Details

Time bar (total: 26.8s)

sample619.0ms

Algorithm
intervals
Results
243.0ms57×body2560valid
218.0ms85×body1280valid
61.0ms57×body640valid
25.0ms27×body320valid
10.0ms20×body160valid
3.0ms10×body80valid

simplify41.0ms

Calls
1 calls:
Slowest
40.0ms
(/ (- x (sin x)) (- x (tan x)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize31.0ms

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)))

rewrite14.0ms

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
8.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series256.0ms

Calls
3 calls:
Slowest
111.0ms
(- x (tan x))
99.0ms
(/ (- x (sin x)) (- x (tan x)))
46.0ms
(- x (sin x))

simplify1.9s

Calls
39 calls:
Slowest
326.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
282.0ms
(- (+ 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)))))
276.0ms
(- (+ 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)))))
232.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
118.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune626.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0ms

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

series240.0ms

Calls
4 calls:
Slowest
72.0ms
(- x (tan x))
68.0ms
(- x (tan x))
67.0ms
(- x (tan x))
33.0ms
(- x (sin x))

simplify862.0ms

Calls
12 calls:
Slowest
232.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
201.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
198.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
116.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
21.0ms
(- x (/ (sin x) (cos x)))

prune690.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
10×add-cbrt-cube add-exp-log
9×associate-/r* associate-/l*
4×pow1 insert-posit16 add-log-exp
3×cbrt-undiv quot-tan clear-num frac-2neg div-exp div-inv
1×sub-neg flip3-- flip--
Calls
4 calls:
Slowest
14.0ms
(/ (sin x) (cos x))
8.0ms
(/ (sin x) (cos x))
7.0ms
(/ (sin x) (cos x))
3.0ms
(- 1 (/ (sin x) x))

series188.0ms

Calls
4 calls:
Slowest
74.0ms
(- 1 (/ (sin x) x))
42.0ms
(/ (sin x) (cos x))
37.0ms
(/ (sin x) (cos x))
36.0ms
(/ (sin x) (cos x))

simplify1.5s

Calls
87 calls:
Slowest
153.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
150.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
148.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
92.0ms
(- (+ (* 1/6 (pow x 2)) (* 1/5040 (pow x 6))) (* 1/120 (pow x 4)))
86.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))

prune1.1s

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
3×pow1 add-cbrt-cube add-exp-log insert-posit16
2×sub-neg *-commutative associate--r+
1×flip3-- diff-log flip-- associate--r-
Calls
3 calls:
Slowest
7.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
3.0ms
(* (* x x) 9/40)
2.0ms
(* (pow x 4) 27/2800)

series578.0ms

Calls
3 calls:
Slowest
479.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
68.0ms
(* (pow x 4) 27/2800)
31.0ms
(* (* x x) 9/40)

simplify565.0ms

Calls
14 calls:
Slowest
182.0ms
(/ (exp (* (* x x) 9/40)) (exp (- (* (pow x 4) 27/2800) -1/2)))
108.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
91.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
88.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
17.0ms
(* 9/40 (pow x 2))

prune393.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

99.1% (0.3b remaining)

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

bsearch195.0ms

end0.0ms

sample16.7s

Algorithm
intervals
Results
7.5s1650×body2560valid
5.0s2798×body1280valid
2.1s1805×body640valid
1.1s482×body160valid
654.0ms907×body320valid
87.0ms358×body80valid