Details

Time bar (total: 52.9s)

sample43.0ms

Algorithm
intervals
Results
11.0ms200×body80valid
5.0ms18×body1280valid
5.0ms256×pre80true
4.0ms18×body640valid
2.0ms14×body320valid
1.0ms6×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01529
13129
210229
345429
4246229
done500029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
235.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
763.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
60.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series897.0ms

Counts
3 → 9
Calls
3 calls:
356.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
427.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
114.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.5s

Counts
120 → 120
Iterations

Useful iterations: 2 (738.0ms)

IterNodesCost
02254035
16973821
245043577
done50023577

prune510.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.5b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
2.4b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
5126×times-frac
3533×*-un-lft-identity
2233×add-sqr-sqrt
1787×add-cube-cbrt
650×distribute-lft-out
223×distribute-lft-out-- difference-of-squares
183×div-inv
167×associate-/r/
113×associate-/r*
76×flip3-+ flip-+
41×add-exp-log
32×add-cbrt-cube
28×div-exp
25×associate-/l*
19×cbrt-undiv
6×add-log-exp
5×associate-/l/
4×pow1
3×frac-2neg 1-exp clear-num
1×+-commutative flip3-- div-sub sum-log flip--
Counts
4 → 1734
Calls
4 calls:
54.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
423.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
344.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.9s
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
185.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
356.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
423.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify1.2s

Counts
1746 → 1746
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0183895692
done500089942

prune5.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize44.0ms

Local error

Found 4 expressions with local error:

1.5b
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.5b
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
2.2b
(- 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
2.3b
(+ (pow (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 3) (pow 1.0 3))

rewrite4.8s

Algorithm
rewrite-expression-head
Rules
2158×times-frac
1796×*-un-lft-identity
1018×add-sqr-sqrt
764×add-cube-cbrt
395×distribute-lft-out
178×associate-/r*
124×difference-of-squares
121×distribute-lft-out--
92×associate-/r/
52×div-inv
43×flip3-+ flip-+
22×add-exp-log add-cbrt-cube
12×cbrt-undiv div-exp
8×associate-/l* add-log-exp
4×pow1 unpow-prod-down cube-prod associate-/l/
2×frac-2neg clear-num
1×+-commutative sub-neg flip3-- diff-log sum-log sum-cubes flip--
Counts
4 → 970
Calls
4 calls:
281.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
269.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
557.0ms
(- 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
3.2s
(+ (pow (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 3) (pow 1.0 3))

series8.3s

Counts
4 → 12
Calls
4 calls:
338.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
410.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
283.0ms
(- 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
7.3s
(+ (pow (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 3) (pow 1.0 3))

simplify1.7s

Counts
982 → 982
Iterations

Useful iterations: done (1.6s)

IterNodesCost
070146694
1207744772
done500243796

prune5.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.5b
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
2.4b
(+ (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
2.4b
(log (exp (+ (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))

rewrite5.8s

Algorithm
rewrite-expression-head
Rules
1235×times-frac
1041×*-un-lft-identity
603×add-sqr-sqrt
453×add-cube-cbrt
219×distribute-lft-out
110×associate-/r*
75×distribute-lft-out-- difference-of-squares
57×associate-/r/
32×div-inv
28×flip3-+ flip-+
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
8×associate-/l*
6×add-log-exp
5×pow1 log-pow
4×log-prod exp-prod associate-/l/
2×frac-2neg clear-num
1×+-commutative rem-log-exp exp-sum sum-log
Counts
4 → 623
Calls
4 calls:
516.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
366.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.3s
(+ (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
3.6s
(log (exp (+ (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
364.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
400.0ms
(+ (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
490.0ms
(log (exp (+ (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)))

simplify1.9s

Counts
635 → 635
Iterations

Useful iterations: done (1.9s)

IterNodesCost
072628736
1218227645
done500226951

prune2.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

regimes303.0ms

Accuracy

9.4% (5.6b remaining)

Error of 11.3b against oracle of 5.7b and baseline of 11.9b

bsearch86.0ms

Steps
ItersRangePoint
4
7.535504516908318e+256
1.2486356859020464e+257
8.272018169352953e+256

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03658
14758
done4758

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s6419×body80valid
304.0ms8000×pre80true
268.0ms516×body1280valid
183.0ms560×body640valid
162.0ms326×body320valid
32.0ms179×body160valid