Details

Time bar (total: 33.4s)

sample78.0ms

Algorithm
intervals
Results
21.0ms203×body80valid
10.0ms23×body640valid
8.0ms256×pre80true
5.0ms9×body1280valid
3.0ms9×body320valid
2.0ms12×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
13129
210229
345229
4209029
done500129

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize31.0ms

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))
3.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.5b
(/ (* (+ 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:
258.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
882.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
87.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series907.0ms

Counts
3 → 9
Calls
3 calls:
383.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
388.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
136.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.8s

Counts
120 → 120
Iterations

Useful iterations: 2 (578.0ms)

IterNodesCost
02254035
16753821
229493577
done50003577

prune496.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- 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)))
5.2b
(+ (* (+ 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:
66.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
319.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
568.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
125.0ms
(+ (* (+ 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:
109.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
270.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
394.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
506.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify2.6s

Counts
307 → 307
Iterations

Useful iterations: done (2.6s)

IterNodesCost
03859712
110519275
246168911
done50028909

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize23.0ms

Local error

Found 4 expressions with local error:

4.0b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.0b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.0b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
10.8b
(+ (* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
49×add-sqr-sqrt *-un-lft-identity
45×times-frac
31×add-cube-cbrt
9×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×cbrt-div pow1/3 div-inv
1×+-commutative sum-log
Counts
4 → 101
Calls
4 calls:
33.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
21.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
34.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.7s
(+ (* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series2.0s

Counts
4 → 12
Calls
4 calls:
495.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
500.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
549.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
471.0ms
(+ (* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify2.8s

Counts
113 → 113
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01553491
13563434
210102826
340092710
done50022538

prune794.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize36.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (/ 1 (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
4.0b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.0b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
10.3b
(+ (* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (/ 1 (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite5.4s

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
42×cbrt-prod
37×*-un-lft-identity
35×add-sqr-sqrt
34×add-cbrt-cube
30×times-frac
23×add-cube-cbrt prod-exp cbrt-unprod
10×cbrt-undiv div-exp
9×pow1 frac-times
7×flip3-+ flip-+
6×associate-*r/ distribute-lft-out-- add-log-exp difference-of-squares
5×associate-*l/
4×associate-*l* associate-/r/
3×pow-prod-down
2×cbrt-div pow1/3 div-inv
1×+-commutative associate-*r* sum-log *-commutative distribute-lft-out
Counts
4 → 115
Calls
4 calls:
2.4s
(* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (/ 1 (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
44.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
25.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.9s
(+ (* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (/ 1 (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series1.9s

Counts
4 → 12
Calls
4 calls:
387.0ms
(* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (/ 1 (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
526.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
529.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
477.0ms
(+ (* (+ alpha beta) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (/ 1 (+ (+ alpha beta) (* 2.0 i)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify2.2s

Counts
127 → 127
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02696903
17126493
229725023
done50004951

prune731.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

regimes296.0ms

Accuracy

-3.2% (7.0b remaining)

Error of 12.9b against oracle of 6.0b and baseline of 12.7b

bsearch246.0ms

Steps
ItersRangePoint
6
6.474159054897439e+198
4.452432688017156e+199
1.1572367599421975e+199
9
2.4212514105288802e+117
3.986541213924317e+124
1.4420370619459206e+124

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
050158
165158
done65158

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s6315×body80valid
373.0ms8000×pre80true
307.0ms528×body1280valid
238.0ms582×body640valid
87.0ms356×body320valid
33.0ms219×body160valid