Details

Time bar (total: 40.6s)

sample479.0ms

Algorithm
intervals
Results
286.0ms93×body2560valid
111.0ms82×body1280valid
44.0ms53×body640valid
11.0ms256×pre80true
10.0ms16×body320valid
3.0ms8×body160valid
1.0ms4×body80valid

simplify47.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
47.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.5b

localize12.0ms

Local error

Found 2 expressions with local error:

3.0b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×*-un-lft-identity
27×times-frac
12×add-cube-cbrt
9×difference-of-squares
7×distribute-lft-out--
6×add-exp-log
5×div-inv
4×add-cbrt-cube add-log-exp
3×pow1 associate-/r* associate-/l*
2×div-exp insert-posit16
1×cbrt-undiv rec-exp clear-num sub-neg frac-2neg flip3-- diff-log 1-exp tan-quot associate-/r/ frac-sub pow-flip flip-- inv-pow
Counts
2 → 63
Calls
2 calls:
Slowest
14.0ms
(- (/ 1 x) (/ 1 (tan x)))
6.0ms
(/ 1 (tan x))

series119.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
82.0ms
(- (/ 1 x) (/ 1 (tan x)))
37.0ms
(/ 1 (tan x))

simplify1.8s

Counts
65 → 69
Calls
65 calls:
Slowest
303.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
267.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
131.0ms
(/ (* (* 1 1) 1) (* (* (tan x) (tan x)) (tan x)))
67.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))
40.0ms
(- (sqrt (/ 1 x)) (/ (sqrt 1) (sqrt (tan x))))

prune531.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (+ 1/3 (* 1/45 (* x x))))
0.2b
(* 1/45 (* x x))
0.1b
(* (pow x 5) 2/945)
0.0b
(+ 1/3 (* 1/45 (* x x)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×add-exp-log
13×add-cbrt-cube associate-*l*
11×pow1
10×*-un-lft-identity add-cube-cbrt
7×associate-*r* prod-exp
6×add-log-exp
5×cbrt-unprod unswap-sqr
4×unpow-prod-down pow-prod-down insert-posit16
3×*-commutative
2×flip3-+ associate-*r/ flip-+ sqr-pow
1×distribute-rgt-in pow-to-exp +-commutative sum-log distribute-lft-in pow-exp
Counts
4 → 81
Calls
4 calls:
Slowest
29.0ms
(* 1/45 (* x x))
19.0ms
(* x (+ 1/3 (* 1/45 (* x x))))
10.0ms
(* (pow x 5) 2/945)
5.0ms
(+ 1/3 (* 1/45 (* x x)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(* x (+ 1/3 (* 1/45 (* x x))))
83.0ms
(* (pow x 5) 2/945)
79.0ms
(+ 1/3 (* 1/45 (* x x)))
35.0ms
(* 1/45 (* x x))

simplify3.4s

Counts
55 → 93
Calls
55 calls:
Slowest
465.0ms
(+ (* 1/3 1/3) (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 (* 1/45 (* x x)))))
259.0ms
(* (exp 1/3) (exp (* 1/45 (* x x))))
243.0ms
(* (* (* x x) x) (* (* (+ 1/3 (* 1/45 (* x x))) (+ 1/3 (* 1/45 (* x x)))) (+ 1/3 (* 1/45 (* x x)))))
236.0ms
(* (* (* 1/45 1/45) 1/45) (* (* (* x x) (* x x)) (* x x)))
189.0ms
(* (* (* (pow x 5) (pow x 5)) (pow x 5)) (* (* 2/945 2/945) 2/945))

prune944.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x 1/3)
0.2b
(* 1/45 (* x x))
0.1b
(* (pow x 5) 2/945)
0.1b
(* x (* 1/45 (* x x)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
22×add-cbrt-cube
20×pow1
19×add-sqr-sqrt
16×associate-*l*
13×prod-exp
11×*-un-lft-identity add-cube-cbrt cbrt-unprod
10×pow-prod-down
8×associate-*r*
5×unswap-sqr
4×unpow-prod-down *-commutative insert-posit16 add-log-exp
2×sqr-pow
1×pow-to-exp pow-exp
Counts
4 → 87
Calls
4 calls:
Slowest
61.0ms
(* x (* 1/45 (* x x)))
25.0ms
(* 1/45 (* x x))
21.0ms
(* (pow x 5) 2/945)
10.0ms
(* x 1/3)

series232.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
97.0ms
(* (pow x 5) 2/945)
69.0ms
(* x (* 1/45 (* x x)))
46.0ms
(* 1/45 (* x x))
19.0ms
(* x 1/3)

simplify3.9s

Counts
61 → 99
Calls
61 calls:
Slowest
630.0ms
(* (* (* x x) x) (* (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/45 (* x x))))
578.0ms
(* (* (* x x) x) (* (* (* 1/45 1/45) 1/45) (* (* (* x x) (* x x)) (* x x))))
398.0ms
(* (* (* x x) x) (* (* (* 1/45 1/45) 1/45) (* (* (* x x) x) (* (* x x) x))))
281.0ms
(* (* (* 1/45 1/45) 1/45) (* (* (* x x) (* x x)) (* x x)))
229.0ms
(* (* (* 1/45 1/45) 1/45) (* (* (* x x) x) (* (* x x) x)))

prune926.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
0.3b
(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))
0.2b
(* 1/45 (* x x))
0.2b
(* 1/45 (* x x))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
16×pow1
14×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×associate-*l*
8×prod-exp cbrt-unprod
7×pow-prod-down
6×associate-*r*
4×associate-*r/ insert-posit16 add-log-exp
3×associate-/r* times-frac flip3-- *-commutative flip-- unswap-sqr
2×distribute-rgt-in cbrt-undiv sub-neg distribute-lft-in div-exp associate-/r/ associate-/l/
1×clear-num frac-2neg div-inv associate-/l* difference-of-squares
Counts
4 → 92
Calls
4 calls:
Slowest
43.0ms
(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))
33.0ms
(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
26.0ms
(* 1/45 (* x x))
25.0ms
(* 1/45 (* x x))

series607.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
297.0ms
(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
202.0ms
(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))
57.0ms
(* 1/45 (* x x))
50.0ms
(* 1/45 (* x x))

simplify10.1s

Counts
66 → 104
Calls
66 calls:
Slowest
808.0ms
(/ (* (* (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))) (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))) (* (* (- 1/3 (* 1/45 (* x x))) (- 1/3 (* 1/45 (* x x)))) (- 1/3 (* 1/45 (* x x)))))
676.0ms
(/ (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))) (cbrt (- 1/3 (* 1/45 (* x x)))))
447.0ms
(/ (* (* (* x x) x) (* (* (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))) (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))) (* (* (- 1/3 (* 1/45 (* x x))) (- 1/3 (* 1/45 (* x x)))) (- 1/3 (* 1/45 (* x x)))))
394.0ms
(+ (log x) (log (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))))
374.0ms
(sqrt (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))

prune910.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample15.7s

Algorithm
intervals
Results
9.6s3283×body2560valid
3.7s2484×body1280valid
1.0s1279×body640valid
771.0ms602×body320valid
316.0ms8000×pre80true
109.0ms301×body160valid
9.0ms51×body80valid