Details

Time bar (total: 37.3s)

sample693.0ms

Algorithm
intervals
Results
280.0ms57×body2560valid
187.0ms85×body1280valid
56.0ms57×body640valid
20.0ms27×body320valid
10.0ms20×body160valid
2.0ms10×body80valid

simplify37.0ms

Calls
1 calls:
Slowest
37.0ms
(/ (- x (sin x)) (- x (tan x)))

prune345.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize18.0ms

Local error

Found 3 expressions with local error:

1.6b
(- x (sin x))
1.6b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite9.0ms

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 (sin x))
1.0ms
(- x (tan x))

series240.0ms

Calls
3 calls:
Slowest
117.0ms
(/ (- x (sin x)) (- x (tan x)))
76.0ms
(- x (tan x))
47.0ms
(- x (sin x))

simplify2.4s

Calls
39 calls:
Slowest
400.0ms
(- (+ 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)))))
388.0ms
(- (+ 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)))))
373.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
280.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
185.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune579.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b
(- x (sin x))
1.6b
(- x (tan x))
1.6b
(- x (tan x))
1.6b
(- x (tan x))

rewrite3.0ms

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 (sin x))
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))
1.0ms
(- x (tan x))

series288.0ms

Calls
4 calls:
Slowest
97.0ms
(- x (tan x))
78.0ms
(- x (tan x))
66.0ms
(- x (tan x))
46.0ms
(- x (sin x))

simplify1.2s

Calls
12 calls:
Slowest
343.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
315.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
271.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
193.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
22.0ms
(- x (/ (sin x) (cos x)))

prune675.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))
0.2b
(/ (sin x) (cos x))
0.2b
(/ (sin x) (cos x))
0.2b
(/ (sin x) (cos x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
11×flip3-+ flip-+
10×add-cbrt-cube add-exp-log frac-sub
9×associate-/r* associate-/l*
6×associate-*l/ add-log-exp
4×expm1-log1p-u frac-times pow1 insert-posit16 log1p-expm1-u
3×cbrt-undiv quot-tan clear-num frac-2neg fma-neg div-exp prod-diff div-inv
2×associate-*r/ sub-div
1×sub-neg flip3-- diff-log associate--l+ flip--
Calls
4 calls:
Slowest
26.0ms
(- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))
5.0ms
(/ (sin x) (cos x))
4.0ms
(/ (sin x) (cos x))
4.0ms
(/ (sin x) (cos x))

series300.0ms

Calls
4 calls:
Slowest
196.0ms
(- (+ 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (/ (sin x) x)))
40.0ms
(/ (sin x) (cos x))
35.0ms
(/ (sin x) (cos x))
28.0ms
(/ (sin x) (cos x))

simplify11.9s

Calls
120 calls:
Slowest
949.0ms
(* (+ (* 1 1) (- (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (* 1 (/ (/ (sin x) (cos x)) x)))) (* (+ (* 1 1) (- (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (* 1 (/ (/ (sin x) (cos x)) x)))) x))
795.0ms
(* (- 1 (/ (/ (sin x) (cos x)) x)) (* (+ (* 1 1) (- (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (* 1 (/ (/ (sin x) (cos x)) x)))) x))
725.0ms
(* (+ (* 1 1) (- (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x)) (* 1 (/ (/ (sin x) (cos x)) x)))) (* (- 1 (/ (/ (sin x) (cos x)) x)) x))
574.0ms
(- (+ (pow 1 3) (pow (/ (/ (sin x) (cos x)) x) 3)) (* (+ (pow 1 3) (pow (/ (/ (sin x) (cos x)) x) 3)) (/ (sin x) x)))
422.0ms
(- (* (- (* 1 1) (* (/ (/ (sin x) (cos x)) x) (/ (/ (sin x) (cos x)) x))) x) (* (- 1 (/ (/ (sin x) (cos x)) x)) (* (+ 1 (/ (/ (sin x) (cos x)) x)) (sin x))))

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

17.6b
(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)

rewrite1.0ms

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
(* 9/40 x)
0.0ms
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
0.0ms
(fma (* 9/40 x) x -1/2)

series169.0ms

Calls
3 calls:
Slowest
100.0ms
(fma (* 9/40 x) x -1/2)
51.0ms
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
17.0ms
(* 9/40 x)

simplify388.0ms

Calls
9 calls:
Slowest
107.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
105.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
102.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
26.0ms
(- (* 9/40 (pow x 2)) 1/2)
19.0ms
(- (* 9/40 (pow x 2)) 1/2)

prune445.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.1b

bsearch216.0ms

end0.0ms

sample15.7s

Algorithm
intervals
Results
7.0s1650×body2560valid
5.3s2798×body1280valid
2.3s1805×body640valid
609.0ms907×body320valid
239.0ms482×body160valid
82.0ms358×body80valid