Details

Time bar (total: 42.2s)

sample49.0ms

Algorithm
intervals
Results
12.0ms204×body80valid
7.0ms256×pre80true
5.0ms24×body640valid
5.0ms20×body1280valid
1.0ms4×body320valid
0.0ms4×body160valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5022
42155
3440
295
132
016

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
21.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity times-frac
32×add-sqr-sqrt
28×add-cube-cbrt
20×add-cbrt-cube add-exp-log
14×flip3-+ associate-/r/ flip-+
12×distribute-lft-out
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv associate-/r* div-exp div-inv
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×associate-*l* associate-*l/ associate-*r/ insert-posit16
3×prod-exp cbrt-unprod
2×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in
1×+-commutative sum-log pow-prod-down *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 148
Calls
4 calls:
40.0ms
(* (+ alpha beta) (- beta alpha))
213.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
698.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
92.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series874.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (+ alpha beta) (- beta alpha))
297.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
402.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
117.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify2.6s

Counts
160 → 160
Iterations
IterNodes
done5003
23624
1789
0267

prune798.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.1b
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
1.2b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
3.6b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
5126×times-frac
3533×*-un-lft-identity
2233×add-sqr-sqrt
1787×add-cube-cbrt
650×distribute-lft-out
223×distribute-lft-out-- difference-of-squares
183×div-inv
167×associate-/r/
113×associate-/r*
76×flip3-+ flip-+
41×add-exp-log
32×add-cbrt-cube
28×div-exp
25×associate-/l*
19×cbrt-undiv
6×add-log-exp
5×associate-/l/
4×pow1 insert-posit16
3×clear-num frac-2neg 1-exp
1×+-commutative sum-log flip3-- div-sub flip--
Counts
4 → 1738
Calls
4 calls:
61.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
370.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
1.4s
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
256.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

series984.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
211.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
360.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
298.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

simplify3.2s

Counts
1750 → 1750
Iterations
IterNodes
done5000
01844

prune8.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.1b
(* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.1b
(* (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
4.1b
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
132×add-exp-log
66×*-un-lft-identity
61×add-sqr-sqrt
59×add-cbrt-cube
58×times-frac prod-exp
51×div-exp
38×add-cube-cbrt
34×associate-*l*
22×associate-*r* cbrt-unprod
18×cbrt-undiv 1-exp
12×pow1
10×distribute-lft-out
8×rec-exp
6×frac-times associate-*r/ associate-/r/ add-log-exp unswap-sqr
4×associate-/r* flip3-+ pow-prod-down associate-*l/ flip-+ insert-posit16 div-inv
3×associate-/l* distribute-lft-out-- difference-of-squares
2×*-commutative
1×+-commutative clear-num sum-log frac-2neg pow-flip inv-pow
Counts
4 → 191
Calls
4 calls:
196.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))
154.0ms
(* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
436.0ms
(* (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
245.0ms
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)

series993.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))
119.0ms
(* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
353.0ms
(* (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
442.0ms
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (/ (+ alpha beta) 1) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)

simplify3.0s

Counts
203 → 203
Iterations
IterNodes
done5002
23002
1928
0308

prune904.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
1.2b
(+ (/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
1.2b
(log (exp (+ (/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))
3.6b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

rewrite3.5s

Algorithm
rewrite-expression-head
Rules
1575×*-un-lft-identity
1535×times-frac
714×add-sqr-sqrt
528×add-cube-cbrt
494×distribute-lft-out
131×associate-/r*
93×distribute-lft-out-- difference-of-squares
69×associate-/r/
38×flip3-+ flip-+ div-inv
18×add-cbrt-cube add-exp-log
9×cbrt-undiv div-exp associate-/l*
8×associate-/l/
6×add-log-exp
5×pow1 log-pow
4×log-prod exp-prod frac-add insert-posit16
2×clear-num frac-2neg
1×+-commutative sum-log rem-log-exp exp-sum
Counts
4 → 758
Calls
4 calls:
194.0ms
(/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
847.0ms
(+ (/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
2.2s
(log (exp (+ (/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))
149.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
231.0ms
(/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
370.0ms
(+ (/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
425.0ms
(log (exp (+ (/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))
314.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (+ (* 2 i) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

simplify2.6s

Counts
770 → 770
Iterations
IterNodes
done5001
12208
0746

prune3.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes317.0ms

Accuracy

17.5% (5.3b remaining)

Error of 11.0b against oracle of 5.6b and baseline of 12.1b

bsearch351.0ms

Steps
ItersRangePoint
9
1.4480514837100701e+199
8.708119158789799e+205
1.553504313722894e+199
8
5.094536971308387e+146
4.38061499353291e+149
7.005757127673538e+146
8
1.8394685690263203e+130
9.906063471096378e+134
1.4836991668770156e+134

simplify17.0ms

Iterations
IterNodes
done63
163
046

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s6395×body80valid
368.0ms8000×pre80true
265.0ms547×body1280valid
222.0ms527×body640valid
89.0ms353×body320valid
29.0ms178×body160valid