Details

Time bar (total: 34.3s)

sample95.0ms

Algorithm
intervals
Results
21.0ms208×body80valid
8.0ms256×pre80true
7.0ms15×body1280valid
6.0ms15×body640valid
4.0ms13×body320valid
1.0ms5×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
015405
131405
2102405
3453405
42483405
done5001405

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize21.0ms

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))
2.3b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite940.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-cbrt-cube add-exp-log
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
241.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
626.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
65.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series972.0ms

Counts
3 → 9
Calls
3 calls:
380.0ms
(/ (/ (* (+ 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)
134.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify3.6s

Counts
120 → 120
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
022559123
169753837
2447952794
done500152794

prune839.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize38.0ms

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))
1.7b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite959.0ms

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-cbrt-cube add-exp-log
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 295
Calls
4 calls:
68.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
288.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
442.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
143.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.0s

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
256.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
369.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
287.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify2.0s

Counts
307 → 307
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0381157787
11138141316
done5001140227

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize73.0ms

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))
1.7b
(* (+ beta alpha) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
4.8b
(+ (* (+ beta alpha) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite5.3s

Algorithm
rewrite-expression-head
Rules
90×add-exp-log
51×add-cbrt-cube
43×prod-exp cbrt-unprod
29×frac-times
27×cbrt-undiv div-exp
17×associate-*l/
16×associate-*r/
13×pow1 *-un-lft-identity
11×flip3-+ flip-+
8×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×pow-prod-down add-log-exp
4×cbrt-div associate-*l*
3×distribute-lft-out
2×pow1/3
1×+-commutative sum-log associate-*r* *-commutative
Counts
4 → 110
Calls
4 calls:
61.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
65.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.6s
(* (+ beta alpha) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
2.6s
(+ (* (+ beta alpha) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
252.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
231.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
413.0ms
(* (+ beta alpha) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
300.0ms
(+ (* (+ beta alpha) (* (* (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify5.3s

Counts
122 → 122
Iterations

Useful iterations: done (5.3s)

IterNodesCost
028092018
189279636
2421877434
done500173214

prune854.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize56.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
3.5b
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
3.5b
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

rewrite423.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
131×*-un-lft-identity
96×add-sqr-sqrt
90×associate-*r*
63×add-cube-cbrt
22×distribute-lft-out
13×add-cbrt-cube add-exp-log
12×distribute-lft-out-- difference-of-squares
10×flip3-+ associate-/r/ flip-+ add-log-exp
6×pow1
5×div-inv
4×associate-*l*
3×cbrt-undiv +-commutative sum-log div-exp prod-exp cbrt-unprod unswap-sqr
2×frac-times associate-*l/
1×pow-prod-down associate-*r/ *-commutative
Counts
4 → 150
Calls
4 calls:
381.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
12.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
12.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
334.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
411.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
402.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
406.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

simplify1.5s

Counts
162 → 162
Iterations

Useful iterations: done (1.4s)

IterNodesCost
027475312
188265324
done500163472

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

regimes629.0ms

Accuracy

13% (5.9b remaining)

Error of 11.8b against oracle of 5.9b and baseline of 12.7b

bsearch134.0ms

Steps
ItersRangePoint
9
2.5571677378596085e+141
6.851744006698495e+147
6.818670779247876e+145

simplify31.0ms

Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
0341178
1421138
2431138
done431138

end0.0ms

sample1.9s

Algorithm
intervals
Results
638.0ms519×body1280valid
545.0ms6316×body80valid
234.0ms8000×pre80true
185.0ms582×body640valid
73.0ms385×body320valid
25.0ms198×body160valid