Details

Time bar (total: 7.4m)

sample190.0ms

Algorithm
intervals
Results
87.0ms50×body2560valid
35.0ms41×body1280valid
27.0ms48×body640valid
12.0ms29×body320valid
12.0ms68×body80valid
6.0ms20×body160valid

simplify60.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
104×*-un-lft-identity
90×times-frac
53×add-cube-cbrt
34×difference-of-squares
21×swap-sqr associate-*r* associate-*l*
17×distribute-lft-out--
15×associate-/r*
7×add-cbrt-cube add-exp-log *-commutative unswap-sqr
6×associate-/l*
4×add-log-exp
2×pow1 cbrt-undiv flip3-- div-exp insert-posit16 flip-- associate-/l/
1×clear-num sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Calls
2 calls:
Slowest
58.0ms
(/ (- 1 (cos x)) (* x x))
10.0ms
(- 1 (cos x))

series115.0ms

Calls
2 calls:
Slowest
75.0ms
(/ (- 1 (cos x)) (* x x))
40.0ms
(- 1 (cos x))

simplify8.5s

Calls
215 calls:
Slowest
746.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
591.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
374.0ms
(/ (- 1 (cos x)) (sqrt x))
254.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
240.0ms
(/ (* (cbrt (- 1 (cos x))) (cbrt (- 1 (cos x)))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 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)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
542×add-sqr-sqrt
435×times-frac
399×associate-*l*
312×*-un-lft-identity
276×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×pow-prod-down associate-*r/ insert-posit16
3×+-commutative 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
73.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
58.0ms
(* (* x x) (+ 1 (cos x)))
23.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series225.0ms

Calls
4 calls:
Slowest
102.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
72.0ms
(* (* x x) (+ 1 (cos x)))
33.0ms
(* (sin x) (sin x))
17.0ms
(+ 1 (cos x))

simplify1.7m

Calls
1002 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) (* 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) (+ 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)))))

prune6.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (tan (/ x 2)) x)
0.1b
(/ (sin x) x)
0.1b
(* (/ (sin x) x) (/ (tan (/ x 2)) x))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
90×frac-times
87×add-sqr-sqrt
76×*-un-lft-identity
75×add-cube-cbrt
70×associate-/l*
69×associate-/r*
40×times-frac
24×clear-num
23×frac-2neg
19×add-cbrt-cube add-exp-log
13×associate-*r* associate-*l*
11×tan-quot associate-/l/
10×associate-*r/
9×associate-*l/
6×cbrt-undiv div-exp
5×pow1
4×prod-exp cbrt-unprod div-inv unswap-sqr
3×insert-posit16 add-log-exp
2×un-div-inv
1×pow-prod-down *-commutative
Calls
3 calls:
Slowest
46.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
9.0ms
(/ (tan (/ x 2)) x)
9.0ms
(/ (sin x) x)

series227.0ms

Calls
3 calls:
Slowest
125.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
66.0ms
(/ (tan (/ x 2)) x)
37.0ms
(/ (sin x) x)

simplify13.6s

Calls
299 calls:
Slowest
655.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (tan (/ x 2)) x) (/ (tan (/ x 2)) x)) (/ (tan (/ x 2)) x)))
412.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
383.0ms
(/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x))
372.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x)))
307.0ms
(/ (* (sin x) (sin (* 1/2 x))) (* (cos (* 1/2 x)) (pow x 2)))

prune2.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cos (* x 1/2)) (/ (sin x) x))
0.1b
(/ (sin x) x)
0.1b
(/ (sin (* x 1/2)) x)
0.1b
(/ (/ (sin (* x 1/2)) x) (/ (cos (* x 1/2)) (/ (sin x) x)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
2179×times-frac
963×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
154×associate-/r/
132×associate-/r*
118×div-inv
73×associate-/l*
34×add-cbrt-cube add-exp-log
21×clear-num frac-2neg
20×cbrt-undiv div-exp
9×associate-/l/
4×pow1 insert-posit16 add-log-exp
Calls
4 calls:
Slowest
64.0ms
(/ (cos (* x 1/2)) (/ (sin x) x))
40.0ms
(/ (/ (sin (* x 1/2)) x) (/ (cos (* x 1/2)) (/ (sin x) x)))
37.0ms
(/ (sin (* x 1/2)) x)
17.0ms
(/ (sin x) x)

series269.0ms

Calls
4 calls:
Slowest
123.0ms
(/ (/ (sin (* x 1/2)) x) (/ (cos (* x 1/2)) (/ (sin x) x)))
56.0ms
(/ (cos (* x 1/2)) (/ (sin x) x))
47.0ms
(/ (sin (* x 1/2)) x)
43.0ms
(/ (sin x) x)

simplify4.9m

Calls
1616 calls:
Slowest
1.0s
(- (- (log (sin (* x 1/2))) (log x)) (- (log (cos (* x 1/2))) (- (log (sin x)) (log x))))
956.0ms
(/ (/ (* (cbrt (sin (* x 1/2))) (cbrt (sin (* x 1/2)))) (sqrt x)) (/ (sqrt (cos (* x 1/2))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x)))))
821.0ms
(/ (/ (* (cbrt (sin (* x 1/2))) (cbrt (sin (* x 1/2)))) (* (cbrt x) (cbrt x))) (/ 1 (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x)))))
789.0ms
(/ (/ (* (cbrt (sin (* x 1/2))) (cbrt (sin (* x 1/2)))) 1) (/ (* (cbrt (cos (* x 1/2))) (cbrt (cos (* x 1/2)))) 1))
744.0ms
(/ (/ (* (cbrt (sin (* x 1/2))) (cbrt (sin (* x 1/2)))) 1) (/ (* (cbrt (cos (* x 1/2))) (cbrt (cos (* x 1/2)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x))))

prune11.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes98.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.2s1528×body2560valid
921.0ms1258×body1280valid
828.0ms1460×body640valid
351.0ms931×body320valid
322.0ms2326×body80valid
155.0ms497×body160valid