Details

Time bar (total: 34.4s)

sample186.0ms

Algorithm
intervals
Results
58.0ms45×body2560valid
40.0ms52×body1280valid
33.0ms72×body80valid
27.0ms49×body640valid
12.0ms27×body320valid
3.0ms11×body160valid

simplify60.0ms

Calls
1 calls:
Slowest
60.0ms
(/ (- 1 (cos x)) (* x x))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize22.0ms

Local error

Found 2 expressions with local error:

14.7b
(/ (- 1 (cos x)) (* x x))
2.6b
(- 1 (cos x))

rewrite11.0ms

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×pow1 flip3-- insert-posit16 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
9.0ms
(/ (- 1 (cos x)) (* x x))
2.0ms
(- 1 (cos x))

series86.0ms

Calls
2 calls:
Slowest
57.0ms
(/ (- 1 (cos x)) (* x x))
29.0ms
(- 1 (cos x))

simplify1.6s

Calls
19 calls:
Slowest
795.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
150.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
139.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
85.0ms
(- (log (- 1 (cos x))) (log (* x x)))
64.0ms
(/ (- 1 (cos x)) (pow x 2))

prune468.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

14.4b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.3b
(* (sin x) (sin x))
0.2b
(+ 1 (cos x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite39.0ms

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×cbrt-undiv div-exp associate-*l* associate-*r/ insert-posit16 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
19.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
8.0ms
(* (* x x) (+ 1 (cos x)))
8.0ms
(* (sin x) (sin x))
2.0ms
(+ 1 (cos x))

series134.0ms

Calls
4 calls:
Slowest
64.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
35.0ms
(* (* x x) (+ 1 (cos x)))
22.0ms
(* (sin x) (sin x))
13.0ms
(+ 1 (cos x))

simplify9.7s

Calls
51 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
(* (* (* (* 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) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x 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)))))
965.0ms
(/ (* (* (* (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: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

14.4b
(/ (* (sin x) (sin x)) (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x)))))
2.7b
(- (* (cos x) (cos x)) (cos x))
0.3b
(pow (cos x) 3)
0.3b
(* (sin x) (sin x))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
28×add-cbrt-cube add-exp-log
15×times-frac
13×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
10×pow1 cbrt-undiv div-exp
9×associate-/r*
6×prod-exp cbrt-unprod add-log-exp
5×associate-/r/
4×insert-posit16
3×unpow-prod-down cube-prod associate-*r* associate-*l* div-inv
2×flip3-+ flip-+ sqr-sin sin-mult
1×pow2 cube-mult pow-to-exp sqr-cos clear-num sub-neg pow-pow frac-2neg pow-plus flip3-- distribute-rgt-out-- diff-log unpow3 div-sub pow-prod-down pow-exp associate--l+ *-commutative pow-prod-up flip-- associate-/l* rem-cube-cbrt difference-of-squares associate-/l/
Calls
4 calls:
Slowest
32.0ms
(/ (* (sin x) (sin x)) (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x)))))
16.0ms
(- (* (cos x) (cos x)) (cos x))
8.0ms
(* (sin x) (sin x))
2.0ms
(pow (cos x) 3)

series212.0ms

Calls
4 calls:
Slowest
119.0ms
(/ (* (sin x) (sin x)) (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x)))))
53.0ms
(- (* (cos x) (cos x)) (cos x))
23.0ms
(pow (cos x) 3)
17.0ms
(* (sin x) (sin x))

simplify11.2s

Calls
82 calls:
Slowest
1.9s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (/ (* (* (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (* (* x x) (+ (pow 1 3) (pow (cos x) 3)))) (* (* x x) (+ (pow 1 3) (pow (cos x) 3)))) (* (* (+ 1 (- (* (cos x) (cos x)) (cos x))) (+ 1 (- (* (cos x) (cos x)) (cos x)))) (+ 1 (- (* (cos x) (cos x)) (cos x))))))
735.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x)))) (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x))))) (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x))))))
725.0ms
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x)))) (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x))))) (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x))))))
323.0ms
(/ (sin x) (* (cbrt (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x))))) (cbrt (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x)))))))
292.0ms
(/ (sin x) (sqrt (/ (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (+ 1 (- (* (cos x) (cos x)) (cos x))))))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

13.8b
(/ (sin x) (* x x))
0.4b
(* (/ (sin x) (* x x)) (tan (/ x 2)))

rewrite19.0ms

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×cbrt-undiv div-exp prod-exp tan-quot cbrt-unprod insert-posit16 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
14.0ms
(* (/ (sin x) (* x x)) (tan (/ x 2)))
4.0ms
(/ (sin x) (* x x))

series105.0ms

Calls
2 calls:
Slowest
80.0ms
(* (/ (sin x) (* x x)) (tan (/ x 2)))
25.0ms
(/ (sin x) (* x x))

simplify2.0s

Calls
34 calls:
Slowest
277.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) (* x x)) (* x x)))
231.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) (* x x)) (* x x))) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))))
216.0ms
(/ (* (sin x) (sin (* 1/2 x))) (* (cos (* 1/2 x)) (pow x 2)))
212.0ms
(/ (* (sin x) (sin (* 1/2 x))) (* (cos (* 1/2 x)) (pow x 2)))
167.0ms
(- (+ (* 1/120 (pow x 3)) (/ 1 x)) (* 1/6 x))

prune496.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch3.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.8s1637×body2560valid
1.4s1227×body1280valid
905.0ms949×body320valid
756.0ms1513×body640valid
232.0ms2223×body80valid
103.0ms451×body160valid