Details

Time bar (total: 3.1m)

sample98.0ms

Algorithm
intervals
Results
28.0ms187×body80valid
14.0ms19×body1280valid
14.0ms26×body640valid
11.0ms256×pre80true
7.0ms16×body320valid
2.0ms8×body160valid

simplify116.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
116.0ms
(/ (+ (/ (/ (* (+ 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: 26.3b

localize61.0ms

Local error

Found 4 expressions with local error:

20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.7b
(+ (/ (/ (* (+ 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) (* 2 i)) 2.0)

rewrite761.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
50×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-cbrt-cube add-exp-log
15×add-log-exp
14×associate-/r/
12×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* sum-log div-exp div-inv
4×frac-times pow1 insert-posit16
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 130
Calls
4 calls:
Slowest
437.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
169.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
101.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)
52.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series821.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
333.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
325.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
127.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
36.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

simplify26.6s

Counts
136 → 142
Calls
136 calls:
Slowest
816.0ms
(/ (* (* (/ (* (+ 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)))
679.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
667.0ms
(/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
656.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
635.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize42.0ms

Local error

Found 4 expressions with local error:

5.8b
(+ (* (+ 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)))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite597.0ms

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
314.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
120.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
97.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
58.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series887.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
336.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
241.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
208.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
102.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.2m

Counts
368 → 311
Calls
368 calls:
Slowest
1.4s
(/ (/ (* (* (- 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)))
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))))
955.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
746.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
736.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune3.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.2b

localize108.0ms

Local error

Found 4 expressions with local error:

5.8b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
5.8b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
5.8b
(+ (* (+ 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)))

rewrite652.0ms

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
356.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
107.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
96.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
86.0ms
(+ (* (+ 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
339.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
290.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
265.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
247.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify33.6s

Counts
127 → 166
Calls
127 calls:
Slowest
1.0s
(* (* (* (+ 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))))
733.0ms
(* (sqrt (+ beta alpha)) (sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
700.0ms
(* (sqrt (+ beta alpha)) (sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
687.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
681.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize95.0ms

Local error

Found 4 expressions with local error:

5.8b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
5.8b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
5.8b
(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
1.8b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite657.0ms

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
358.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
145.0ms
(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ 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)
74.0ms
(+ (* (+ 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
362.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
259.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
241.0ms
(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
225.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify33.3s

Counts
127 → 166
Calls
127 calls:
Slowest
1.2s
(* (* (* (+ 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))))
1.1s
(* (sqrt (+ beta alpha)) (sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
1.1s
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
725.0ms
(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
660.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune3.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.2b

regimes429.0ms

Accuracy

9.4% (5.7b remaining)

Error of 11.6b against oracle of 6.0b and baseline of 12.2b

bsearch96.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s6373×body80valid
448.0ms485×body1280valid
417.0ms8000×pre80true
368.0ms600×body640valid
217.0ms357×body320valid
54.0ms185×body160valid