Details

Time bar (total: 22.0s)

sample31.0ms

Algorithm
intervals
Results
8.0ms213×body80valid
4.0ms256×pre80true
3.0ms13×body1280valid
2.0ms14×body640valid
1.0ms10×body320valid
1.0ms6×body160valid

simplify549.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
13129
210129
340829
4143729
done500029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize14.0ms

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)
19.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite419.0ms

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:
92.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
299.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series585.0ms

Counts
3 → 9
Calls
3 calls:
229.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms
(+ (/ (/ (* (+ 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)))

simplify977.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (335.0ms)

IterNodesCost
02254035
16773821
230773577
done50003577

prune355.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize14.0ms

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))
3.1b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.6b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite393.0ms

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-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:
23.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
95.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
202.0ms
(* (+ 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))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series765.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
165.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
239.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
283.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify2.1s

Counts
307 → 307
Iterations

Useful iterations: 2 (983.0ms)

IterNodesCost
03859712
110809275
249068911
done50008911

prune817.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
3.1b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.2b
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
3.6b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
134×*-un-lft-identity
99×add-sqr-sqrt
90×associate-*r*
66×add-cube-cbrt
22×distribute-lft-out
14×add-exp-log
13×add-cbrt-cube
12×distribute-lft-out-- difference-of-squares
10×flip3-+ associate-/r/ flip-+
8×pow1
6×log-prod add-log-exp
5×div-inv
4×log-div exp-prod associate-*l*
3×cbrt-undiv div-exp exp-sum prod-exp cbrt-unprod unswap-sqr
2×frac-times exp-diff associate-*l/ log-pow
1×+-commutative associate-*r/ rem-log-exp pow-prod-down sum-log *-commutative rem-exp-log
Counts
4 → 159
Calls
4 calls:
52.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
201.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
54.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
54.0ms
(+ (* (+ 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:
291.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
228.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
274.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
273.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify1.5s

Counts
171 → 171
Iterations

Useful iterations: 2 (572.0ms)

IterNodesCost
03285575
19325281
242294823
done50014823

prune542.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (/ (- 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)))
3.1b
(* (+ 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))))
6.2b
(+ (* (+ 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)

rewrite1.4s

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-exp-log add-cbrt-cube
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 frac-2neg associate-*l/ clear-num associate-/l/
1×+-commutative associate-*r/ pow-prod-down sum-log *-commutative
Counts
4 → 2569
Calls
4 calls:
239.0ms
(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
103.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
629.0ms
(* (+ 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))))
148.0ms
(+ (* (+ 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)

series926.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
222.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
236.0ms
(* (+ 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))))
291.0ms
(+ (* (+ 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)

simplify4.3s

Counts
2581 → 2581
Iterations

Useful iterations: 1 (3.3s)

IterNodesCost
01739137324
14508120451
done5001120451

prune3.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.8b

regimes280.0ms

Accuracy

54.9% (3.8b remaining)

Error of 7.8b against oracle of 4.0b and baseline of 12.4b

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03477
14277
done4277

end0.0ms

sample830.0ms

Algorithm
intervals
Results
261.0ms6353×body80valid
126.0ms8000×pre80true
104.0ms511×body1280valid
93.0ms572×body640valid
48.0ms375×body320valid
15.0ms189×body160valid