ (- 1 (cos x)) (* x x))
1.5b
(- 1 (cos x))

rewrite21.0ms

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
15.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series88.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
63.0ms
(/ (- 1 (cos x)) (* x x))
25.0ms
(- 1 (cos x))

simplify2.6s

Counts
35 → 53
Calls
35 calls:
Slowest
819.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
669.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
258.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
101.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
82.0ms
(- (pow 1 3) (pow (cos x) 3))

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

14.9b
(/ (* (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)))

rewrite130.0ms

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
48.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
42.0ms
(* (* x x) (+ 1 (cos x)))
27.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series200.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
58.0ms
(* (* x x) (+ 1 (cos x)))
23.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

simplify12.7s

Counts
73 → 108
Calls
73 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)))))
1.2s
(/ (* (* (* (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)))))
1.1s
(/ (* (* (* (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)))))

prune1.0s

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))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite77.0ms

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
34.0ms
(* (/ (sin x) x) (/ (sin x) x))
15.0ms
(/ (sin x) x)
15.0ms
(/ (sin x) x)
10.0ms
(+ (cos x) 1)

series179.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
58.0ms
(/ (sin x) x)
55.0ms
(* (/ (sin x) x) (/ (sin x) x))
46.0ms
(/ (sin x) x)
19.0ms
(+ (cos x) 1)

simplify4.8s

Counts
138 → 149
Calls
138 calls:
Slowest
440.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
434.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
370.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
206.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
191.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x 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

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
41×*-un-lft-identity
40×times-frac
35×add-cube-cbrt
16×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
12×pow1
9×add-log-exp
8×exp-prod
5×log-pow
4×cbrt-undiv log-prod div-exp prod-exp cbrt-unprod insert-posit16 div-inv unswap-sqr
3×distribute-lft-out
2×sum-log exp-sum rem-exp-log
1×pow2 frac-times +-commutative flip3-+ pow-plus rem-log-exp pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 114
Calls
4 calls:
Slowest
23.0ms
(exp (+ (cos x) 1))
21.0ms
(* (/ (sin x) x) (/ (sin x) x))
14.0ms
(log (exp (+ (cos x) 1)))
5.0ms
(+ (cos x) 1)

series200.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(exp (+ (cos x) 1))
76.0ms
(* (/ (sin x) x) (/ (sin x) x))
23.0ms
(log (exp (+ (cos x) 1)))
19.0ms
(+ (cos x) 1)

simplify4.0s

Counts
106 → 126
Calls
106 calls:
Slowest
425.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
203.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))
198.0ms
(- (+ (exp 2) (* 1/6 (* (exp 2) (pow x 4)))) (* 1/2 (* (exp 2) (pow x 2))))
194.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)))
194.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.0s1636×body2560valid
988.0ms1249×body1280valid
764.0ms1509×body640valid
761.0ms855×body320valid
273.0ms2255×body80valid
122.0ms496×body160valid