Details

Time bar (total: 24.8s)

sample97.0ms

Algorithm
intervals
Results
30.0ms199×body80valid
17.0ms27×body640valid
13.0ms256×pre80true
10.0ms13×body1280valid
5.0ms12×body320valid
1.0ms5×body160valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done2042
42042
3440
295
132
016

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize56.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
19.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite860.0ms

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-- insert-posit16 flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 114
Calls
3 calls:
158.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
629.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
71.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series889.0ms

Counts
3 → 9
Calls
3 calls:
356.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
409.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
124.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify1.2s

Counts
123 → 123
Iterations
IterNodes
done2001
22001
1697
0228

prune864.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b
(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i))))
1.5b
(+ (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
59×add-cbrt-cube add-exp-log
56×add-sqr-sqrt
55×times-frac
39×associate-*r*
38×add-cube-cbrt
22×prod-exp cbrt-unprod
19×associate-*l*
18×cbrt-undiv div-exp
11×pow1
10×distribute-lft-out
8×associate-/r/
6×frac-times associate-*l/ add-log-exp
4×associate-/r* flip3-+ pow-prod-down associate-*r/ flip-+ insert-posit16 div-inv unswap-sqr
3×associate-/l* distribute-lft-out-- difference-of-squares
2×flip3-- *-commutative flip-- associate-/l/
1×+-commutative clear-num sum-log frac-2neg div-sub
Counts
4 → 170
Calls
4 calls:
205.0ms
(/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
415.0ms
(* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
143.0ms
(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i))))
276.0ms
(+ (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
354.0ms
(* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
204.0ms
(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i))))
426.0ms
(+ (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.5s

Counts
182 → 182
Iterations
IterNodes
done2002
22002
11021
0300

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))
0.1b
(* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i))))))
1.5b
(+ 1.0 (* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))))
1.5b
(log (exp (+ 1.0 (* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))))))

rewrite749.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
57×add-cbrt-cube add-exp-log
53×add-sqr-sqrt
52×times-frac
40×associate-*l*
33×add-cube-cbrt
27×associate-*r*
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
16×distribute-lft-out
12×pow1
6×frac-times associate-*r/ associate-/r/ add-log-exp
4×log-prod flip3-+ pow-prod-down associate-*l/ log-pow flip-+ insert-posit16 distribute-lft-out-- difference-of-squares unswap-sqr
3×exp-prod div-inv
2×*-commutative
1×+-commutative sum-log rem-log-exp exp-sum
Counts
4 → 159
Calls
4 calls:
306.0ms
(* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))
382.0ms
(* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i))))))
16.0ms
(+ 1.0 (* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))))
39.0ms
(log (exp (+ 1.0 (* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))
309.0ms
(* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i))))))
276.0ms
(+ 1.0 (* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))))
305.0ms
(log (exp (+ 1.0 (* (/ (+ beta alpha) (+ (* 2 i) (+ beta alpha))) (* (/ (+ alpha (- beta (* 2 i))) (+ 2.0 (+ (* 2 i) (+ beta alpha)))) (/ (- beta alpha) (+ alpha (- beta (* 2 i)))))))))

simplify1.5s

Counts
171 → 171
Iterations
IterNodes
done2006
22006
1949
0295

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b
(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha))
0.4b
(* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i))))
3.2b
(+ (* (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
95×add-cbrt-cube
88×prod-exp
46×cbrt-unprod
44×div-exp
42×*-un-lft-identity
41×frac-times
38×associate-*r*
35×add-sqr-sqrt
34×times-frac associate-*l/
28×add-cube-cbrt
23×cbrt-undiv
20×pow1 associate-*l*
18×associate-*r/
15×flip3-- flip--
10×pow-prod-down
9×rec-exp 1-exp
6×associate-/r/ distribute-lft-out add-log-exp
4×insert-posit16
3×flip3-+ un-div-inv *-commutative flip-+ div-inv
2×distribute-rgt-in sub-neg distribute-lft-in unswap-sqr
1×+-commutative sum-log distribute-lft-out-- difference-of-squares
Counts
4 → 213
Calls
4 calls:
793.0ms
(* (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
120.0ms
(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha))
185.0ms
(* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i))))
686.0ms
(+ (* (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
355.0ms
(* (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
141.0ms
(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha))
199.0ms
(* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i))))
380.0ms
(+ (* (* (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (- beta alpha)) (/ 1 (- (+ alpha beta) (* 2 i)))) (/ (- (+ alpha beta) (* 2 i)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.5s

Counts
225 → 225
Iterations
IterNodes
done2003
22003
11213
0375

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.4b

regimes528.0ms

Accuracy

3.6% (6.5b remaining)

Error of 12.5b against oracle of 6.0b and baseline of 12.7b

bsearch398.0ms

Steps
ItersRangePoint
9
4.9642756113544824e+172
2.410526659644446e+179
1.480588010249348e+179
5
3.592400399742957e+118
9.0083899952393e+118
3.6345013768301078e+118
9
1.3838521750995308e+35
6.535630972949253e+41
2.0760474421781283e+39

simplify76.0ms

Iterations
IterNodes
done77
177
057

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s6311×body80valid
841.0ms530×body1280valid
465.0ms599×body640valid
399.0ms8000×pre80true
235.0ms354×body320valid
60.0ms206×body160valid