Details

Time bar (total: 2.2m)

sample152.0ms

Algorithm
intervals
Results
62.0ms50×body2560valid
27.0ms48×body640valid
27.0ms41×body1280valid
11.0ms29×body320valid
10.0ms68×body80valid
5.0ms20×body160valid

simplify49.0ms

Calls
1 calls:
Slowest
49.0ms
(/ (- 1 (cos x)) (* x x))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize23.0ms

Local error

Found 2 expressions with local error:

14.9b
(/ (- 1 (cos x)) (* x x))
3.0b
(- 1 (cos x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
111×*-un-lft-identity
90×times-frac
60×add-cube-cbrt
34×difference-of-squares
21×swap-sqr associate-*r* associate-*l*
17×distribute-lft-out--
15×associate-/r*
9×prod-diff
7×add-cbrt-cube add-exp-log *-commutative unswap-sqr
6×associate-/l*
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 cbrt-undiv flip3-- div-exp insert-posit16 log1p-expm1-u flip-- associate-/l/
1×clear-num sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Calls
2 calls:
Slowest
22.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series136.0ms

Calls
2 calls:
Slowest
103.0ms
(/ (- 1 (cos x)) (* x x))
33.0ms
(- 1 (cos x))

simplify9.1s

Calls
235 calls:
Slowest
637.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
630.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
305.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
182.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
179.0ms
(/ (* (cbrt (- 1 (cos x))) (cbrt (- 1 (cos x)))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

15.0b
(/ (* (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)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
543×add-sqr-sqrt
435×times-frac
399×associate-*l*
313×*-un-lft-identity
277×add-cube-cbrt
212×associate-*r*
161×swap-sqr
150×unswap-sqr
82×*-commutative
32×add-cbrt-cube add-exp-log
29×associate-/r*
18×distribute-lft-out
16×pow1
15×associate-/l*
13×prod-exp cbrt-unprod
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u
3×+-commutative fma-def flip3-+ flip-+
2×distribute-rgt-in distribute-lft-in associate-/r/ sqr-sin sin-mult
1×pow2 clear-num sum-log frac-2neg pow-plus div-sub pow-sqr pow-prod-up div-inv associate-/l/
Calls
4 calls:
Slowest
87.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
35.0ms
(* (* x x) (+ 1 (cos x)))
11.0ms
(* (sin x) (sin x))
7.0ms
(+ 1 (cos x))

series213.0ms

Calls
4 calls:
Slowest
106.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
67.0ms
(* (* x x) (+ 1 (cos x)))
20.0ms
(+ 1 (cos x))
19.0ms
(* (sin x) (sin x))

simplify1.6m

Calls
1004 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)))))
1.0s
(/ (* (* (* (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)))))

prune5.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
115×times-frac
102×*-un-lft-identity
72×add-sqr-sqrt add-cube-cbrt
22×associate-/l*
15×distribute-lft-out
13×associate-/r* add-cbrt-cube add-exp-log
9×associate-/l/
8×div-inv
6×add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u
3×fma-def
2×flip3-+ associate-/r/ flip-+
1×+-commutative sum-log
Calls
4 calls:
Slowest
16.0ms
(/ (/ (sin x) x) (+ (cos x) 1))
14.0ms
(/ (sin x) x)
8.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series174.0ms

Calls
4 calls:
Slowest
59.0ms
(/ (/ (sin x) x) (+ (cos x) 1))
46.0ms
(/ (sin x) x)
45.0ms
(/ (sin x) x)
23.0ms
(+ (cos x) 1)

simplify7.2s

Calls
197 calls:
Slowest
445.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
425.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
422.0ms
(/ (/ (cbrt (sin x)) (cbrt x)) (+ (cos x) 1))
309.0ms
(/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (* (cbrt (+ (cos x) 1)) (cbrt (+ (cos x) 1))))
172.0ms
(/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)) (* (cbrt (+ (cos x) 1)) (cbrt (+ (cos x) 1))))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin x))
0.6b
(cbrt (sin x))
0.6b
(cbrt (sin x))
0.4b
(* (cbrt (sin x)) (cbrt (sin x)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
8×add-cbrt-cube
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative
Calls
4 calls:
Slowest
18.0ms
(* (cbrt (sin x)) (cbrt (sin x)))
3.0ms
(cbrt (sin x))
3.0ms
(cbrt (sin x))
2.0ms
(cbrt (sin x))

series531.0ms

Calls
4 calls:
Slowest
152.0ms
(cbrt (sin x))
135.0ms
(* (cbrt (sin x)) (cbrt (sin x)))
125.0ms
(cbrt (sin x))
119.0ms
(cbrt (sin x))

simplify1.8s

Calls
68 calls:
Slowest
273.0ms
(- (pow x 1/3) (+ (* 1/18 (pow (pow x 7) 1/3)) (* 1/3240 (pow (pow x 13) 1/3))))
238.0ms
(- (+ (pow x 2/3) (* 1/405 (pow (pow x 14) 1/3))) (* 1/9 (pow (pow x 8) 1/3)))
229.0ms
(- (pow x 1/3) (+ (* 1/18 (pow (pow x 7) 1/3)) (* 1/3240 (pow (pow x 13) 1/3))))
221.0ms
(- (pow x 1/3) (+ (* 1/18 (pow (pow x 7) 1/3)) (* 1/3240 (pow (pow x 13) 1/3))))
127.0ms
(* (* (* (cbrt (sin x)) (cbrt (sin x))) (cbrt (sin x))) (* (* (cbrt (sin x)) (cbrt (sin x))) (cbrt (sin x))))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes50.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.3s1528×body2560valid
922.0ms1258×body1280valid
779.0ms1460×body640valid
352.0ms931×body320valid
318.0ms2326×body80valid
109.0ms497×body160valid