Details

Time bar (total: 49.3s)

sample187.0ms

Algorithm
intervals
Results
65.0ms54×body1280valid
52.0ms37×body2560valid
33.0ms59×body640valid
12.0ms30×body320valid
7.0ms57×body80valid
5.0ms19×body160valid

simplify61.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
61.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize19.0ms

Local error

Found 2 expressions with local error:

11.7b
(/ (- 1 (cos x)) (* x x))
2.5b
(- 1 (cos x))

rewrite32.0ms

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
25.0ms
(/ (- 1 (cos x)) (* x x))
6.0ms
(- 1 (cos x))

series92.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
67.0ms
(/ (- 1 (cos x)) (* x x))
25.0ms
(- 1 (cos x))

simplify3.5s

Counts
55 → 69
Calls
55 calls:
Slowest
700.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
689.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
247.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
144.0ms
(fma (- (cbrt (cos x))) (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x)))))
143.0ms
(fma (sqrt 1) (sqrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune480.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

11.7b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.3b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite81.0ms

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
30.0ms
(* (* x x) (+ 1 (cos x)))
28.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
17.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series233.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
72.0ms
(* (* x x) (+ 1 (cos x)))
33.0ms
(* (sin x) (sin x))
18.0ms
(+ 1 (cos x))

simplify12.4s

Counts
75 → 119
Calls
75 calls:
Slowest
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)))))
1.1s
(/ (* (* (* (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)))))
1000.0ms
(/ (* (* (* (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)))))

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

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
Counts
4 → 155
Calls
4 calls:
Slowest
30.0ms
(* (/ (sin x) x) (/ (sin x) x))
28.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
10.0ms
(+ (cos x) 1)
8.0ms
(/ (sin x) x)

series227.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
57.0ms
(* (/ (sin x) x) (/ (sin x) x))
52.0ms
(/ (sin x) x)
19.0ms
(+ (cos x) 1)

simplify9.8s

Counts
144 → 167
Calls
144 calls:
Slowest
549.0ms
(/ (* (/ (* (* (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)))
520.0ms
(/ (* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
512.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
507.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
436.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
22×add-sqr-sqrt
19×*-un-lft-identity
16×associate-*r*
15×add-cube-cbrt
11×times-frac
10×prod-exp cbrt-unprod
9×cbrt-undiv div-exp
8×pow1
7×associate-*l*
6×add-log-exp
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u
3×fma-def flip3-+ flip-+ unswap-sqr
2×pow-prod-down associate-*r/ associate-/r/ *-commutative div-inv distribute-lft-out
1×+-commutative clear-num associate-/r* sum-log frac-2neg associate-/l* associate-/l/
Counts
4 → 108
Calls
4 calls:
Slowest
37.0ms
(/ (* (sin x) (/ (sin x) x)) (* (+ (cos x) 1) x))
33.0ms
(* (+ (cos x) 1) x)
24.0ms
(* (sin x) (/ (sin x) x))
6.0ms
(+ (cos x) 1)

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(/ (* (sin x) (/ (sin x) x)) (* (+ (cos x) 1) x))
47.0ms
(* (sin x) (/ (sin x) x))
46.0ms
(* (+ (cos x) 1) x)
11.0ms
(+ (cos x) 1)

simplify12.9s

Counts
69 → 120
Calls
69 calls:
Slowest
1.4s
(/ (* (* (* (sin x) (/ (sin x) x)) (* (sin x) (/ (sin x) x))) (* (sin x) (/ (sin x) x))) (* (* (* (+ (cos x) 1) x) (* (+ (cos x) 1) x)) (* (+ (cos x) 1) x)))
1.2s
(/ (* (* (* (sin x) (sin x)) (sin x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)) (* (* x x) x)))
1.2s
(/ (* (* (* (sin x) (sin x)) (sin x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* (* (+ (cos x) 1) x) (* (+ (cos x) 1) x)) (* (+ (cos x) 1) x)))
1.2s
(/ (* (* (* (sin x) (/ (sin x) x)) (* (sin x) (/ (sin x) x))) (* (sin x) (/ (sin x) x))) (* (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)) (* (* x x) x)))
1.1s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x))) (* (* (* (+ (cos x) 1) x) (* (+ (cos x) 1) x)) (* (+ (cos x) 1) x)))

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes123.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.7s1534×body2560valid
1.7s1249×body1280valid
898.0ms1504×body640valid
331.0ms940×body320valid
238.0ms2277×body80valid
106.0ms496×body160valid