Details

Time bar (total: 35.7s)

sample787.0ms

Algorithm
intervals
Results
233.0ms87×body1280valid
228.0ms48×body2560valid
176.0ms64×body640valid
29.0ms31×body320valid
6.0ms12×body160valid
4.0ms14×body80valid

simplify37.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize19.0ms

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)))

rewrite76.0ms

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
51.0ms
(/ (- x (sin x)) (- x (tan x)))
12.0ms
(- x (sin x))
8.0ms
(- x (tan x))

series295.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
109.0ms
(- x (tan x))
109.0ms
(/ (- x (sin x)) (- x (tan x)))
76.0ms
(- x (sin x))

simplify3.1s

Counts
82 → 92
Calls
82 calls:
Slowest
441.0ms
(- (+ 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)))))
411.0ms
(- (+ 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)))))
283.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
276.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
195.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune841.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.3b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (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
76.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
11.0ms
(/ (sin x) (- x (tan x)))
9.0ms
(- x (tan x))
8.0ms
(- x (tan x))

series527.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
294.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
87.0ms
(- x (tan x))
78.0ms
(/ (sin x) (- x (tan x)))
68.0ms
(- x (tan x))

simplify4.2s

Counts
95 → 110
Calls
95 calls:
Slowest
433.0ms
(- (+ 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)))))
272.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
245.0ms
(- (/ x (- (pow x 3) (pow (tan x) 3))) (/ (sin x) (- (pow x 3) (pow (tan x) 3))))
232.0ms
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))

prune875.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.3b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite102.0ms

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
73.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
15.0ms
(/ (sin x) (- x (tan x)))
7.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series474.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
243.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
90.0ms
(/ (sin x) (- x (tan x)))
72.0ms
(- x (tan x))
69.0ms
(- x (tan x))

simplify4.0s

Counts
95 → 110
Calls
95 calls:
Slowest
498.0ms
(- (+ 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
(- (+ 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)))))
240.0ms
(- (/ x (- (pow x 3) (pow (tan x) 3))) (/ (sin x) (- (pow x 3) (pow (tan x) 3))))
220.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
216.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

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))

rewrite33.0ms

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
8.0ms
(- x (tan x))
8.0ms
(- x (tan x))
8.0ms
(- x (tan x))
8.0ms
(- x (tan x))

series305.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(- x (tan x))
83.0ms
(- x (tan x))
67.0ms
(- x (tan x))
55.0ms
(- x (tan x))

simplify1.3s

Counts
28 → 72
Calls
28 calls:
Slowest
297.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
226.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
216.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
204.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
24.0ms
(- x (/ (sin x) (cos x)))

prune911.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch190.0ms

end0.0ms

sample16.1s

Algorithm
intervals
Results
6.5s1551×body2560valid
5.9s2810×body1280valid
2.5s1866×body640valid
755.0ms928×body320valid
222.0ms462×body160valid
95.0ms383×body80valid