Details

Time bar (total: 16.4s)

sample50.0ms

Algorithm
intervals
Results
15.0ms57×body1280valid
10.0ms47×body640valid
7.0ms121×body80valid
3.0ms18×body320valid
1.0ms13×body160valid

simplify118.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
3.0b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
26.0ms
(/ x (+ x 1.0))
34.0ms
(/ (+ x 1.0) (- x 1.0))
172.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series303.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(/ x (+ x 1.0))
58.0ms
(/ (+ x 1.0) (- x 1.0))
182.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.3s

Counts
113 → 113

prune327.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.3b
(/ 3.0 (pow x 3))
0.5b
(/ (- 1.0) (pow x 2))
5.4b
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
143×times-frac
120×add-sqr-sqrt
105×*-un-lft-identity
78×add-cube-cbrt
48×unpow-prod-down
29×distribute-rgt-neg-in
27×distribute-lft-neg-in
20×associate-/r*
18×sqr-pow
15×difference-of-squares
14×add-exp-log
13×cube-prod associate-/l* unpow2
11×add-log-exp
10×distribute-lft-out--
9×neg-mul-1
8×add-cbrt-cube
6×div-exp
5×frac-sub
4×pow1 cube-mult diff-log unpow3
3×sub-neg flip3-- flip--
2×cbrt-undiv associate--l- neg-sub0 pow-to-exp frac-2neg div-sub pow-exp associate--l+ clear-num div-inv
1×distribute-frac-neg
Counts
4 → 234
Calls
4 calls:
140.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
14.0ms
(/ 3.0 (pow x 3))
14.0ms
(/ (- 1.0) (pow x 2))
1.1s
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
51.0ms
(/ 3.0 (pow x 3))
28.0ms
(/ (- 1.0) (pow x 2))
47.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify1.3s

Counts
246 → 246

prune647.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

5.4b
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
18.5b
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))
18.5b
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))
18.5b
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
59×add-sqr-sqrt
40×times-frac
36×cbrt-prod
28×distribute-lft-out--
20×difference-of-squares
16×frac-sub
15×cbrt-div
9×add-log-exp
8×flip3-- flip--
7×add-cube-cbrt
4×pow1 add-exp-log unpow-prod-down distribute-rgt-neg-in cube-prod add-cbrt-cube sqr-pow
3×pow1/3 diff-log
2×sub-neg associate--l+
1×associate--l-
Counts
4 → 103
Calls
4 calls:
1.2s
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
423.0ms
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))
456.0ms
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))
448.0ms
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))

series650.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
197.0ms
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))
184.0ms
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))
234.0ms
(cbrt (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))))

simplify808.0ms

Counts
115 → 115

prune510.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ x (+ x 1.0)) 3)
0.0b
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b
(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.9b
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite490.0ms

Algorithm
rewrite-expression-head
Rules
354×*-un-lft-identity
216×times-frac
190×add-sqr-sqrt
104×unpow-prod-down cube-prod
78×add-cube-cbrt
66×distribute-lft-out
61×distribute-lft-out--
44×difference-of-squares
24×swap-sqr
22×add-exp-log add-cbrt-cube
18×associate-*r* associate-*l*
16×associate-/r/
14×sqr-pow
13×pow1
8×div-inv
6×cbrt-undiv pow-unpow flip3-+ div-exp flip-+ add-log-exp
4×cube-div pow-exp prod-exp cbrt-unprod rem-cube-cbrt unswap-sqr
3×flip3-- flip--
2×cube-mult pow-to-exp pow-pow unpow3
1×difference-cubes pow2 frac-times sub-neg pow-plus diff-log associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up frac-sub
Counts
4 → 303
Calls
4 calls:
15.0ms
(pow (/ x (+ x 1.0)) 3)
75.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
36.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
339.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series557.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(pow (/ x (+ x 1.0)) 3)
61.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
84.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
354.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify691.0ms

Counts
315 → 315

prune630.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes62.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch187.0ms

Steps
ItersRangePoint
10
555.6593536559827
1339704296388782.2
14760.896472035072
10
-248837311.7084542
-0.0006576197608759923
-11119.68978976541

simplify1.2s

end0.0ms

sample1.3s

Algorithm
intervals
Results
537.0ms4104×body80valid
262.0ms1704×body1280valid
213.0ms1221×body640valid
90.0ms640×body320valid
23.0ms331×body160valid