Details

Time bar (total: 57.5s)

sample598.0ms

Algorithm
intervals
Results
196.0ms54×body2560valid
184.0ms80×body1280valid
69.0ms69×body640valid
19.0ms29×body320valid
5.0ms13×body160valid
2.0ms11×body80valid

simplify64.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize18.0ms

Local error

Found 3 expressions with local error:

1.2b
(- x (tan x))
1.2b
(- x (sin 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)))
6.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series221.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
111.0ms
(/ (- x (sin x)) (- x (tan x)))
67.0ms
(- x (tan x))
43.0ms
(- x (sin x))

simplify6.0s

Counts
125 → 92
Calls
125 calls:
Slowest
428.0ms
(- (+ 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)))))
402.0ms
(- (+ 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)))))
375.0ms
(* (* (- x (sin x)) (- x (sin x))) (- x (sin x)))
351.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
335.0ms
(* (* (- x (tan x)) (- x (tan x))) (- x (tan x)))

prune825.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.2b
(- x (tan x))
1.2b
(- x (tan x))
0.2b
(/ (sin x) (- x (tan x)))

rewrite76.0ms

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
48.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
17.0ms
(/ (sin x) (- x (tan x)))
4.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series958.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
512.0ms
(- x (tan x))
303.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
74.0ms
(/ (sin x) (- x (tan x)))
68.0ms
(- x (tan x))

simplify7.9s

Counts
139 → 110
Calls
139 calls:
Slowest
506.0ms
(* (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))) (/ (sin x) (- x (tan x))))
479.0ms
(- (+ 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)))))
475.0ms
(- (+ 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
(+ (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (+ (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))) (* (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))))
379.0ms
(- (pow (/ x (- x (tan x))) 3) (pow (/ (sin x) (- x (tan x))) 3))

prune849.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b
(- x (tan x))
1.2b
(- x (sin x))
0.1b
(* (/ 1 (- x (tan x))) (- x (sin x)))
0.0b
(/ 1 (- x (tan x)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
45×*-un-lft-identity
32×times-frac
24×add-cube-cbrt
21×associate-*l*
17×add-exp-log
11×add-cbrt-cube
10×distribute-lft-out-- difference-of-squares
8×add-log-exp
7×pow1
6×flip3-- flip--
5×associate-/r* associate-*r*
4×sub-neg div-exp prod-exp associate-/r/ insert-posit16
3×associate-/l* unswap-sqr
2×distribute-rgt-in frac-times cbrt-undiv rec-exp distribute-lft-in diff-log 1-exp associate-*r/ cbrt-unprod div-inv
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative pow-flip inv-pow
Counts
4 → 126
Calls
4 calls:
Slowest
42.0ms
(* (/ 1 (- x (tan x))) (- x (sin x)))
8.0ms
(/ 1 (- x (tan x)))
5.0ms
(- x (sin x))
4.0ms
(- x (tan x))

series308.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(* (/ 1 (- x (tan x))) (- x (sin x)))
68.0ms
(- x (tan x))
63.0ms
(/ 1 (- x (tan x)))
54.0ms
(- x (sin x))

simplify13.9s

Counts
167 → 138
Calls
167 calls:
Slowest
952.0ms
(* (* (* (/ 1 (- x (tan x))) (/ 1 (- x (tan x)))) (/ 1 (- x (tan x)))) (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))))
552.0ms
(/ (* (* 1 1) 1) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
479.0ms
(- (+ 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)))))
469.0ms
(- (+ 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)))))
432.0ms
(* (/ 1 (- x (tan x))) (- (* x x) (* (sin x) (sin x))))

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x x) 27/2800)
0.1b
(* (* x x) (- (* (* x x) 27/2800) 9/40))
0.0b
(- (* (* x x) 27/2800) 9/40)

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×associate-*r* pow-prod-down prod-exp cbrt-unprod
5×*-un-lft-identity add-cube-cbrt add-log-exp
3×sub-neg insert-posit16
2×distribute-rgt-in distribute-lft-in flip3-- associate-*l* associate-*r/ *-commutative flip-- unswap-sqr
1×diff-log
Counts
3 → 59
Calls
3 calls:
Slowest
92.0ms
(* (* x x) (- (* (* x x) 27/2800) 9/40))
20.0ms
(* (* x x) 27/2800)
20.0ms
(- (* (* x x) 27/2800) 9/40)

series300.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
154.0ms
(* (* x x) (- (* (* x x) 27/2800) 9/40))
104.0ms
(- (* (* x x) 27/2800) 9/40)
43.0ms
(* (* x x) 27/2800)

simplify6.5s

Counts
74 → 68
Calls
74 calls:
Slowest
544.0ms
(* (* x x) (- (pow (* (* x x) 27/2800) 3) (pow 9/40 3)))
414.0ms
(exp (* (* x x) (- (* (* x x) 27/2800) 9/40)))
362.0ms
(+ (* (* (* x x) 27/2800) (* (* x x) 27/2800)) (+ (* 9/40 9/40) (* (* (* x x) 27/2800) 9/40)))
331.0ms
(- (* (* (* x x) 27/2800) (* (* x x) 27/2800)) (* 9/40 9/40))
305.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* 27/2800 27/2800) 27/2800))

prune494.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes56.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch209.0ms

end0.0ms

sample16.8s

Algorithm
intervals
Results
7.0s1674×body2560valid
5.6s2715×body1280valid
2.6s1832×body640valid
715.0ms963×body320valid
678.0ms480×body160valid
80.0ms336×body80valid