Details

Time bar (total: 51.8s)

sample41.0ms

Algorithm
intervals
Results
10.0ms201×body80valid
5.0ms256×pre80true
4.0ms19×body640valid
4.0ms14×body1280valid
2.0ms13×body320valid
1.0ms9×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
015405
131405
297405
3448405
42146405
done5003405

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.1s

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
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 124
Calls
4 calls:
22.0ms
(+ (+ alpha beta) (* 2.0 i))
226.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
742.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
54.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series971.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (+ alpha beta) (* 2.0 i))
374.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
445.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
115.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify3.1s

Counts
136 → 136
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
023562701
170857784
2317356781
done500556781

prune932.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.8b
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite926.0ms

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 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 → 129
Calls
4 calls:
68.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
161.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
95.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
592.0ms
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series882.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
333.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
151.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
283.0ms
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify3.3s

Counts
141 → 141
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
022355102
168047917
2297446591
done500646591

prune959.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.2b
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.8b
(+ 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
1.8b
(log (exp (+ 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))))

rewrite2.8s

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-cbrt-cube add-exp-log
9×cbrt-undiv div-exp
8×associate-/l*
6×add-log-exp
5×pow1 log-pow
4×log-prod exp-prod associate-/l/
2×clear-num frac-2neg
1×+-commutative sum-log rem-log-exp exp-sum
Counts
4 → 623
Calls
4 calls:
300.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
210.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
420.0ms
(+ 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
1.8s
(log (exp (+ 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
214.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
330.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
419.0ms
(+ 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
448.0ms
(log (exp (+ 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))))

simplify3.2s

Counts
635 → 635
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0726464385
12147431422
done5001422914

prune3.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize139.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.2b
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.8b
(+ (* (* 1.0 1.0) 1.0) (* (* (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))
2.1b
(- 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
2158×times-frac
1786×*-un-lft-identity
1018×add-sqr-sqrt
764×add-cube-cbrt
390×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-cbrt-cube add-exp-log
12×cbrt-undiv div-exp
8×associate-/l* add-log-exp
4×pow1 associate-/l/
2×clear-num frac-2neg pow3
1×+-commutative sum-log sub-neg flip3-- diff-log sum-cubes flip--
Counts
4 → 965
Calls
4 calls:
249.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
229.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.3s
(+ (* (* 1.0 1.0) 1.0) (* (* (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))
468.0ms
(- 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))

series10.4s

Counts
4 → 12
Calls
4 calls:
295.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
352.0ms
(/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
9.5s
(+ (* (* 1.0 1.0) 1.0) (* (* (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))
274.0ms
(- 1.0 (/ (+ alpha beta) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))

simplify3.7s

Counts
977 → 977
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0700750807
12079707880
done5001699668

prune6.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

regimes643.0ms

Accuracy

21.2% (5.6b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 13.0b

bsearch129.0ms

Steps
ItersRangePoint
9
2.365330768656473e+186
5.407649855954466e+193
5.3206985442429606e+193

simplify18.0ms

Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
031939
141899
done41899

end0.0ms

sample2.3s

Algorithm
intervals
Results
582.0ms613×body640valid
536.0ms6266×body80valid
273.0ms8000×pre80true
260.0ms564×body1280valid
196.0ms349×body320valid
100.0ms208×body160valid