Details

Time bar (total: 8.1m)

sample42.0ms

Algorithm
intervals
Results
10.0ms195×body80valid
5.0ms256×pre80true
5.0ms23×body640valid
4.0ms16×body1280valid
2.0ms14×body320valid
1.0ms8×body160valid

simplify670.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.2b
(/ (* (+ 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:
222.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
785.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
112.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series908.0ms

Counts
3 → 9
Calls
3 calls:
329.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
448.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
131.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.5s

Counts
120 → 120

prune500.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize17.0ms

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))))
0.9b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.6b
(+ (/ (/ (+ 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:
75.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
516.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
321.0ms
(/ (/ (+ 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)

series1.6s

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
221.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
796.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
472.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify2.6s

Counts
1746 → 1746

prune5.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.4b
(/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1))))
0.8b
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
1.6b
(+ (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 1.0)

rewrite1.1m

Algorithm
rewrite-expression-head
Rules
308065×times-frac
173795×*-un-lft-identity
119839×add-sqr-sqrt
103657×add-cube-cbrt
48126×sqrt-prod
26978×distribute-lft-out
8091×distribute-lft-out-- difference-of-squares
8031×div-inv
6093×associate-/r/
2699×flip3-+ flip-+
2546×associate-/r*
153×add-exp-log
120×div-exp
115×associate-/l*
95×add-cbrt-cube
69×cbrt-undiv
7×rec-exp 1-exp
6×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num
1×+-commutative sum-log
Counts
4 → 60278
Calls
4 calls:
447.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.7s
(/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1))))
651.0ms
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
38.5s
(+ (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
375.0ms
(/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1))))
281.0ms
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
474.0ms
(+ (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 1.0)

simplify1.7m

Counts
60290 → 60290

prune2.4m

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
0.8b
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
1.0b
(- (* 1.0 1.0) (* (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 1.0))
1.5b
(+ (pow (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 3) (pow 1.0 3))

rewrite2.0m

Algorithm
rewrite-expression-head
Rules
17656×times-frac
12066×*-un-lft-identity
7460×add-sqr-sqrt
6068×add-cube-cbrt
2303×distribute-lft-out
2160×sqrt-prod
696×distribute-lft-out-- difference-of-squares
524×associate-/r/
472×div-inv
233×flip3-+ flip-+
178×associate-/l*
56×associate-/r*
46×add-exp-log add-cbrt-cube
30×cbrt-undiv div-exp
8×add-log-exp
4×pow1 unpow-prod-down cube-prod
2×frac-2neg clear-num associate-/l/
1×+-commutative sub-neg flip3-- distribute-rgt-out-- diff-log sum-log sum-cubes flip--
Counts
4 → 5296
Calls
4 calls:
392.0ms
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
394.0ms
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
8.0ms
(- (* 1.0 1.0) (* (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 1.0))
2.0m
(+ (pow (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 3) (pow 1.0 3))

series5.4s

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
182.0ms
(/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))
212.0ms
(- (* 1.0 1.0) (* (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 1.0))
4.8s
(+ (pow (/ (/ 1 (sqrt 1)) (/ (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (+ alpha beta) (sqrt 1)))) 3) (pow 1.0 3))

simplify5.0s

Counts
5308 → 5308

prune20.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

regimes330.0ms

Accuracy

-9% (7.1b remaining)

Error of 13.1b against oracle of 6.0b and baseline of 12.5b

bsearch168.0ms

Steps
ItersRangePoint
7
2.752894759070865e+208
7.369999236997822e+209
1.4682017070687658e+209
5
9.308894831247315e+164
2.040616743577687e+165
1.262557062960946e+165
3
1.6187759830994239e+40
1.9607399768961668e+40
1.9393672272838702e+40

simplify1.2s

end0.0ms

sample1.3s

Algorithm
intervals
Results
420.0ms6335×body80valid
216.0ms8000×pre80true
179.0ms498×body1280valid
140.0ms576×body640valid
55.0ms384×body320valid
22.0ms207×body160valid