Details

Time bar (total: 19.2s)

sample127.0ms

Algorithm
intervals
Results
58.0ms57×body2560valid
24.0ms38×body1280valid
16.0ms35×body640valid
8.0ms27×body320valid
8.0ms80×body80valid
4.0ms19×body160valid

simplify46.0ms

Calls
1 calls:
Slowest
46.0ms
(/ (- 1 (cos x)) (* x x))

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize26.0ms

Local error

Found 2 expressions with local error:

16.8b
(/ (- 1 (cos x)) (* x x))
2.1b
(- 1 (cos x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×times-frac associate-/l*
2×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip-- add-log-exp associate-/l/
1×cbrt-undiv clear-num associate-/r* sub-neg frac-2neg div-sub div-exp div-inv
Calls
2 calls:
Slowest
10.0ms
(/ (- 1 (cos x)) (* x x))
2.0ms
(- 1 (cos x))

series118.0ms

Calls
2 calls:
Slowest
76.0ms
(/ (- 1 (cos x)) (* x x))
42.0ms
(- 1 (cos x))

simplify1.3s

Calls
19 calls:
Slowest
589.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
147.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
144.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
88.0ms
(- (log (- 1 (cos x))) (log (* x x)))
49.0ms
(/ (- 1 (cos x)) (pow x 2))

prune372.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

16.5b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.5b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
11×pow1
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-*r* prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp associate-*l* associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×pow-prod-down associate-/r/ *-commutative sqr-sin sin-mult
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-prod-up div-inv associate-/l* associate-/l/
Calls
4 calls:
Slowest
12.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
9.0ms
(* (sin x) (sin x))
9.0ms
(* (* x x) (+ 1 (cos x)))
2.0ms
(+ 1 (cos x))

series186.0ms

Calls
4 calls:
Slowest
90.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
64.0ms
(* (* x x) (+ 1 (cos x)))
21.0ms
(* (sin x) (sin x))
12.0ms
(+ 1 (cos x))

simplify7.4s

Calls
51 calls:
Slowest
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)))))
956.0ms
(/ (* (* (* (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)))))
919.0ms
(/ (* (* (* (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)))))
856.0ms
(/ (* (* (* (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)))))
481.0ms
(- (+ (log (sin x)) (log (sin x))) (+ (log (* x x)) (log (+ 1 (cos x)))))

prune911.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

16.1b
(/ (sin x) (* x x))
0.2b
(* (/ (sin x) (* x x)) (tan (/ x 2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
7×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
6×times-frac
4×pow1
3×associate-*r* associate-/l*
2×expm1-log1p-u cbrt-undiv div-exp prod-exp tan-quot cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
1×frac-times clear-num associate-/r* frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Calls
2 calls:
Slowest
9.0ms
(* (/ (sin x) (* x x)) (tan (/ x 2)))
4.0ms
(/ (sin x) (* x x))

series149.0ms

Calls
2 calls:
Slowest
110.0ms
(* (/ (sin x) (* x x)) (tan (/ x 2)))
38.0ms
(/ (sin x) (* x x))

simplify1.9s

Calls
34 calls:
Slowest
307.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) (* x x)) (* x x)))
261.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) (* x x)) (* x x))) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))))
258.0ms
(/ (* (sin x) (sin (* 1/2 x))) (* (cos (* 1/2 x)) (pow x 2)))
189.0ms
(+ (- (log (sin x)) (log (* x x))) (log (tan (/ x 2))))
171.0ms
(/ (* (sin x) (sin (* 1/2 x))) (* (cos (* 1/2 x)) (pow x 2)))

prune462.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin x))
0.6b
(cbrt (sin x))
0.6b
(cbrt (sin x))
0.5b
(* (cbrt (sin x)) (cbrt (sin x)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
10.0ms
(* (cbrt (sin x)) (cbrt (sin x)))
1.0ms
(cbrt (sin x))
1.0ms
(cbrt (sin x))
1.0ms
(cbrt (sin x))

series808.0ms

Calls
4 calls:
Slowest
380.0ms
(cbrt (sin x))
156.0ms
(cbrt (sin x))
145.0ms
(cbrt (sin x))
127.0ms
(* (cbrt (sin x)) (cbrt (sin x)))

simplify627.0ms

Calls
41 calls:
Slowest
146.0ms
(- (pow x 1/3) (+ (* 1/18 (pow (pow x 7) 1/3)) (* 1/3240 (pow (pow x 13) 1/3))))
120.0ms
(- (pow x 1/3) (+ (* 1/18 (pow (pow x 7) 1/3)) (* 1/3240 (pow (pow x 13) 1/3))))
112.0ms
(- (+ (pow x 2/3) (* 1/405 (pow (pow x 14) 1/3))) (* 1/9 (pow (pow x 8) 1/3)))
103.0ms
(- (pow x 1/3) (+ (* 1/18 (pow (pow x 7) 1/3)) (* 1/3240 (pow (pow x 13) 1/3))))
9.0ms
(pow (pow (sin x) 2) 1/3)

prune797.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch2.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.8s1643×body2560valid
848.0ms1297×body1280valid
544.0ms1406×body640valid
245.0ms2273×body80valid
231.0ms899×body320valid
88.0ms482×body160valid