Details

Time bar (total: 20.1s)

sample33.0ms

Algorithm
intervals
Results
8.0ms211×body80valid
4.0ms256×pre80true
3.0ms16×body1280valid
2.0ms17×body640valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114
done500114

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.1b
(/ (/ (* (+ alpha beta) (- 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)) 1.0)
18.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite792.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity times-frac
32×add-sqr-sqrt
28×add-cube-cbrt
20×add-exp-log add-cbrt-cube
14×flip3-+ associate-/r/ flip-+
12×distribute-lft-out
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv div-exp associate-/r* div-inv
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×associate-*r/ associate-*l* associate-*l/
3×prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in clear-num
1×+-commutative pow-prod-down sum-log *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 144
Calls
4 calls:
32.0ms
(* (+ alpha beta) (- beta alpha))
171.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
532.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
51.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series674.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (+ alpha beta) (- beta alpha))
252.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
297.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
84.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify118.0ms

Counts
156 → 156
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07672103
143531976
250031976
done50031976

prune421.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.1b
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.9b
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1250×times-frac
1055×*-un-lft-identity
619×add-sqr-sqrt
461×add-cube-cbrt
218×distribute-lft-out
96×associate-/l*
79×distribute-lft-out-- difference-of-squares
60×associate-/r/
33×div-inv
30×associate-/r*
26×flip3-- flip--
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1 flip3-+ flip-+
3×frac-2neg clear-num
1×+-commutative sum-log
Counts
4 → 645
Calls
4 calls:
74.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
201.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
55.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
726.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series738.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
245.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
85.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
294.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify151.0ms

Counts
657 → 657
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0178313720
1500113481
done500113481

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.9b
(+ (log (exp (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
2.9b
(log (exp (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
2167×times-frac
1804×*-un-lft-identity
1021×add-sqr-sqrt
775×add-cube-cbrt
392×distribute-lft-out
364×log-pow
362×exp-prod
123×distribute-lft-out-- difference-of-squares
96×associate-/r/
93×associate-/l*
53×div-inv
41×flip3-- flip--
25×associate-/r*
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×pow1 log-prod
5×add-log-exp
4×flip3-+ flip-+
3×associate-+l+ associate-/l/
2×frac-2neg clear-num
1×+-commutative rem-log-exp sum-log
Counts
4 → 984
Calls
4 calls:
203.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
55.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
2.3s
(+ (log (exp (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
411.0ms
(log (exp (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

series897.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
81.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
302.0ms
(+ (log (exp (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
257.0ms
(log (exp (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

simplify194.0ms

Counts
996 → 996
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0210618529
1500118215
done500118215

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
0.1b
(/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.9b
(+ (/ (/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
5563×times-frac
3829×*-un-lft-identity
2453×add-sqr-sqrt
1979×add-cube-cbrt
688×distribute-lft-out
284×associate-/l*
237×distribute-lft-out-- difference-of-squares
192×associate-/r/
112×div-inv
93×associate-/r*
82×flip3-+ flip-+
62×add-exp-log
43×div-exp
32×add-cbrt-cube
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
3×frac-2neg clear-num associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 1901
Calls
4 calls:
264.0ms
(/ (/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
73.0ms
(/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
44.0ms
(/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.1s
(+ (/ (/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series769.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(/ (/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
81.0ms
(/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
126.0ms
(/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
307.0ms
(+ (/ (/ (+ alpha beta) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify451.0ms

Counts
1913 → 1913
Iterations

Useful iterations: 1 (78.0ms)

IterNodesCost
0474947454
1500245663
done500245663

prune3.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

regimes218.0ms

Accuracy

14.8% (5.5b remaining)

Error of 11.7b against oracle of 6.1b and baseline of 12.6b

bsearch77.0ms

Steps
ItersRangePoint
8
1.598288092058601e+139
7.397337972832879e+141
5.849296461317042e+141

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05750
15750
done5750

end0.0ms

sample825.0ms

Algorithm
intervals
Results
227.0ms6317×body80valid
112.0ms8000×pre80true
104.0ms523×body1280valid
89.0ms609×body640valid
36.0ms336×body320valid
15.0ms215×body160valid