Details

Time bar (total: 1.2m)

sample511.0ms

Algorithm
intervals
Results
177.0ms51×body2560valid
125.0ms97×body1280valid
78.0ms57×body640valid
53.0ms26×body320valid
6.0ms16×body160valid
2.0ms9×body80valid

simplify39.0ms

Calls
1 calls:
Slowest
38.0ms
(/ (- x (sin x)) (- x (tan x)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize29.0ms

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)))

rewrite28.0ms

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×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u 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)))
2.0ms
(- x (tan x))
1.0ms
(- x (sin x))

series179.0ms

Calls
3 calls:
Slowest
90.0ms
(/ (- x (sin x)) (- x (tan x)))
60.0ms
(- x (tan x))
29.0ms
(- x (sin x))

simplify2.4s

Calls
39 calls:
Slowest
422.0ms
(- (+ 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)))))
420.0ms
(- (+ 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)))))
305.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
299.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
186.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune727.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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
90×prod-diff
75×add-sqr-sqrt
72×*-un-lft-identity
70×add-cube-cbrt
64×times-frac
50×associate-/r/
28×flip3-- flip--
25×div-inv
6×add-cbrt-cube fma-neg add-exp-log add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×associate-/r* sub-neg distribute-rgt-out-- 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
14.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms
(/ (sin x) (- x (tan x)))
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))

series413.0ms

Calls
4 calls:
Slowest
219.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
74.0ms
(- x (tan x))
71.0ms
(/ (sin x) (- x (tan x)))
49.0ms
(- x (tan x))

simplify40.6s

Calls
239 calls:
Slowest
784.0ms
(fma (- (/ (cbrt (sin x)) (cbrt (- x (tan x))))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (cbrt (sin x)) (cbrt (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))
546.0ms
(fma (sqrt (/ x (- x (tan x)))) (sqrt (/ x (- x (tan x)))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
542.0ms
(fma (- (/ (sin x) (cbrt (- x (tan x))))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))
511.0ms
(fma 1 (/ x (- x (tan x))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
509.0ms
(fma (- (/ (sin x) (cbrt (- x (tan x))))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 sub-neg *-un-lft-identity flip3-- add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u 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))

series232.0ms

Calls
4 calls:
Slowest
76.0ms
(- x (tan x))
57.0ms
(- x (tan x))
52.0ms
(- x (tan x))
47.0ms
(- x (tan x))

simplify1.2s

Calls
12 calls:
Slowest
326.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
276.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
251.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
248.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
14.0ms
(- x (/ (sin x) (cos x)))

prune652.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
9×times-frac
8×associate-/r/ add-log-exp
6×fma-def flip3-- add-cbrt-cube add-exp-log flip--
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u div-inv
3×distribute-lft-neg-in associate-/r* distribute-rgt-out 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
22.0ms
(+ (/ 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))

series486.0ms

Calls
4 calls:
Slowest
272.0ms
(+ (/ x (- x (tan x))) (- (/ (sin x) (- x (tan x)))))
89.0ms
(/ (sin x) (- x (tan x)))
66.0ms
(- x (tan x))
59.0ms
(- x (tan x))

simplify4.0s

Calls
58 calls:
Slowest
474.0ms
(- (+ 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)))))
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)))))
346.0ms
(+ (/ (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
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))
329.0ms
(+ (* x (- x (tan x))) (* (- x (tan x)) (- (sin x))))

prune802.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

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

bsearch211.0ms

end0.0ms

sample16.9s

Algorithm
intervals
Results
6.7s1598×body2560valid
5.2s2760×body1280valid
2.4s1849×body640valid
2.0s931×body320valid
211.0ms474×body160valid
96.0ms388×body80valid