Details

Time bar (total: 17.0s)

sample55.0ms

Algorithm
intervals
Results
18.0ms63×body1280valid
11.0ms45×body640valid
7.0ms117×body80valid
4.0ms23×body320valid
1.0ms8×body160valid

simplify197.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
981×*-un-lft-identity
736×times-frac
585×add-sqr-sqrt
468×prod-diff
419×add-cube-cbrt
189×distribute-lft-out
94×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
47×div-inv
29×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 596
Calls
3 calls:
11.0ms
(/ x (+ x 1.0))
44.0ms
(/ (+ x 1.0) (- x 1.0))
147.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series277.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(/ x (+ x 1.0))
47.0ms
(/ (+ x 1.0) (- x 1.0))
187.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.5s

Counts
605 → 605
Iterations

Useful iterations: done (3.4s)

IterNodesCost
052334216
1119930851
2282322735
done500016848

prune655.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.2b
(/ 3.0 (pow x 3))
0.3b
(/ 1.0 (* x x))
5.5b
(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
42×times-frac
34×add-sqr-sqrt add-cube-cbrt
14×add-exp-log
13×associate-/r*
12×unpow-prod-down cube-prod
11×fma-def add-cbrt-cube add-log-exp
6×associate-/l*
5×div-exp frac-add distribute-lft-out
4×pow1 expm1-log1p-u cube-mult unpow3 sum-log log1p-expm1-u sqr-pow
3×cbrt-undiv flip3-+ flip-+ div-inv
2×+-commutative frac-2neg clear-num
1×pow-to-exp associate-+l+ pow-exp prod-exp cbrt-unprod
Counts
4 → 136
Calls
4 calls:
39.0ms
(+ (/ 1.0 (* x x)) (/ 3.0 x))
13.0ms
(/ 3.0 (pow x 3))
16.0ms
(/ 1.0 (* x x))
256.0ms
(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (/ 1.0 (* x x)) (/ 3.0 x))
61.0ms
(/ 3.0 (pow x 3))
45.0ms
(/ 1.0 (* x x))
37.0ms
(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify1.1s

Counts
148 → 148
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02021801
14551547
216241460
done50001457

prune379.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cbrt (- x 1.0)) 3)
0.4b
(pow (cbrt (- x 1.0)) 3)
0.4b
(pow (cbrt (- x 1.0)) 3)
23.6b
(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (pow (cbrt (- x 1.0)) 3)))

rewrite705.0ms

Algorithm
rewrite-expression-head
Rules
3237×*-un-lft-identity
2751×times-frac
1898×add-sqr-sqrt
1692×prod-diff
1553×add-cube-cbrt
754×cbrt-prod
685×distribute-lft-out
604×unpow-prod-down cube-prod
226×associate-/r/
164×difference-of-squares
155×distribute-lft-out--
113×div-inv
95×flip3-+ flip-+
77×sqr-pow
75×cube-mult unpow3
42×cube-div cbrt-div
22×flip3-- flip--
18×fma-neg
9×pow-unpow
7×pow1 add-exp-log
6×pow-pow add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-to-exp pow1/3 pow-exp rem-cube-cbrt
1×sub-neg diff-log frac-sub
Counts
4 → 1858
Calls
4 calls:
17.0ms
(pow (cbrt (- x 1.0)) 3)
19.0ms
(pow (cbrt (- x 1.0)) 3)
18.0ms
(pow (cbrt (- x 1.0)) 3)
348.0ms
(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (pow (cbrt (- x 1.0)) 3)))

series1.5s

Counts
4 → 12
Calls
4 calls:
415.0ms
(pow (cbrt (- x 1.0)) 3)
429.0ms
(pow (cbrt (- x 1.0)) 3)
389.0ms
(pow (cbrt (- x 1.0)) 3)
225.0ms
(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (pow (cbrt (- x 1.0)) 3)))

simplify1.9s

Counts
1870 → 1870
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01095152700
12352115966
done500063170

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.4b
(pow (cbrt (- x 1.0)) 3)
0.4b
(pow (cbrt (- x 1.0)) 3)
33.6b
(fma x (/ 1 (+ 1.0 x)) (/ (- (+ 1.0 x)) (- x 1.0)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod add-sqr-sqrt *-un-lft-identity
16×unpow-prod-down cube-prod
15×add-cube-cbrt
6×pow1 add-exp-log pow-unpow cbrt-div
5×distribute-lft-out-- difference-of-squares
4×cube-div expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
2×cube-mult pow-to-exp unpow3 pow-exp rem-cube-cbrt sqr-pow
1×fma-udef
Counts
4 → 103
Calls
4 calls:
11.0ms
(cbrt (- x 1.0))
19.0ms
(pow (cbrt (- x 1.0)) 3)
20.0ms
(pow (cbrt (- x 1.0)) 3)
1.0ms
(fma x (/ 1 (+ 1.0 x)) (/ (- (+ 1.0 x)) (- x 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
143.0ms
(cbrt (- x 1.0))
441.0ms
(pow (cbrt (- x 1.0)) 3)
444.0ms
(pow (cbrt (- x 1.0)) 3)
143.0ms
(fma x (/ 1 (+ 1.0 x)) (/ (- (+ 1.0 x)) (- x 1.0)))

simplify932.0ms

Counts
115 → 115
Iterations

Useful iterations: done (926.0ms)

IterNodesCost
01651426
14231083
21158953
done5000945

prune509.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes58.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.4b

bsearch123.0ms

Steps
ItersRangePoint
9
0.0033303272193615503
311302.39110615524
11917.97074271185
7
-41918.349557210015
-1608.0958488538781
-13754.175701540715

simplify16.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03178
15063
25863
36063
done6063

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s1770×body1280valid
256.0ms1220×body640valid
189.0ms4059×body80valid
131.0ms660×body320valid
26.0ms291×body160valid