Details

Time bar (total: 8.4m)

sample93.0ms

Algorithm
intervals
Results
23.0ms200×body80valid
21.0ms16×body640valid
17.0ms24×body1280valid
10.0ms256×pre80true
3.0ms9×body320valid
2.0ms7×body160valid

simplify117.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
117.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize26.0ms

Local error

Found 4 expressions with local error:

20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(* (+ alpha beta) (- beta alpha))

rewrite827.0ms

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:
Slowest
551.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
171.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
54.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
47.0ms
(* (+ alpha beta) (- beta alpha))

series942.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
414.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
352.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
106.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
69.0ms
(* (+ alpha beta) (- beta alpha))

simplify29.1s

Counts
159 → 160
Calls
159 calls:
Slowest
711.0ms
(/ (* (* (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
677.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
675.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
670.0ms
(* (+ (* alpha alpha) (- (* beta beta) (* alpha beta))) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha))))
664.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize57.0ms

Local error

Found 4 expressions with local error:

2.0b
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
1.7b
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
0.1b
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

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
113×associate-/r*
79×distribute-lft-out-- difference-of-squares
59×associate-/r/
33×div-inv
29×flip3-+ flip-+
20×add-cbrt-cube add-exp-log
13×associate-/l*
10×cbrt-undiv div-exp
6×add-log-exp associate-/l/
4×pow1 insert-posit16
3×clear-num frac-2neg
1×+-commutative sum-log flip3-- div-sub flip--
Counts
4 → 650
Calls
4 calls:
Slowest
561.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
279.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
204.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
30.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series907.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
337.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
244.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
216.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
109.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify3.6m

Counts
1067 → 662
Calls
1067 calls:
Slowest
1.2s
(/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
937.0ms
(/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))))
888.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ 1 (+ (+ alpha beta) (* 2 i))))
822.0ms
(/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (/ (+ (sqrt beta) (sqrt alpha)) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))))))
789.0ms
(/ (cbrt (+ beta alpha)) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

prune8.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize77.0ms

Local error

Found 4 expressions with local error:

2.0b
(log (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))
2.0b
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
1.7b
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
0.1b
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
1235×times-frac
1041×*-un-lft-identity
603×add-sqr-sqrt
453×add-cube-cbrt
219×distribute-lft-out
110×associate-/r*
75×distribute-lft-out-- difference-of-squares
57×associate-/r/
32×div-inv
28×flip3-+ flip-+
18×add-cbrt-cube add-exp-log
9×cbrt-undiv div-exp
8×associate-/l*
6×add-log-exp
5×pow1 log-pow
4×log-prod exp-prod insert-posit16 associate-/l/
2×clear-num frac-2neg
1×+-commutative sum-log rem-log-exp exp-sum
Counts
4 → 627
Calls
4 calls:
Slowest
1.6s
(log (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))
508.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
254.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
184.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
367.0ms
(/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
290.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
253.0ms
(log (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))
220.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

simplify3.6m

Counts
1033 → 639
Calls
1033 calls:
Slowest
1.2s
(/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
1.0s
(/ (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))))
894.0ms
(/ (* (cbrt (+ beta alpha)) (cbrt (+ beta alpha))) (/ 1 (/ (sqrt (- beta alpha)) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))))))
858.0ms
(/ (* (cbrt (+ beta alpha)) (cbrt (+ beta alpha))) (/ (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ 1 (sqrt (+ (+ alpha beta) (* 2 i))))))
767.0ms
(/ (sqrt (+ beta alpha)) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (cbrt (- beta alpha)) (sqrt (+ (+ alpha beta) (* 2 i))))))

prune9.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize47.0ms

Local error

Found 4 expressions with local error:

2.0b
(log (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0))))
2.0b
(log (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0))))
2.0b
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
2.0b
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)

rewrite4.1s

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×log-prod log-pow
10×add-sqr-sqrt sqrt-pow1 add-cube-cbrt
8×pow1 exp-prod sqrt-prod add-log-exp
6×add-exp-log
4×add-cbrt-cube insert-posit16 distribute-lft-out
2×+-commutative sum-log flip3-+ pow1/2 rem-log-exp exp-sum flip-+
Counts
4 → 72
Calls
4 calls:
Slowest
1.6s
(log (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0))))
1.4s
(log (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0))))
560.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
523.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
508.0ms
(log (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0))))
501.0ms
(log (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0))))
246.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)
231.0ms
(+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)

simplify8.9s

Counts
42 → 84
Calls
42 calls:
Slowest
541.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
341.0ms
(log (sqrt (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))))
329.0ms
(log (sqrt (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))))
321.0ms
(log (sqrt (exp (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))))
320.0ms
(log (* (cbrt (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0)))) (cbrt (sqrt (exp (+ (/ (+ beta alpha) (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) 1.0))))))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

regimes369.0ms

Accuracy

-11.6% (7.0b remaining)

Error of 12.4b against oracle of 5.4b and baseline of 11.6b

bsearch354.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.0s6452×body80valid
455.0ms8000×pre80true
398.0ms473×body1280valid
396.0ms540×body640valid
207.0ms355×body320valid
50.0ms180×body160valid