Details

Time bar (total: 11.2s)

sample20.0ms

Algorithm
intervals
Results
5.0ms51×body1280valid
3.0ms43×body640valid
3.0ms134×body80valid
1.0ms20×body320valid
0.0ms8×body160valid

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
11213
21613
31913
42113
52713
63913
75813
87713
99913
1011313
1111913
1212313
done12313

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.7b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite125.0ms

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:
10.0ms
(/ x (+ x 1.0))
25.0ms
(/ (+ x 1.0) (- x 1.0))
86.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series199.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
42.0ms
(/ (+ x 1.0) (- x 1.0))
124.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts
113 → 113
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01761584
13901503
210221427
323881414
done50001412

prune212.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
4.9b
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
10.2b
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
15.6b
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
287×add-sqr-sqrt
258×*-un-lft-identity
201×times-frac
144×difference-of-squares
108×unpow-prod-down cube-prod
106×associate-*l*
72×sqr-pow
66×add-cube-cbrt
51×distribute-lft-out
45×distribute-lft-out--
25×associate-/r*
11×add-exp-log add-cbrt-cube add-log-exp
9×difference-cubes
6×pow1 flip3-+ flip-+
5×frac-sub
4×frac-times associate-*r/ associate-/r/ associate-/l*
3×flip3-- associate-*r* sum-log flip--
2×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ associate--r+ unswap-sqr
1×+-commutative sub-neg associate-+r+ frac-2neg diff-log pow-prod-down clear-num *-commutative
Counts
4 → 308
Calls
4 calls:
18.0ms
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
51.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
62.0ms
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
173.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
55.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
179.0ms
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
72.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify1.9s

Counts
320 → 320
Iterations

Useful iterations: 2 (866.0ms)

IterNodesCost
03578185
111797283
246587031
done50027031

prune640.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
10.2b
(- (/ x (+ x 1.0)) (+ (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x)) (* (* 1.0 (+ x 1.0)) (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))))))
14.7b
(* (* 1.0 (+ x 1.0)) (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))))
15.6b
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x))

rewrite508.0ms

Algorithm
rewrite-expression-head
Rules
415×add-sqr-sqrt
379×*-un-lft-identity
302×times-frac
210×difference-of-squares
156×unpow-prod-down cube-prod
107×associate-*r* associate-*l*
104×sqr-pow
95×add-cube-cbrt
76×distribute-lft-out
66×distribute-lft-out--
30×add-exp-log add-cbrt-cube
25×associate-/r*
14×pow1
13×difference-cubes
12×prod-exp cbrt-unprod
10×associate-*r/ associate-*l/
9×add-log-exp
7×frac-sub
6×flip3-+ pow-prod-down associate-/r/ flip-+
5×cbrt-undiv div-exp frac-add
4×frac-times flip3-- flip-- associate-/l*
3×div-inv
2×diff-log *-commutative associate-/l/ unswap-sqr
1×sub-neg frac-2neg clear-num sum-log associate--r+
Counts
4 → 427
Calls
4 calls:
52.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
179.0ms
(- (/ x (+ x 1.0)) (+ (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x)) (* (* 1.0 (+ x 1.0)) (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))))))
112.0ms
(* (* 1.0 (+ x 1.0)) (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))))
128.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x))

series354.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
177.0ms
(- (/ x (+ x 1.0)) (+ (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x)) (* (* 1.0 (+ x 1.0)) (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))))))
58.0ms
(* (* 1.0 (+ x 1.0)) (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))))
67.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x))

simplify919.0ms

Counts
439 → 439
Iterations

Useful iterations: done (895.0ms)

IterNodesCost
045910259
114099431
done50018691

prune886.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

4.1b
(* (+ x 1.0) (/ (sqrt (+ x 1.0)) (+ (* x x) (* 1.0 (+ x 1.0)))))
4.9b
(- (/ x (+ x 1.0)) (+ (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x)) (* (* 1.0 (* (+ x 1.0) (/ (sqrt (+ x 1.0)) (+ (* x x) (* 1.0 (+ x 1.0)))))) (/ (sqrt (+ x 1.0)) (- x 1.0)))))
4.9b
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
15.6b
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x))

rewrite460.0ms

Algorithm
rewrite-expression-head
Rules
312×add-sqr-sqrt
282×*-un-lft-identity
225×times-frac
146×difference-of-squares
110×associate-*l*
108×unpow-prod-down cube-prod
80×add-cube-cbrt
72×sqr-pow
55×distribute-lft-out
46×distribute-lft-out--
28×associate-*r*
25×associate-/r*
23×add-exp-log associate-*l/ add-cbrt-cube
14×associate-*r/
13×sqrt-prod frac-sub
11×pow1 frac-times frac-add
9×difference-cubes flip3-+ flip-+ add-log-exp
8×prod-exp cbrt-unprod
6×associate-/r/
5×unswap-sqr
4×cbrt-undiv div-exp pow-prod-down associate-/l*
3×flip3-- flip-- div-inv
2×diff-log *-commutative associate-/l/
1×sub-neg frac-2neg clear-num sum-log associate--r+
Counts
4 → 355
Calls
4 calls:
60.0ms
(* (+ x 1.0) (/ (sqrt (+ x 1.0)) (+ (* x x) (* 1.0 (+ x 1.0)))))
193.0ms
(- (/ x (+ x 1.0)) (+ (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x)) (* (* 1.0 (* (+ x 1.0) (/ (sqrt (+ x 1.0)) (+ (* x x) (* 1.0 (+ x 1.0)))))) (/ (sqrt (+ x 1.0)) (- x 1.0)))))
54.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
128.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x))

series521.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(* (+ x 1.0) (/ (sqrt (+ x 1.0)) (+ (* x x) (* 1.0 (+ x 1.0)))))
262.0ms
(- (/ x (+ x 1.0)) (+ (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x)) (* (* 1.0 (* (+ x 1.0) (/ (sqrt (+ x 1.0)) (+ (* x x) (* 1.0 (+ x 1.0)))))) (/ (sqrt (+ x 1.0)) (- x 1.0)))))
54.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
73.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x))

simplify697.0ms

Counts
367 → 367
Iterations

Useful iterations: done (682.0ms)

IterNodesCost
055110039
116209385
done50008907

prune976.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.8b

bsearch89.0ms

Steps
ItersRangePoint
10
0.0001820196720056695
1126179.5725289274
16225.269930825421
9
-76786.820650899
-0.0002772006047103471
-11521.054321825985

simplify9.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02879
14164
24864
35164
done5164

end0.0ms

sample541.0ms

Algorithm
intervals
Results
165.0ms1661×body1280valid
98.0ms1234×body640valid
98.0ms4166×body80valid
36.0ms600×body320valid
14.0ms339×body160valid