Details

Time bar (total: 42.5s)

sample158.0ms

Algorithm
intervals
Results
78.0ms57×body2560valid
23.0ms35×body1280valid
22.0ms44×body640valid
13.0ms34×body320valid
8.0ms72×body80valid
3.0ms14×body160valid

simplify65.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize22.0ms

Local error

Found 2 expressions with local error:

16.5b
(/ (- 1 (cos x)) (* x x))
2.3b
(- 1 (cos x))

rewrite35.0ms

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
28.0ms
(/ (- 1 (cos x)) (* x x))
6.0ms
(- 1 (cos x))

series94.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(/ (- 1 (cos x)) (* x x))
29.0ms
(- 1 (cos x))

simplify3.9s

Counts
55 → 69
Calls
55 calls:
Slowest
789.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
656.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
307.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
174.0ms
(fma (- (cbrt (cos x))) (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x)))))
153.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune576.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

16.2b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.3b
(* (* x x) (+ 1 (cos x)))
0.2b
(* (sin x) (sin x))

rewrite77.0ms

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
32.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
21.0ms
(* (* x x) (+ 1 (cos x)))
17.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series170.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
53.0ms
(* (* x x) (+ 1 (cos x)))
26.0ms
(* (sin x) (sin x))
11.0ms
(+ 1 (cos x))

simplify12.2s

Counts
75 → 119
Calls
75 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)))))
1.2s
(/ (* (* (* (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)))))
1.0s
(/ (* (* (* (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)))))
960.0ms
(/ (* (* (* (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)))))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1)
0.2b
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
0.1b
(* (/ (sin x) x) (/ (sin x) x))
0.1b
(/ (sin x) x)

rewrite104.0ms

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
38.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
30.0ms
(* (/ (sin x) x) (/ (sin x) x))
19.0ms
(/ (sin x) x)
12.0ms
(+ (cos x) 1)

series246.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
63.0ms
(* (/ (sin x) x) (/ (sin x) x))
53.0ms
(/ (sin x) x)
19.0ms
(+ (cos x) 1)

simplify9.2s

Counts
144 → 167
Calls
144 calls:
Slowest
495.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
489.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
485.0ms
(/ (* (/ (* (* (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)))
481.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
445.0ms
(/ (* (* (* (/ (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)))

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

16.2b
(/ (* (sin x) (sin x)) (* x (fma (cos x) x x)))
0.3b
(fma (cos x) x x)
0.2b
(* (sin x) (sin x))
0.1b
(* x (fma (cos x) x x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
14×add-sqr-sqrt
13×pow1
10×*-un-lft-identity add-cube-cbrt
6×associate-*r* associate-*l* prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr fma-udef
2×pow-prod-down *-commutative sqr-sin sin-mult unswap-sqr
1×pow2 distribute-rgt-in clear-num associate-/r* frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-sqr pow-prod-up div-inv associate-/l* associate-/l/
Counts
4 → 90
Calls
4 calls:
Slowest
19.0ms
(* (sin x) (sin x))
15.0ms
(/ (* (sin x) (sin x)) (* x (fma (cos x) x x)))
5.0ms
(* x (fma (cos x) x x))
0.0ms
(fma (cos x) x x)

series333.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(/ (* (sin x) (sin x)) (* x (fma (cos x) x x)))
92.0ms
(* x (fma (cos x) x x))
54.0ms
(fma (cos x) x x)
33.0ms
(* (sin x) (sin x))

simplify6.8s

Counts
61 → 102
Calls
61 calls:
Slowest
795.0ms
(* (* (* x x) x) (* (* (fma (cos x) x x) (fma (cos x) x x)) (fma (cos x) x x)))
665.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* x (fma (cos x) x x)) (* x (fma (cos x) x x))) (* x (fma (cos x) x x))))
601.0ms
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* x x) x) (* (* (fma (cos x) x x) (fma (cos x) x x)) (fma (cos x) x x))))
582.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
521.0ms
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* x (fma (cos x) x x)) (* x (fma (cos x) x x))) (* x (fma (cos x) x x))))

prune972.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s1624×body2560valid
1.3s1340×body1280valid
670.0ms1404×body640valid
372.0ms988×body320valid
308.0ms2163×body80valid
105.0ms481×body160valid