Details

Time bar (total: 2.6m)

sample82.0ms

Algorithm
intervals
Results
23.0ms200×body80valid
16.0ms16×body1280valid
11.0ms256×pre80true
10.0ms21×body640valid
6.0ms15×body320valid
1.0ms4×body160valid

simplify142.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
142.0ms
(/ (+ (/ (/ (* (+ 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: 27.5b

localize54.0ms

Local error

Found 3 expressions with local error:

23.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.3b
(+ (/ (/ (* (+ 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))

rewrite792.0ms

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
577.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
160.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
54.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series850.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
394.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
339.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
116.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify26.1s

Counts
128 → 123
Calls
128 calls:
Slowest
1.1s
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
714.0ms
(/ (* (* (/ (* (+ 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)))
629.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
627.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
627.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize60.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.0b
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite651.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
45×add-sqr-sqrt
35×times-frac
26×add-cube-cbrt
21×associate-*r*
20×add-cbrt-cube add-exp-log
8×flip3-+ flip-+
7×associate-/r* distribute-lft-out-- difference-of-squares associate-/l/
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod insert-posit16 distribute-lft-out
3×div-inv
2×clear-num frac-2neg associate-*r/ unswap-sqr
1×+-commutative sum-log flip3-- div-sub pow-prod-down *-commutative flip--
Counts
4 → 133
Calls
4 calls:
Slowest
356.0ms
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
127.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
118.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
48.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series756.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
310.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
242.0ms
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
115.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
89.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify13.8s

Counts
122 → 145
Calls
122 calls:
Slowest
1.1s
(/ (* (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
975.0ms
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))))
618.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
548.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
415.0ms
(* (+ (pow beta 3) (pow alpha 3)) (- beta alpha))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize30.0ms

Local error

Found 4 expressions with local error:

4.3b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.0b
(* (+ alpha beta) (/ (/ (- 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)))

rewrite675.0ms

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
339.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
161.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
110.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
48.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
363.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
313.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
238.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
128.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.2m

Counts
368 → 311
Calls
368 calls:
Slowest
1.1s
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.0s
(/ (/ (* (* (- 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)))
893.0ms
(* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (/ (* (* (/ (- 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))))
711.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
707.0ms
(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

prune4.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize68.0ms

Local error

Found 4 expressions with local error:

4.3b
(+ (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
2.0b
(* (+ alpha beta) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
0.1b
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite957.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
60×add-exp-log
56×*-un-lft-identity
49×times-frac
36×add-cbrt-cube
32×add-cube-cbrt
25×associate-*l* prod-exp
19×associate-*r*
17×div-exp
13×cbrt-unprod
12×frac-times
11×pow1
9×cbrt-undiv flip3-+ flip-+
8×associate-*r/
7×distribute-lft-out-- difference-of-squares
6×associate-*l/ associate-/r/ add-log-exp unswap-sqr
5×associate-/l*
4×rec-exp 1-exp pow-prod-down un-div-inv insert-posit16 distribute-lft-out
3×associate-/r* div-inv
2×*-commutative associate-/l/
1×+-commutative clear-num sum-log frac-2neg flip3-- div-sub flip--
Counts
4 → 168
Calls
4 calls:
Slowest
340.0ms
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
301.0ms
(+ (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
281.0ms
(* (+ alpha beta) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
30.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(+ (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
316.0ms
(* (+ alpha beta) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
220.0ms
(* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
107.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify25.4s

Counts
165 → 180
Calls
165 calls:
Slowest
730.0ms
(* (- (* alpha alpha) (* beta beta)) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
663.0ms
(* (+ (pow alpha 3) (pow beta 3)) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
636.0ms
(* (- (* alpha alpha) (* beta beta)) (* (- beta alpha) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
606.0ms
(* (+ (* alpha alpha) (- (* beta beta) (* alpha beta))) (+ (+ alpha beta) (* 2 i)))
548.0ms
(+ (log (+ alpha beta)) (+ (- (log (- beta alpha)) (log (+ (+ alpha beta) (* 2 i)))) (- 0 (log (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

regimes408.0ms

Accuracy

-9.3% (6.6b remaining)

Error of 12.4b against oracle of 5.8b and baseline of 11.8b

bsearch307.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s6435×body80valid
430.0ms8000×pre80true
404.0ms575×body640valid
359.0ms467×body1280valid
180.0ms351×body320valid
80.0ms172×body160valid