Details

Time bar (total: 17.8s)

sample33.0ms

Algorithm
intervals
Results
8.0ms203×body80valid
4.0ms256×pre80true
4.0ms19×body1280valid
3.0ms18×body640valid
1.0ms10×body320valid
0.0ms6×body160valid

simplify922.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
13129
210129
340829
4143729
done500029

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize12.0ms

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))
1.4b
(+ (/ (/ (* (+ 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)))

rewrite434.0ms

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:
93.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
307.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
28.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series585.0ms

Counts
3 → 9
Calls
3 calls:
227.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
278.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
80.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify998.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (375.0ms)

IterNodesCost
02254035
16773821
229283577
done50003577

prune359.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
8.4b
(+ (* (/ (/ (+ alpha beta) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 distribute-lft-out
1×+-commutative sum-log
Counts
4 → 53
Calls
4 calls:
32.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
30.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
137.0ms
(+ (* (/ (/ (+ alpha beta) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series823.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
190.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
174.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms
(+ (* (/ (/ (+ alpha beta) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify1.4s

Counts
65 → 65
Iterations

Useful iterations: 3 (518.0ms)

IterNodesCost
01182021
13161991
29701811
338341320
done50001320

prune271.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
0.1b
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.4b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite745.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×add-sqr-sqrt
21×associate-*r*
20×times-frac
19×add-exp-log add-cube-cbrt add-cbrt-cube
8×flip3-+ flip-+
7×pow1
6×distribute-lft-out add-log-exp
5×cbrt-undiv div-exp associate-/l/
4×frac-times unpow-prod-down cube-prod associate-*l* associate-*l/ prod-exp associate-/r* associate-/r/ cbrt-unprod
3×pow-unpow distribute-lft-out-- difference-of-squares
2×cube-div associate-*r/ div-inv unswap-sqr
1×+-commutative cube-mult pow-to-exp pow-pow frac-2neg unpow3 pow-prod-down pow-exp clear-num sum-log *-commutative associate-/l* rem-cube-cbrt sqr-pow
Counts
4 → 116
Calls
4 calls:
363.0ms
(pow (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
79.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
55.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
243.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
749.0ms
(pow (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
231.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
82.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
281.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify1.1s

Counts
128 → 128
Iterations

Useful iterations: 2 (449.0ms)

IterNodesCost
02413877
17173600
231663222
done50003222

prune455.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.2b
(- (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
1.3b
(+ (pow 1.0 3) (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3))

rewrite667.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
48×add-sqr-sqrt
42×associate-*r*
32×times-frac
24×add-cube-cbrt
14×add-exp-log add-cbrt-cube
8×pow1 associate-*l* add-log-exp
7×flip3-+ flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares
4×frac-times unpow-prod-down cube-prod associate-*l/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
2×cbrt-undiv associate-*r/ div-exp pow-prod-down *-commutative div-inv
1×+-commutative sub-neg flip3-- diff-log sum-log sum-cubes flip--
Counts
4 → 121
Calls
4 calls:
55.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
55.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
339.0ms
(- (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
213.0ms
(+ (pow 1.0 3) (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3))

series4.8s

Counts
4 → 12
Calls
4 calls:
82.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
83.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
187.0ms
(- (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
4.4s
(+ (pow 1.0 3) (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3))

simplify852.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (294.0ms)

IterNodesCost
01873322
15213146
221462854
done50002854

prune560.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

regimes371.0ms

Accuracy

74.1% (1.7b remaining)

Error of 7.3b against oracle of 5.6b and baseline of 12.1b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03789
14589
done4589

end0.0ms

sample820.0ms

Algorithm
intervals
Results
257.0ms6377×body80valid
124.0ms8000×pre80true
112.0ms538×body1280valid
84.0ms545×body640valid
42.0ms347×body320valid
15.0ms193×body160valid