Details

Time bar (total: 34.4s)

sample158.0ms

Algorithm
intervals
Results
60.0ms54×body2560valid
31.0ms49×body1280valid
28.0ms28×body320valid
18.0ms37×body640valid
8.0ms79×body80valid
2.0ms9×body160valid

simplify64.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
64.0ms
(/ (- 1 (cos x)) (* x x))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

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
33.0ms
(/ (- 1 (cos x)) (* x x))
6.0ms
(- 1 (cos x))

series96.0ms

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

simplify3.6s

Counts
55 → 69
Calls
55 calls:
Slowest
721.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
607.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
278.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
190.0ms
(fma 1 1 (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
171.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune498.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite94.0ms

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
36.0ms
(* (* x x) (+ 1 (cos x)))
24.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
22.0ms
(* (sin x) (sin x))
11.0ms
(+ 1 (cos x))

series170.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
47.0ms
(* (* x x) (+ 1 (cos x)))
34.0ms
(* (sin x) (sin x))
12.0ms
(+ 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)))))
1.2s
(/ (* (* (* (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)))))
1.0s
(/ (* (* (* (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)))))

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize28.0ms

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)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
58×times-frac
51×*-un-lft-identity
49×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×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×fma-def
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 → 148
Calls
4 calls:
Slowest
16.0ms
(* (/ (sin x) x) (/ (sin x) x))
15.0ms
(/ (sin x) x)
8.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series170.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(* (/ (sin x) x) (/ (sin x) x))
50.0ms
(/ (sin x) x)
47.0ms
(/ (sin x) x)
11.0ms
(+ (cos x) 1)

simplify5.2s

Counts
140 → 160
Calls
140 calls:
Slowest
456.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
399.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
397.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
227.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
195.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

16.6b
(/ (sin x) (* x x))
0.1b
(* (/ (sin x) (* x x)) (tan (/ x 2)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
7×*-un-lft-identity times-frac associate-*l* add-cube-cbrt
5×prod-exp cbrt-unprod
4×pow1 cbrt-undiv div-exp
3×associate-*r* associate-/l*
2×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
1×frac-times clear-num associate-/r* frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
2 → 57
Calls
2 calls:
Slowest
47.0ms
(* (/ (sin x) (* x x)) (tan (/ x 2)))
21.0ms
(/ (sin x) (* x x))

series182.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
134.0ms
(* (/ (sin x) (* x x)) (tan (/ x 2)))
48.0ms
(/ (sin x) (* x x))

simplify3.1s

Counts
42 → 63
Calls
42 calls:
Slowest
354.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) (* x x)) (* x x)))
297.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) x) (* (* x x) x)))
285.0ms
(- (+ (* 1/120 (pow x 3)) (/ 1 x)) (* 1/6 x))
283.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) (* x x)) (* x x))) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))))
276.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) x) (* (* x x) x))) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))))

prune494.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch3.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.8s1619×body2560valid
1.6s1226×body1280valid
803.0ms1493×body640valid
531.0ms465×body160valid
401.0ms930×body320valid
253.0ms2267×body80valid