Details

Time bar (total: 56.7s)

sample59.0ms

Algorithm
intervals
Results
17.0ms204×body80valid
7.0ms256×pre80true
6.0ms21×body640valid
6.0ms12×body1280valid
4.0ms15×body320valid
1.0ms4×body160valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5003
42146
3448
297
131
015

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize23.0ms

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))
1.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.3b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite975.0ms

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:
232.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
677.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
60.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series903.0ms

Counts
3 → 9
Calls
3 calls:
382.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
399.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
122.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.2s

Counts
120 → 120
Iterations
IterNodes
done5016
23101
1690
0225

prune795.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize193.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
0.1b
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
1.2b
(+ (* (* 1.0 1.0) 1.0) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))
2.9b
(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
62×*-un-lft-identity times-frac
42×associate-*l*
38×add-cube-cbrt
36×associate-*r*
28×add-cbrt-cube add-exp-log
8×pow1 cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod add-log-exp unswap-sqr
6×distribute-lft-out distribute-lft-out-- difference-of-squares
5×flip3-+ flip-+
4×div-inv
2×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
1×+-commutative sum-log sub-neg flip3-- diff-log cube-unmult pow3 sum-cubes flip--
Counts
4 → 150
Calls
4 calls:
301.0ms
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
361.0ms
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
2.4s
(+ (* (* 1.0 1.0) 1.0) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))
8.0ms
(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

series10.0s

Counts
4 → 12
Calls
4 calls:
430.0ms
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
396.0ms
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
8.8s
(+ (* (* 1.0 1.0) 1.0) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))
416.0ms
(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

simplify2.9s

Counts
162 → 162
Iterations
IterNodes
done5001
23232
1730
0217

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

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))
1.6b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.4b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite801.0ms

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:
39.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
232.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
410.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
104.0ms
(+ (* (+ 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:
110.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
267.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
348.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
416.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify3.3s

Counts
307 → 307
Iterations
IterNodes
done5001
24222
11123
0385

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize51.0ms

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))) (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)))
1.6b
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
8.0b
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
6211×times-frac
4294×*-un-lft-identity
3048×add-sqr-sqrt
2585×sqrt-prod
2326×add-cube-cbrt
1077×associate-*r*
645×distribute-lft-out
339×distribute-lft-out-- difference-of-squares
262×associate-/r/
174×associate-/l*
134×flip3-+ flip-+
131×div-inv
36×sqrt-div
32×add-cbrt-cube add-exp-log
15×cbrt-undiv div-exp
14×associate-/r*
11×unswap-sqr
6×pow1 add-log-exp
5×div-sub
4×associate-*l* prod-exp cbrt-unprod
2×frac-times clear-num frac-2neg associate-*l/ associate-/l/
1×+-commutative sum-log pow-prod-down associate-*r/ *-commutative
Counts
4 → 2569
Calls
4 calls:
524.0ms
(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
200.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.1s
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
277.0ms
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
195.0ms
(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
272.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
345.0ms
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
401.0ms
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify5.7s

Counts
2581 → 2581
Iterations
IterNodes
done5000
14696
01739

prune12.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

regimes490.0ms

Accuracy

-4.2% (7.1b remaining)

Error of 13.0b against oracle of 5.9b and baseline of 12.7b

bsearch348.0ms

Steps
ItersRangePoint
9
2.628270585905548e+189
6.763305669356735e+196
2.3715132359409687e+190
9
1.2660772541077468e+119
1.7770422633715175e+125
5.575334987974758e+121
0
4.937143571252759e+27
4.963011288434656e+27
4.947264647020424e+27

simplify26.0ms

Iterations
IterNodes
done66
166
051

end0.0ms

sample2.2s

Algorithm
intervals
Results
546.0ms6312×body80valid
544.0ms370×body320valid
318.0ms8000×pre80true
257.0ms544×body1280valid
217.0ms561×body640valid
32.0ms213×body160valid