Details

Time bar (total: 36.7s)

sample574.0ms

Algorithm
intervals
Results
173.0ms48×body2560valid
150.0ms87×body1280valid
60.0ms64×body640valid
33.0ms12×body160valid
27.0ms31×body320valid
3.0ms14×body80valid

simplify64.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
63.0ms
(/ (- x (sin x)) (- x (tan x)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize21.0ms

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)))

rewrite60.0ms

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
34.0ms
(/ (- x (sin x)) (- x (tan x)))
13.0ms
(- x (sin x))
9.0ms
(- x (tan x))

series241.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
91.0ms
(- x (tan x))
80.0ms
(/ (- x (sin x)) (- x (tan x)))
66.0ms
(- x (sin x))

simplify3.2s

Counts
82 → 92
Calls
82 calls:
Slowest
452.0ms
(- (+ 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)))))
416.0ms
(- (+ 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)))))
269.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
232.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
178.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune829.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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)))

rewrite73.0ms

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
43.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
18.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series563.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
263.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
117.0ms
(/ (sin x) (- x (tan x)))
93.0ms
(- x (tan x))
89.0ms
(- x (tan x))

simplify4.6s

Counts
95 → 110
Calls
95 calls:
Slowest
596.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
464.0ms
(- (+ 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)))))
455.0ms
(- (+ 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
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
248.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune939.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

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)))

rewrite97.0ms

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
61.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
21.0ms
(/ (sin x) (- x (tan x)))
9.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series526.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
91.0ms
(- x (tan x))
79.0ms
(/ (sin x) (- x (tan x)))
66.0ms
(- x (tan x))

simplify4.5s

Counts
95 → 110
Calls
95 calls:
Slowest
459.0ms
(- (+ 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)))))
427.0ms
(- (+ 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)))))
334.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
266.0ms
(+ (/ (pow (sin x) 2) (* (cos x) (pow x 2))) (+ (/ (pow (sin x) 3) (* (pow (cos x) 2) (pow x 3))) (/ (sin x) x)))
253.0ms
(- (/ x (- (pow x 3) (pow (tan x) 3))) (/ (sin x) (- (pow x 3) (pow (tan x) 3))))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize71.0ms

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))

rewrite19.0ms

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
5.0ms
(- x (tan x))
5.0ms
(- x (tan x))
4.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series320.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(- x (tan x))
81.0ms
(- x (tan x))
80.0ms
(- x (tan x))
74.0ms
(- x (tan x))

simplify1.4s

Counts
28 → 72
Calls
28 calls:
Slowest
282.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
248.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
247.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
246.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
25.0ms
(- x (/ (sin x) (cos x)))

prune986.0ms

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

bsearch193.0ms

end0.0ms

sample16.2s

Algorithm
intervals
Results
6.7s1551×body2560valid
4.8s2810×body1280valid
3.1s1866×body640valid
737.0ms928×body320valid
635.0ms462×body160valid
133.0ms383×body80valid