Details

Time bar (total: 32.9s)

sample84.0ms

Algorithm
intervals
Results
26.0ms201×body80valid
12.0ms15×body1280valid
11.0ms256×pre80true
9.0ms17×body640valid
5.0ms11×body320valid
3.0ms12×body160valid

simplify2.1s

Counts
1 → 1
Iterations
IterNodes
done5022
42155
3440
295
132
016

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2 i))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
2.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
22.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite806.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
48×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-cbrt-cube add-exp-log
14×associate-/r/
12×flip3-+ flip-+
11×distribute-lft-out add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
4×frac-times pow1 sum-log insert-posit16
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 128
Calls
4 calls:
28.0ms
(+ (+ alpha beta) (* 2 i))
179.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
556.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
40.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series894.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (+ alpha beta) (* 2 i))
343.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
389.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
126.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify2.2s

Counts
140 → 140
Iterations
IterNodes
done5002
23125
1716
0239

prune712.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
2.8b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

rewrite754.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
45×add-sqr-sqrt
35×times-frac
26×add-cube-cbrt
21×associate-*r*
20×add-cbrt-cube add-exp-log
8×flip3-+ flip-+
7×associate-/r* distribute-lft-out-- difference-of-squares associate-/l/
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod insert-posit16 distribute-lft-out
3×div-inv
2×clear-num frac-2neg associate-*r/ unswap-sqr
1×+-commutative sum-log flip3-- div-sub pow-prod-down *-commutative flip--
Counts
4 → 133
Calls
4 calls:
152.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
88.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
63.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
449.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series957.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
88.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
123.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
408.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

simplify2.7s

Counts
145 → 145
Iterations
IterNodes
done5002
22916
1691
0231

prune830.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
2.8b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
3.5b
(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
25×add-sqr-sqrt
17×add-cube-cbrt
15×times-frac
8×log-prod
7×add-exp-log
6×pow1 add-cbrt-cube add-log-exp
5×associate-/l*
4×log-div exp-prod flip3-+ exp-sum flip-+ insert-posit16 distribute-lft-out-- difference-of-squares
3×associate-/r* distribute-lft-out
2×exp-diff associate-/r/ log-pow associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-sub div-exp rem-log-exp div-inv flip-- rem-exp-log
Counts
4 → 89
Calls
4 calls:
299.0ms
(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
59.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
443.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
248.0ms
(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
385.0ms
(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
122.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
388.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
362.0ms
(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))

simplify1.6s

Counts
101 → 101
Iterations
IterNodes
done5014
21419
1465
0188

prune695.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.3b

localize112.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))
0.3b
(/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))
2.1b
(- 1.0 (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i)))))
2.7b
(+ (* (* (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i)))) (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i))))) (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i))))) (* (* 1.0 1.0) 1.0))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt *-un-lft-identity
30×times-frac
24×add-cube-cbrt
10×associate-/l*
9×distribute-lft-out-- difference-of-squares
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r*
4×pow1 associate-/r/ insert-posit16 associate-/l/
3×flip3-+ flip3-- flip-+ flip--
2×cbrt-undiv clear-num frac-2neg div-sub div-exp pow3 div-inv
1×+-commutative sum-log sub-neg diff-log sum-cubes
Counts
4 → 110
Calls
4 calls:
35.0ms
(/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))
54.0ms
(/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))
89.0ms
(- 1.0 (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i)))))
980.0ms
(+ (* (* (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i)))) (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i))))) (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i))))) (* (* 1.0 1.0) 1.0))

series8.2s

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))
105.0ms
(/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))
415.0ms
(- 1.0 (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i)))))
7.6s
(+ (* (* (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i)))) (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i))))) (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ beta alpha) (* 2 i)))) (+ (+ 2.0 alpha) (+ beta (* 2 i))))) (* (* 1.0 1.0) 1.0))

simplify1.8s

Counts
122 → 122
Iterations
IterNodes
done5001
21683
1483
0172

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.2b

regimes498.0ms

Accuracy

10.6% (6.9b remaining)

Error of 11.2b against oracle of 4.3b and baseline of 12.0b

bsearch140.0ms

Steps
ItersRangePoint
6
3.1264821752554173e+212
1.4111558406918674e+213
1.0677683986829125e+213

simplify6.0ms

Iterations
IterNodes
done42
142
031

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s6400×body80valid
689.0ms556×body640valid
438.0ms8000×pre80true
359.0ms473×body1280valid
152.0ms354×body320valid
90.0ms217×body160valid