Details

Time bar (total: 27.1s)

sample58.0ms

Algorithm
intervals
Results
13.0ms207×body80valid
6.0ms24×body640valid
6.0ms256×pre80true
4.0ms13×body1280valid
1.0ms6×body320valid
1.0ms6×body160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5001
42483
3453
2102
131
015

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.1b
(+ (/ (/ (* (+ 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)))

rewrite772.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
48×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-cbrt-cube add-exp-log
14×associate-/r/
12×flip3-+ flip-+
11×distribute-lft-out add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
4×frac-times pow1 sum-log
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 124
Calls
4 calls:
22.0ms
(+ (+ alpha beta) (* 2.0 i))
157.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
535.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
55.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series893.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (+ alpha beta) (* 2.0 i))
300.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
437.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
121.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.8s

Counts
136 → 136
Iterations
IterNodes
done5002
24533
1716
0235

prune952.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize46.0ms

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))
0.9b
(* (+ alpha beta) (/ (/ (- 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))) 1.0)

rewrite964.0ms

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:
59.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
278.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
504.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
107.0ms
(+ (* (+ 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:
136.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
265.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
366.0ms
(* (+ 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)

simplify1.4s

Counts
307 → 307
Iterations
IterNodes
done5001
11142
0385

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.9b
(* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.6b
(+ (* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
11.6b
(cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

rewrite779.0ms

Algorithm
rewrite-expression-head
Rules
106×*-un-lft-identity
95×add-sqr-sqrt
93×times-frac
54×add-cube-cbrt
43×associate-*r*
27×swap-sqr
25×associate-*l*
21×add-exp-log
20×add-cbrt-cube
18×distribute-lft-out--
13×pow1
12×difference-of-squares
10×associate-/r/
8×frac-times flip3-+ associate-*l/ flip-+
7×cbrt-div
6×prod-exp cbrt-unprod add-log-exp unswap-sqr
5×cbrt-prod cbrt-undiv div-exp associate-*r/ div-inv distribute-lft-out
2×pow-prod-down *-commutative
1×pow2 +-commutative sum-log pow-plus pow1/3 pow3 pow-sqr pow-prod-up rem-cbrt-cube
Counts
4 → 171
Calls
4 calls:
199.0ms
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
279.0ms
(* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
76.0ms
(+ (* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
206.0ms
(cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
192.0ms
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
457.0ms
(* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
402.0ms
(+ (* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
184.0ms
(cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

simplify1.4s

Counts
183 → 183
Iterations
IterNodes
done5001
11066
0317

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.9b
(* (+ alpha beta) (/ (/ (- 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))) 1.0)
2.6b
(log (exp (+ (* (+ 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
306×times-frac
274×*-un-lft-identity
195×add-sqr-sqrt
132×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
27×distribute-lft-out-- difference-of-squares
22×associate-/r/
21×associate-/l*
18×add-cbrt-cube add-exp-log
14×flip3-+ flip-+
11×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×log-prod associate-/r* associate-*l* log-pow
3×exp-prod prod-exp cbrt-unprod unswap-sqr
2×frac-times div-sub associate-*l/
1×+-commutative clear-num sum-log frac-2neg rem-log-exp exp-sum pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
4 → 271
Calls
4 calls:
216.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
355.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
107.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
404.0ms
(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series1.6s

Counts
4 → 12
Calls
4 calls:
306.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
406.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
482.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
396.0ms
(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify1.5s

Counts
283 → 283
Iterations
IterNodes
done5001
11165
0394

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

regimes551.0ms

Accuracy

-13.1% (7.5b remaining)

Error of 13.2b against oracle of 5.7b and baseline of 12.3b

bsearch234.0ms

Steps
ItersRangePoint
8
5.969670028271364e+165
2.0864758149000452e+170
2.2669802580153736e+166
9
1.2707568867468327e+57
9.927202395589815e+62
9.76982660809476e+62

simplify20.0ms

Iterations
IterNodes
done60
160
047

end0.0ms

sample2.5s

Algorithm
intervals
Results
602.0ms6362×body80valid
535.0ms329×body320valid
413.0ms8000×pre80true
280.0ms542×body1280valid
232.0ms583×body640valid
29.0ms184×body160valid