Details

Time bar (total: 29.9s)

sample87.0ms

Algorithm
intervals
Results
26.0ms199×body80valid
15.0ms21×body1280valid
14.0ms23×body640valid
11.0ms256×pre80true
6.0ms11×body320valid
1.0ms2×body160valid

simplify665.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize26.0ms

Local error

Found 3 expressions with local error:

22.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite576.0ms

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
394.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
136.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
42.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series771.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
328.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
324.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
119.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify1.3s

Counts
123 → 123

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

localize36.0ms

Local error

Found 4 expressions with local error:

3.6b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.2b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite486.0ms

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
250.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
123.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
64.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
43.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series889.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
295.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
238.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
235.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
121.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify2.0s

Counts
311 → 311

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize47.0ms

Local error

Found 4 expressions with local error:

3.6b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
3.6b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
3.6b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.2b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite581.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
131×*-un-lft-identity
96×add-sqr-sqrt
90×associate-*r*
63×add-cube-cbrt
22×distribute-lft-out
13×add-cbrt-cube add-exp-log
12×distribute-lft-out-- difference-of-squares
10×flip3-+ associate-/r/ flip-+ add-log-exp
6×pow1
5×div-inv
4×associate-*l* insert-posit16
3×cbrt-undiv +-commutative sum-log div-exp prod-exp cbrt-unprod unswap-sqr
2×frac-times associate-*l/
1×pow-prod-down associate-*r/ *-commutative
Counts
4 → 154
Calls
4 calls:
Slowest
340.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
91.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
76.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
70.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
312.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
276.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
266.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
261.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify2.0s

Counts
166 → 166

prune2.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize119.0ms

Local error

Found 4 expressions with local error:

7.7b
(+ (* (* (+ 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)
4.0b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
4.0b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
4.0b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

rewrite768.0ms

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
694.0ms
(+ (* (* (+ 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)
24.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
23.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
23.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
499.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
475.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
469.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
304.0ms
(+ (* (* (+ 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)

simplify2.3s

Counts
117 → 117

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

regimes368.0ms

Accuracy

11.4% (5.6b remaining)

Error of 11.4b against oracle of 5.8b and baseline of 12.2b

bsearch142.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.5s6384×body80valid
460.0ms537×body1280valid
359.0ms8000×pre80true
317.0ms562×body640valid
136.0ms346×body320valid
45.0ms171×body160valid