Details

Time bar (total: 28.5s)

sample39.0ms

Algorithm
intervals
Results
11.0ms216×body80valid
5.0ms256×pre80true
4.0ms15×body1280valid
2.0ms11×body640valid
1.0ms7×body320valid
1.0ms7×body160valid

simplify1.8s

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: 25.3b

localize30.0ms

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))
2.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.4b
(/ (* (+ 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:
250.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
910.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
64.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series806.0ms

Counts
3 → 9
Calls
3 calls:
319.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
374.0ms
(+ (/ (/ (* (+ 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)))

simplify2.9s

Counts
120 → 120
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
02254035
16973821
245043577
done50023577

prune573.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.6b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.1b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
62.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
326.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
509.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
164.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
243.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
350.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
403.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify799.0ms

Counts
307 → 307
Iterations

Useful iterations: done (781.0ms)

IterNodesCost
03859712
111429287
done50008943

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.6b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
2.6b
(* (+ alpha beta) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
3.1b
(+ (* (+ alpha beta) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite3.0s

Algorithm
rewrite-expression-head
Rules
90×add-exp-log
56×add-cbrt-cube
43×prod-exp cbrt-unprod
29×frac-times
27×cbrt-undiv div-exp
17×associate-*l/
16×associate-*r/
13×pow1
11×flip3-+ flip-+
9×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-prod pow-prod-down add-log-exp
4×cbrt-div associate-*l*
2×pow1/3
1×+-commutative associate-*r* sum-log *-commutative distribute-lft-out
Counts
4 → 108
Calls
4 calls:
32.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
28.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
1.5s
(* (+ alpha beta) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
1.5s
(+ (* (+ alpha beta) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
246.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
232.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
381.0ms
(* (+ alpha beta) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
523.0ms
(+ (* (+ alpha beta) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify3.0s

Counts
120 → 120
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02737052
19376575
248903947
done50013941

prune582.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- beta alpha))
0.6b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
2.6b
(* (+ alpha beta) (/ (pow (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) 3) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.1b
(+ (* (+ alpha beta) (/ (pow (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) 3) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
860×times-frac
686×*-un-lft-identity
501×add-sqr-sqrt
462×associate-*r*
448×cbrt-prod
358×add-cube-cbrt
221×unpow-prod-down cube-prod
115×distribute-lft-out
49×distribute-lft-out-- difference-of-squares
20×cbrt-div
18×add-exp-log associate-/r/
13×flip3-+ flip-+ unswap-sqr
9×add-cbrt-cube div-inv
6×pow1 add-log-exp
5×div-exp prod-exp sqr-pow
4×cube-mult unpow3 associate-*l*
2×frac-times pow1/3 associate-*l/ pow-exp cbrt-unprod
1×cbrt-undiv +-commutative pow-to-exp flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 539
Calls
4 calls:
8.0ms
(cbrt (- beta alpha))
26.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
871.0ms
(* (+ alpha beta) (/ (pow (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) 3) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
231.0ms
(+ (* (+ alpha beta) (/ (pow (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) 3) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
236.0ms
(cbrt (- beta alpha))
270.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
438.0ms
(* (+ alpha beta) (/ (pow (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) 3) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
472.0ms
(+ (* (+ alpha beta) (/ (pow (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))) 3) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify1.4s

Counts
551 → 551
Iterations

Useful iterations: done (1.3s)

IterNodesCost
067117208
1203815883
done500114686

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

regimes358.0ms

Accuracy

15.5% (5.2b remaining)

Error of 11.0b against oracle of 5.8b and baseline of 12.0b

bsearch152.0ms

Steps
ItersRangePoint
10
3.868550392986014e+208
9.534905038333449e+219
7.762470963936792e+219

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03457
14157
done4157

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s6412×body80valid
260.0ms8000×pre80true
190.0ms497×body1280valid
174.0ms560×body640valid
113.0ms189×body160valid
84.0ms342×body320valid