Details

Time bar (total: 30.7s)

sample556.0ms

Algorithm
intervals
Results
197.0ms51×body2560valid
173.0ms97×body1280valid
103.0ms57×body640valid
19.0ms26×body320valid
7.0ms16×body160valid
2.0ms9×body80valid

simplify36.0ms

Calls
1 calls:
Slowest
36.0ms
(/ (- x (sin x)) (- x (tan x)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize48.0ms

Local error

Found 3 expressions with local error:

1.5b
(- x (tan x))
1.3b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
4×flip3-- flip--
3×pow1 associate-/r* insert-posit16 associate-/l* add-log-exp
2×sub-neg associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Calls
3 calls:
Slowest
4.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
1.0ms
(- x (sin x))

series211.0ms

Calls
3 calls:
Slowest
113.0ms
(/ (- x (sin x)) (- x (tan x)))
60.0ms
(- x (tan x))
38.0ms
(- x (sin x))

simplify2.1s

Calls
39 calls:
Slowest
319.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
305.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
294.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
225.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
128.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune580.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.5b
(- x (tan x))
1.5b
(- x (tan x))
1.1b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt
10×times-frac
6×flip3-- add-cbrt-cube add-exp-log associate-/r/ flip-- add-log-exp
4×pow1 insert-posit16
3×associate-/r* sub-neg distribute-rgt-out-- div-inv associate-/l*
2×difference-of-squares
1×cbrt-undiv clear-num frac-2neg diff-log div-exp frac-sub distribute-lft-out-- sub-div
Calls
4 calls:
Slowest
15.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
8.0ms
(/ (sin x) (- x (tan x)))
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))

series405.0ms

Calls
4 calls:
Slowest
209.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
83.0ms
(- x (tan x))
57.0ms
(- x (tan x))
55.0ms
(/ (sin x) (- x (tan x)))

simplify3.2s

Calls
55 calls:
Slowest
351.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
339.0ms
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))
286.0ms
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))
270.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
228.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune742.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.5b
(- x (tan x))
1.5b
(- x (tan x))
1.5b
(- x (tan x))
1.5b
(- x (tan x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 sub-neg *-un-lft-identity flip3-- add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 flip-- add-log-exp
Calls
4 calls:
Slowest
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))

series233.0ms

Calls
4 calls:
Slowest
74.0ms
(- x (tan x))
60.0ms
(- x (tan x))
53.0ms
(- x (tan x))
45.0ms
(- x (tan x))

simplify1.0s

Calls
12 calls:
Slowest
239.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
239.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
221.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
191.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
22.0ms
(- x (/ (sin x) (cos x)))

prune718.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b
(- x (tan x))
1.5b
(- x (tan x))
1.1b
(+ (/ x (- x (tan x))) (- (/ (sin x) (- x (tan x)))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt
9×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/r/
5×flip3-- flip--
4×pow1 insert-posit16
3×distribute-lft-neg-in associate-/r* distribute-rgt-out div-inv associate-/l*
2×sum-log sub-neg distribute-lft-out
1×neg-sub0 cbrt-undiv +-commutative clear-num associate-+r- distribute-rgt-neg-in frac-2neg flip3-+ div-exp unsub-neg neg-log frac-add flip-+ distribute-neg-frac
Calls
4 calls:
Slowest
20.0ms
(+ (/ x (- x (tan x))) (- (/ (sin x) (- x (tan x)))))
9.0ms
(/ (sin x) (- x (tan x)))
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))

series466.0ms

Calls
4 calls:
Slowest
255.0ms
(+ (/ x (- x (tan x))) (- (/ (sin x) (- x (tan x)))))
79.0ms
(/ (sin x) (- x (tan x)))
72.0ms
(- x (tan x))
59.0ms
(- x (tan x))

simplify3.5s

Calls
54 calls:
Slowest
377.0ms
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))
362.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
355.0ms
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))
338.0ms
(+ (* x (- x (tan x))) (* (- x (tan x)) (- (sin x))))
284.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))

prune825.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch173.0ms

end0.0ms

sample15.7s

Algorithm
intervals
Results
7.4s1598×body2560valid
5.1s2760×body1280valid
2.0s1849×body640valid
756.0ms931×body320valid
242.0ms474×body160valid
94.0ms388×body80valid