Details

Time bar (total: 1.4m)

sample95.0ms

Algorithm
intervals
Results
33.0ms210×body80valid
13.0ms256×pre80true
11.0ms19×body640valid
10.0ms12×body1280valid
6.0ms10×body320valid
2.0ms5×body160valid

simplify793.0ms

Counts
1 → 1
Iterations
IterNodes
42155
3440
295
132
016

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2 i))
0.1b
(/ (/ (* (+ 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)
23.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite796.0ms

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 insert-posit16
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 128
Calls
4 calls:
37.0ms
(+ (+ alpha beta) (* 2 i))
196.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
519.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
42.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series871.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (+ alpha beta) (* 2 i))
308.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
401.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
127.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify985.0ms

Counts
140 → 140
Iterations
IterNodes
23006
1715
0239

prune840.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize54.0ms

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))))
1.5b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
2.1b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

rewrite1.2s

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:
37.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
299.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
567.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
187.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
213.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
363.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
317.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

simplify19.8s

Counts
1750 → 1750
Iterations
IterNodes
16131
01844

prune6.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize93.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
2.1b
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
2.1b
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
2.1b
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))

rewrite486.0ms

Algorithm
rewrite-expression-head
Rules
4304×times-frac
3564×*-un-lft-identity
2004×add-sqr-sqrt
1524×add-cube-cbrt
780×distribute-lft-out
356×associate-/r*
240×distribute-lft-out-- difference-of-squares
184×associate-/r/
104×div-inv
84×flip3-+ flip-+
40×add-cbrt-cube add-exp-log
24×cbrt-undiv div-exp
16×associate-/l*
8×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
Counts
4 → 1876
Calls
4 calls:
98.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
98.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
99.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
105.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
283.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
338.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
281.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
305.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))

simplify19.0s

Counts
1888 → 1888
Iterations
IterNodes
28066
11856
0628

prune12.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize124.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
2.9b
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))
2.9b
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))
2.9b
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
1121×times-frac
939×*-un-lft-identity
549×add-sqr-sqrt
411×add-cube-cbrt
195×distribute-lft-out
89×associate-/r*
69×distribute-lft-out-- difference-of-squares
63×cbrt-prod
52×associate-/r/
29×div-inv
24×flip3-+ flip-+
13×add-cbrt-cube add-exp-log
6×cbrt-undiv div-exp
4×pow1 insert-posit16 associate-/l* add-log-exp
3×cbrt-div pow1/3
2×associate-/l/
1×clear-num frac-2neg
Counts
4 → 562
Calls
4 calls:
143.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
13.0ms
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))
12.0ms
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))
27.0ms
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))

series1.6s

Counts
4 → 12
Calls
4 calls:
331.0ms
(/ (+ beta alpha) (/ (+ 2.0 (+ (* i 2) (+ beta alpha))) (/ (- beta alpha) (+ (* i 2) (+ beta alpha)))))
458.0ms
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))
427.0ms
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))
390.0ms
(cbrt (/ (- beta alpha) (+ (* i 2) (+ beta alpha))))

simplify6.2s

Counts
574 → 574
Iterations
IterNodes
27798
11936
0678

prune4.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

regimes578.0ms

Accuracy

14% (5.8b remaining)

Error of 11.9b against oracle of 6.1b and baseline of 12.9b

bsearch199.0ms

Steps
ItersRangePoint
8
3.1473004476260794e+245
1.5939102620761225e+250
1.2994643925028505e+247

simplify34.0ms

Iterations
IterNodes
263
163
050

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.5s6299×body80valid
536.0ms8000×pre80true
455.0ms527×body1280valid
351.0ms596×body640valid
166.0ms378×body320valid
55.0ms200×body160valid