Details

Time bar (total: 39.8s)

sample128.0ms

Algorithm
intervals
Results
61.0ms47×body2560valid
19.0ms38×body1280valid
19.0ms44×body640valid
10.0ms30×body320valid
9.0ms84×body80valid
2.0ms13×body160valid

simplify37.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
37.0ms
(/ (- 1 (cos x)) (* x x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize12.0ms

Local error

Found 2 expressions with local error:

13.6b
(/ (- 1 (cos x)) (* x x))
1.5b
(- 1 (cos x))

rewrite39.0ms

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
32.0ms
(/ (- 1 (cos x)) (* x x))
6.0ms
(- 1 (cos x))

series97.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
72.0ms
(/ (- 1 (cos x)) (* x x))
25.0ms
(- 1 (cos x))

simplify3.7s

Counts
55 → 69
Calls
55 calls:
Slowest
701.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
681.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
272.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
176.0ms
(fma (sqrt 1) (sqrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
151.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune595.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

13.6b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.3b
(* (* x x) (+ 1 (cos x)))
0.3b
(* (sin x) (sin x))

rewrite91.0ms

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
33.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
31.0ms
(* (* x x) (+ 1 (cos x)))
21.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series177.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
60.0ms
(* (* x x) (+ 1 (cos x)))
32.0ms
(* (sin x) (sin x))
13.0ms
(+ 1 (cos x))

simplify12.3s

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)))))
1.1s
(/ (* (* (* (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)))))
1.0s
(/ (* (* (* (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)))))
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

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize26.0ms

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) (/ (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
29.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
20.0ms
(/ (sin x) x)
16.0ms
(* (/ (sin x) x) (/ (sin x) x))
10.0ms
(+ (cos x) 1)

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
76.0ms
(* (/ (sin x) x) (/ (sin x) x))
37.0ms
(/ (sin x) x)
19.0ms
(+ (cos x) 1)

simplify9.3s

Counts
144 → 167
Calls
144 calls:
Slowest
543.0ms
(/ (* (/ (* (* (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)))
499.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
478.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
431.0ms
(/ (* (* (* (/ (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)))
423.0ms
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (* 1 1) (* (cos x) 1))
0.4b
(pow (cos x) 3)
0.3b
(* (cos x) (cos x))
0.2b
(+ (pow (cos x) 3) (pow 1 3))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
16×add-sqr-sqrt
14×add-cube-cbrt
12×pow1 fma-def
10×unpow-prod-down cube-prod
8×add-log-exp
7×add-cbrt-cube add-exp-log
6×distribute-lft-out
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cube-mult pow-unpow swap-sqr associate-*r* associate-*l*
2×unpow3 sqr-pow
1×pow2 pow-to-exp +-commutative sqr-cos sum-log sub-neg pow-pow flip3-+ pow-plus flip3-- distribute-rgt-out-- fma-neg diff-log prod-diff pow-prod-down pow-exp prod-exp pow-sqr cos-mult sum-cubes *-commutative pow-prod-up cbrt-unprod flip-+ flip-- rem-cube-cbrt unswap-sqr
Counts
4 → 107
Calls
4 calls:
Slowest
20.0ms
(+ (pow (cos x) 3) (pow 1 3))
15.0ms
(- (* 1 1) (* (cos x) 1))
12.0ms
(* (cos x) (cos x))
10.0ms
(pow (cos x) 3)

series151.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
49.0ms
(pow (cos x) 3)
40.0ms
(+ (pow (cos x) 3) (pow 1 3))
36.0ms
(- (* 1 1) (* (cos x) 1))
25.0ms
(* (cos x) (cos x))

simplify2.7s

Counts
74 → 119
Calls
74 calls:
Slowest
305.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
169.0ms
(pow (* (cbrt (cos x)) (cbrt (cos x))) 3)
163.0ms
(pow (* (cbrt (cos x)) (cbrt (cos x))) 3)
150.0ms
(- (+ (* 7/8 (pow x 4)) 1) (* 3/2 (pow x 2)))
150.0ms
(pow (* (cbrt (cos x)) (cbrt (cos x))) 3)

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.3s1566×body2560valid
1.2s1258×body1280valid
802.0ms1522×body640valid
447.0ms971×body320valid
296.0ms2176×body80valid
185.0ms507×body160valid