Details

Time bar (total: 45.2s)

sample180.0ms

Algorithm
intervals
Results
68.0ms54×body2560valid
38.0ms49×body1280valid
26.0ms28×body320valid
23.0ms37×body640valid
10.0ms79×body80valid
3.0ms9×body160valid

simplify43.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
43.0ms
(/ (- 1 (cos x)) (* x x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize13.0ms

Local error

Found 2 expressions with local error:

17.2b
(/ (- 1 (cos x)) (* x x))
0.9b
(- 1 (cos x))

rewrite50.0ms

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
39.0ms
(/ (- 1 (cos x)) (* x x))
9.0ms
(- 1 (cos x))

series97.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
71.0ms
(/ (- 1 (cos x)) (* x x))
26.0ms
(- 1 (cos x))

simplify2.3s

Counts
35 → 53
Calls
35 calls:
Slowest
607.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
562.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
308.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
120.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
74.0ms
(- (log (- 1 (cos x))) (+ (log x) (log x)))

prune462.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

17.2b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.5b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite112.0ms

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
47.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
35.0ms
(* (* x x) (+ 1 (cos x)))
20.0ms
(* (sin x) (sin x))
9.0ms
(+ 1 (cos x))

series186.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
54.0ms
(* (* x x) (+ 1 (cos x)))
22.0ms
(* (sin x) (sin x))
15.0ms
(+ 1 (cos x))

simplify11.5s

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)))))
1.1s
(/ (* (* (* (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)))))
948.0ms
(/ (* (* (* (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)))))
919.0ms
(/ (* (* (* (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)))))

prune915.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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
25.0ms
(* (/ (sin x) x) (/ (sin x) x))
17.0ms
(/ (sin x) x)
13.0ms
(/ (sin x) x)
9.0ms
(+ (cos x) 1)

series145.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
47.0ms
(* (/ (sin x) x) (/ (sin x) x))
46.0ms
(/ (sin x) x)
34.0ms
(/ (sin x) x)
17.0ms
(+ (cos x) 1)

simplify4.4s

Counts
138 → 149
Calls
138 calls:
Slowest
517.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
384.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
336.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
202.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))
176.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

17.2b
(/ (* (sin x) (sin x)) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))))
1.0b
(- (* (cos x) (cos x)) (* 1 (cos x)))
0.4b
(pow (cos x) 3)
0.4b
(+ (pow 1 3) (pow (cos x) 3))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
46×add-cbrt-cube add-exp-log
18×*-un-lft-identity
17×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
8×add-log-exp
7×add-sqr-sqrt unpow-prod-down cube-prod add-cube-cbrt
6×distribute-lft-out
5×pow1
4×insert-posit16
3×pow-unpow
2×cube-mult
1×pow-to-exp +-commutative sqr-cos clear-num associate-/r* sum-log sub-neg pow-pow frac-2neg flip3-+ times-frac flip3-- distribute-rgt-out-- diff-log unpow3 div-sub pow-exp associate--l+ associate-*r/ associate-/r/ sum-cubes flip-+ sqr-sin div-inv flip-- sin-mult associate-/l* rem-cube-cbrt sqr-pow associate-/l/
Counts
4 → 95
Calls
4 calls:
Slowest
67.0ms
(/ (* (sin x) (sin x)) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))))
27.0ms
(- (* (cos x) (cos x)) (* 1 (cos x)))
16.0ms
(+ (pow 1 3) (pow (cos x) 3))
5.0ms
(pow (cos x) 3)

series327.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(/ (* (sin x) (sin x)) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))))
61.0ms
(- (* (cos x) (cos x)) (* 1 (cos x)))
49.0ms
(+ (pow 1 3) (pow (cos x) 3))
43.0ms
(pow (cos x) 3)

simplify16.9s

Counts
66 → 107
Calls
66 calls:
Slowest
2.0s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))))
1.8s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))) (* (* x x) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))))
1.5s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))))
1.4s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) x) (* (* x x) x)) (* (* (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))))
1.4s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x)))))) (/ (+ (pow 1 3) (pow (cos x) 3)) (+ (* 1 1) (- (* (cos x) (cos x)) (* 1 (cos x))))))))

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes73.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.0s1619×body2560valid
932.0ms1226×body1280valid
782.0ms1493×body640valid
400.0ms930×body320valid
226.0ms2267×body80valid
142.0ms465×body160valid