Details

Time bar (total: 38.9s)

sample447.0ms

Algorithm
intervals
Results
189.0ms46×body2560valid
99.0ms80×body1280valid
54.0ms70×body640valid
21.0ms36×body320valid
4.0ms12×body160valid
3.0ms12×body80valid

simplify58.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
57.0ms
(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize37.0ms

Local error

Found 3 expressions with local error:

1.4b
(- x (sin x))
1.4b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt *-un-lft-identity
25×times-frac
15×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×pow1 insert-posit16
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
3 → 83
Calls
3 calls:
Slowest
17.0ms
(/ (- x (sin x)) (- x (tan x)))
7.0ms
(- x (sin x))
4.0ms
(- x (tan x))

series253.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
110.0ms
(/ (- x (sin x)) (- x (tan x)))
90.0ms
(- x (tan x))
53.0ms
(- x (sin x))

simplify3.3s

Counts
82 → 92
Calls
82 calls:
Slowest
453.0ms
(- (+ 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)))))
333.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
302.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
227.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune961.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.4b
(- x (tan x))
1.4b
(- x (tan x))
0.2b
(/ (sin x) (- x (tan x)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
44×add-sqr-sqrt
33×times-frac
18×distribute-lft-out--
16×add-cube-cbrt
12×difference-of-squares
10×add-log-exp
6×flip3-- add-cbrt-cube add-exp-log associate-/r/ flip--
5×associate-/r*
4×pow1 insert-posit16
3×sub-neg distribute-rgt-out-- diff-log div-inv associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp frac-sub sub-div
Counts
4 → 98
Calls
4 calls:
Slowest
83.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
12.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series504.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
278.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
86.0ms
(/ (sin x) (- x (tan x)))
81.0ms
(- x (tan x))
58.0ms
(- x (tan x))

simplify4.1s

Counts
95 → 110
Calls
95 calls:
Slowest
497.0ms
(- (+ 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)))))
401.0ms
(- (+ 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)))))
273.0ms
(- (/ x (- (pow x 3) (pow (tan x) 3))) (/ (sin x) (- (pow x 3) (pow (tan x) 3))))
261.0ms
(- (* x (- x (tan x))) (* (- x (tan x)) (sin x)))
240.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.4b
(- x (tan x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-log-exp
4×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
Slowest
9.0ms
(- x (tan x))
8.0ms
(- x (tan x))
8.0ms
(- x (tan x))
8.0ms
(- x (tan x))

series759.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
490.0ms
(- x (tan x))
101.0ms
(- x (tan x))
92.0ms
(- x (tan x))
75.0ms
(- x (tan x))

simplify1.3s

Counts
28 → 72
Calls
28 calls:
Slowest
324.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
280.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
245.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
230.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
24.0ms
(- x (/ (sin x) (cos x)))

prune625.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

17.3b
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
0.2b
(* (* x x) 9/40)
0.1b
(* (* x x) (* x x))
0.1b
(* (* (* x x) (* x x)) 27/2800)

rewrite348.0ms

Algorithm
rewrite-expression-head
Rules
138×pow1
39×add-cbrt-cube pow-prod-down add-exp-log
36×pow-prod-up
24×prod-exp cbrt-unprod
22×pow-sqr
18×pow-plus
13×pow2
9×add-log-exp
8×add-sqr-sqrt
7×associate-*r*
6×*-un-lft-identity add-cube-cbrt
4×insert-posit16
3×associate-*l* *-commutative unswap-sqr
2×diff-log
1×sum-log sub-neg flip3-- swap-sqr flip-- associate--r+
Counts
4 → 128
Calls
4 calls:
Slowest
171.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
100.0ms
(* (* (* x x) (* x x)) 27/2800)
45.0ms
(* (* x x) (* x x))
27.0ms
(* (* x x) 9/40)

series199.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
63.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
52.0ms
(* (* x x) (* x x))
51.0ms
(* (* (* x x) (* x x)) 27/2800)
32.0ms
(* (* x x) 9/40)

simplify6.6s

Counts
111 → 140
Calls
111 calls:
Slowest
513.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
415.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
395.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
381.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
372.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch144.0ms

end0.0ms

sample16.9s

Algorithm
intervals
Results
8.2s1654×body2560valid
5.5s2790×body1280valid
1.9s1833×body640valid
748.0ms912×body320valid
262.0ms484×body160valid
83.0ms327×body80valid