Details

Time bar (total: 2.1m)

sample88.0ms

Algorithm
intervals
Results
25.0ms201×body80valid
19.0ms19×body640valid
12.0ms18×body1280valid
10.0ms256×pre80true
4.0ms12×body320valid
1.0ms6×body160valid

simplify107.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
107.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize46.0ms

Local error

Found 3 expressions with local error:

21.3b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.2b
(+ (/ (/ (* (+ 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))

rewrite758.0ms

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:
Slowest
519.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
167.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
68.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series827.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
402.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
283.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
141.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify26.0s

Counts
128 → 123
Calls
128 calls:
Slowest
738.0ms
(/ (* (* (/ (* (+ 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)))
700.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
617.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
611.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
597.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize47.0ms

Local error

Found 4 expressions with local error:

5.4b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
1.8b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite660.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-cbrt-cube add-exp-log
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×associate-*l* insert-posit16
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 299
Calls
4 calls:
Slowest
366.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
154.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
90.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
37.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series963.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
344.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
268.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
221.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
130.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.2m

Counts
368 → 311
Calls
368 calls:
Slowest
1.1s
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
987.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
730.0ms
(/ (/ (- (sqrt beta) (sqrt alpha)) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
721.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
702.0ms
(* (sqrt (+ beta alpha)) (sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize101.0ms

Local error

Found 4 expressions with local error:

8.5b
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
49×add-sqr-sqrt *-un-lft-identity
45×times-frac
31×add-cube-cbrt
9×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×cbrt-div pow1/3 div-inv
1×+-commutative sum-log
Counts
4 → 105
Calls
4 calls:
Slowest
1.4s
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
23.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
23.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
20.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
496.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
465.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
460.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
300.0ms
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)

simplify5.0s

Counts
79 → 117
Calls
79 calls:
Slowest
406.0ms
(* (exp (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))) (exp 1.0))
325.0ms
(cbrt (/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i)))))
234.0ms
(cbrt (/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3))))
226.0ms
(cbrt (/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i)))))
222.0ms
(cbrt (/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3))))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize118.0ms

Local error

Found 4 expressions with local error:

8.5b
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
8.5b
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
8.5b
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
4.4b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
19×add-sqr-sqrt *-un-lft-identity
15×times-frac
13×add-cube-cbrt
10×add-log-exp
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×+-commutative sum-log distribute-lft-out-- difference-of-squares
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 67
Calls
4 calls:
Slowest
891.0ms
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
877.0ms
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
776.0ms
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
27.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
461.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
334.0ms
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
309.0ms
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
295.0ms
(+ (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)

simplify4.0s

Counts
37 → 79
Calls
37 calls:
Slowest
405.0ms
(* (exp (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))) (exp 1.0))
390.0ms
(* (exp (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))) (exp 1.0))
371.0ms
(* (exp (* (+ beta alpha) (* (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))) (exp 1.0))
248.0ms
(cbrt (/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3))))
230.0ms
(cbrt (/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i)))))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

regimes531.0ms

Accuracy

72.3% (1.8b remaining)

Error of 7.7b against oracle of 5.9b and baseline of 12.4b

bsearch21.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s6362×body80valid
808.0ms8000×pre80true
476.0ms554×body640valid
409.0ms546×body1280valid
169.0ms345×body320valid
79.0ms193×body160valid