Details

Time bar (total: 1.2m)

sample581.0ms

Algorithm
intervals
Results
197.0ms99×body1280valid
183.0ms45×body2560valid
62.0ms61×body640valid
61.0ms28×body320valid
5.0ms11×body160valid
3.0ms12×body80valid

simplify57.0ms

Calls
1 calls:
Slowest
56.0ms
(/ (- x (sin x)) (- x (tan x)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize16.0ms

Local error

Found 3 expressions with local error:

2.0b
(- x (tan x))
1.5b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite12.0ms

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))

series282.0ms

Calls
3 calls:
Slowest
126.0ms
(/ (- x (sin x)) (- x (tan x)))
108.0ms
(- x (tan x))
47.0ms
(- x (sin x))

simplify2.5s

Calls
39 calls:
Slowest
436.0ms
(- (+ 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)))))
425.0ms
(- (+ 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)))))
385.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
284.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
171.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune589.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 3 expressions with local error:

16.6b
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
0.1b
(* 9/40 x)
0.1b
(fma (* 9/40 x) x -1/2)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×*-commutative
Calls
3 calls:
Slowest
0.0ms
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
0.0ms
(* 9/40 x)
0.0ms
(fma (* 9/40 x) x -1/2)

series80.0ms

Calls
3 calls:
Slowest
38.0ms
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
29.0ms
(fma (* 9/40 x) x -1/2)
13.0ms
(* 9/40 x)

simplify498.0ms

Calls
9 calls:
Slowest
148.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
147.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
119.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
25.0ms
(- (* 9/40 (pow x 2)) 1/2)
23.0ms
(- (* 9/40 (pow x 2)) 1/2)

prune350.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

2.0b
(- x (tan x))
2.0b
(- x (tan x))
2.0b
(- x (tan x))
1.5b
(- x (sin x))

rewrite2.0ms

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))
0.0ms
(- x (sin x))
0.0ms
(- x (tan x))
0.0ms
(- x (tan x))

series220.0ms

Calls
4 calls:
Slowest
62.0ms
(- x (tan x))
61.0ms
(- x (tan x))
57.0ms
(- x (tan x))
39.0ms
(- x (sin x))

simplify1.2s

Calls
12 calls:
Slowest
357.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
336.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
268.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
130.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
24.0ms
(- x (/ (sin x) (cos x)))

prune656.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

2.0b
(- x (tan x))
2.0b
(- x (tan x))
1.5b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite32.0ms

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
19.0ms
(- (/ 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))

series457.0ms

Calls
4 calls:
Slowest
245.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
82.0ms
(/ (sin x) (- x (tan x)))
72.0ms
(- x (tan x))
59.0ms
(- x (tan x))

simplify43.6s

Calls
239 calls:
Slowest
654.0ms
(fma (/ x (- (* x x) (* (tan x) (tan x)))) (+ x (tan x)) (- (* (/ (cbrt (sin x)) (cbrt (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
634.0ms
(fma (* (cbrt (/ x (- x (tan x)))) (cbrt (/ x (- x (tan x))))) (cbrt (/ x (- x (tan x)))) (- (* (/ (sqrt (sin x)) (cbrt (- x (tan x)))) (/ (sqrt (sin x)) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
563.0ms
(fma 1 (/ x (- x (tan x))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
558.0ms
(fma (* (cbrt (/ x (- x (tan x)))) (cbrt (/ x (- x (tan x))))) (cbrt (/ x (- x (tan x)))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
545.0ms
(fma x (/ 1 (- 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 (1 fresh and 3 done)

Merged error: 0.0b

regimes65.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch169.0ms

end0.0ms

sample16.6s

Algorithm
intervals
Results
7.3s1640×body2560valid
5.6s2732×body1280valid
2.5s1876×body640valid
759.0ms942×body320valid
203.0ms456×body160valid
90.0ms354×body80valid