Details

Time bar (total: 29.4s)

sample49.0ms

Algorithm
intervals
Results
10.0ms204×body80valid
10.0ms256×pre80true
4.0ms17×body1280valid
2.0ms16×body320valid
2.0ms12×body640valid
1.0ms7×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01529
13129
210229
345429
4246229
done500029

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.1b

localize44.0ms

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))
2.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

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:
253.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
865.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
83.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series1.0s

Counts
3 → 9
Calls
3 calls:
411.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
458.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
154.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.8s

Counts
120 → 120
Iterations

Useful iterations: 2 (821.0ms)

IterNodesCost
02254035
16973821
245043577
done50023577

prune718.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.1b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
603×times-frac
484×*-un-lft-identity
408×add-sqr-sqrt
260×add-cube-cbrt
219×sqrt-prod
153×associate-*r*
67×distribute-lft-out
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
34×associate-*l*
32×add-exp-log add-cbrt-cube
25×associate-/l*
21×flip3-+ flip-+
19×div-inv
15×unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 485
Calls
4 calls:
1.0s
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
268.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
217.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
252.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
289.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
190.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
441.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify1.1s

Counts
497 → 497
Iterations

Useful iterations: done (1.1s)

IterNodesCost
056820612
1183919194
done500018591

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.1b
(+ (cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
11.0b
(cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

rewrite616.0ms

Algorithm
rewrite-expression-head
Rules
295×times-frac
259×*-un-lft-identity
187×add-sqr-sqrt
139×add-cube-cbrt
108×sqrt-prod
36×distribute-lft-out
25×associate-/l*
24×distribute-lft-out-- difference-of-squares
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
8×cbrt-prod
6×add-log-exp
4×pow1 cbrt-undiv sqrt-div div-exp
3×cube-div cbrt-div associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative cube-mult frac-times unpow-prod-down pow1/3 unpow3 cube-prod associate-*r/ associate-*l/ sum-log rem-cbrt-cube sqr-pow
Counts
4 → 280
Calls
4 calls:
314.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
251.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.0ms
(+ (cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
3.0ms
(cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

series1.4s

Counts
4 → 12
Calls
4 calls:
402.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
206.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
453.0ms
(+ (cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
376.0ms
(cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

simplify622.0ms

Counts
292 → 292
Iterations

Useful iterations: done (600.0ms)

IterNodesCost
045911881
1118110879
done500110686

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.8b
(+ (cbrt (pow (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
11.0b
(cbrt (pow (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

rewrite922.0ms

Algorithm
rewrite-expression-head
Rules
1167×times-frac
1089×sqrt-prod
1011×*-un-lft-identity
563×add-sqr-sqrt
515×add-cube-cbrt
224×distribute-lft-out
67×associate-/l*
50×sqrt-div
42×associate-/r/
24×distribute-lft-out-- difference-of-squares
22×flip3-+ flip-+
21×div-inv
17×associate-/r*
14×add-exp-log add-cbrt-cube
8×cbrt-prod
6×cbrt-undiv div-exp add-log-exp
4×pow1
3×cube-div cbrt-div
2×frac-2neg div-sub clear-num associate-/l/
1×+-commutative cube-mult frac-times unpow-prod-down pow1/3 unpow3 cube-prod associate-*r/ associate-*l/ sum-log rem-cbrt-cube sqr-pow
Counts
4 → 758
Calls
4 calls:
480.0ms
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
310.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
28.0ms
(+ (cbrt (pow (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
5.0ms
(cbrt (pow (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

series1.4s

Counts
4 → 12
Calls
4 calls:
209.0ms
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
382.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
447.0ms
(+ (cbrt (pow (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
335.0ms
(cbrt (pow (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

simplify1.3s

Counts
770 → 770
Iterations

Useful iterations: done (1.2s)

IterNodesCost
079640062
1209135895
done500032868

prune3.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

regimes610.0ms

Accuracy

14.4% (5.3b remaining)

Error of 11.1b against oracle of 5.8b and baseline of 12.0b

bsearch135.0ms

Steps
ItersRangePoint
7
1.169644349722028e+194
4.08921074783013e+195
6.987572166618589e+194

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03980
14980
done4980

end0.0ms

sample2.0s

Algorithm
intervals
Results
624.0ms6400×body80valid
349.0ms581×body640valid
289.0ms8000×pre80true
229.0ms478×body1280valid
87.0ms368×body320valid
27.0ms173×body160valid