Details

Time bar (total: 34.2s)

sample138.0ms

Algorithm
intervals
Results
58.0ms52×body2560valid
27.0ms38×body1280valid
18.0ms43×body640valid
13.0ms37×body320valid
7.0ms69×body80valid
4.0ms17×body160valid

simplify42.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
42.0ms
(/ (- 1 (cos x)) (* x x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize31.0ms

Local error

Found 2 expressions with local error:

14.3b
(/ (- 1 (cos x)) (* x x))
1.9b
(- 1 (cos x))

rewrite24.0ms

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
17.0ms
(/ (- 1 (cos x)) (* x x))
6.0ms
(- 1 (cos x))

series119.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
97.0ms
(/ (- 1 (cos x)) (* x x))
22.0ms
(- 1 (cos x))

simplify3.8s

Counts
55 → 69
Calls
55 calls:
Slowest
703.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
642.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
364.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
162.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
149.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

prune586.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

14.2b
(/ (* (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)))

rewrite103.0ms

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
57.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
22.0ms
(* (* x x) (+ 1 (cos x)))
12.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series193.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
53.0ms
(* (* x x) (+ 1 (cos x)))
34.0ms
(* (sin x) (sin x))
18.0ms
(+ 1 (cos x))

simplify12.8s

Counts
75 → 119
Calls
75 calls:
Slowest
1.7s
(/ (* (* (* (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)))))
951.0ms
(/ (* (* (* (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)))))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

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
35.0ms
(* (/ (sin x) x) (/ (sin x) x))
8.0ms
(/ (sin x) x)
8.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series192.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
60.0ms
(/ (sin x) x)
56.0ms
(* (/ (sin x) x) (/ (sin x) x))
56.0ms
(/ (sin x) x)
20.0ms
(+ (cos x) 1)

simplify4.7s

Counts
140 → 160
Calls
140 calls:
Slowest
479.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
391.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
345.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
230.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
177.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
22×add-sqr-sqrt add-cube-cbrt
18×times-frac
9×add-exp-log
8×add-cbrt-cube
6×associate-/r* associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log-prod insert-posit16 log1p-expm1-u
3×fma-def
2×cbrt-undiv log-div clear-num frac-2neg flip3-+ div-exp flip-+ div-inv distribute-lft-out
1×+-commutative sum-log rem-log-exp log-pow
Counts
4 → 96
Calls
4 calls:
Slowest
22.0ms
(/ (sin x) x)
15.0ms
(/ (sin x) x)
12.0ms
(+ (cos x) 1)
8.0ms
(log (+ (cos x) 1))

series197.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(log (+ (cos x) 1))
50.0ms
(/ (sin x) x)
46.0ms
(/ (sin x) x)
20.0ms
(+ (cos x) 1)

simplify2.2s

Counts
71 → 108
Calls
71 calls:
Slowest
496.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
447.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
169.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (* 1/96 (pow x 4))))
137.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))
121.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes90.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.7s1595×body2560valid
873.0ms1500×body640valid
855.0ms1263×body1280valid
669.0ms2241×body80valid
447.0ms909×body320valid
113.0ms492×body160valid