Details

Time bar (total: 2.4m)

sample84.0ms

Algorithm
intervals
Results
25.0ms198×body80valid
20.0ms18×body1280valid
10.0ms256×pre80true
6.0ms15×body640valid
6.0ms17×body320valid
2.0ms8×body160valid

simplify122.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
122.0ms
(/ (+ (/ (/ (* (+ 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: 22.0b

localize61.0ms

Local error

Found 3 expressions with local error:

18.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
3.0b
(+ (/ (/ (* (+ 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))

rewrite782.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-cbrt-cube add-exp-log
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp
5×add-log-exp
4×frac-times
3×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 162
Calls
3 calls:
Slowest
564.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
142.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
74.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series789.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
380.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
311.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
96.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify32.9s

Counts
169 → 171
Calls
169 calls:
Slowest
740.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
736.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
707.0ms
(/ (* (* (/ (* (+ 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)))
691.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
685.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune2.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.3b

localize45.0ms

Local error

Found 4 expressions with local error:

3.0b
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
3.0b
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.0b
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
36×add-sqr-sqrt
32×times-frac
26×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
8×add-cbrt-cube add-exp-log
7×associate-/r*
5×pow1 distribute-lft-out-- difference-of-squares
4×expm1-log1p-u log-prod log-pow insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×exp-prod
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+ fma-udef div-inv
1×flip3-- div-sub rem-log-exp exp-sum flip--
Counts
4 → 115
Calls
4 calls:
Slowest
20.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))
15.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
5.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
1.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series596.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
201.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
186.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
129.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
79.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))

simplify9.0s

Counts
107 → 127
Calls
107 calls:
Slowest
442.0ms
(+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha)))))
290.0ms
(log (* (cbrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))) (cbrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))))
262.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))
244.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
239.0ms
(sqrt (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.2b

localize30.0ms

Local error

Found 3 expressions with local error:

13.8b
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
162×*-un-lft-identity
118×add-sqr-sqrt
80×add-cube-cbrt
26×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
10×add-cbrt-cube add-exp-log
7×associate-/r* flip3-+ flip-+ div-inv
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 div-sub insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×clear-num frac-2neg
1×flip3-- fma-udef flip--
Counts
3 → 184
Calls
3 calls:
Slowest
206.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
56.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series633.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
257.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
251.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
125.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify42.9s

Counts
252 → 193
Calls
252 calls:
Slowest
1.3s
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
943.0ms
(/ (/ (* (* (- 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)))
792.0ms
(/ (/ beta (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
783.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
771.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.2b

localize45.0ms

Local error

Found 4 expressions with local error:

13.8b
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
2.6b
(log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
0.3b
(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
148×*-un-lft-identity
104×add-sqr-sqrt
74×add-cube-cbrt
22×distribute-lft-out
21×associate-/l*
15×distribute-lft-out-- difference-of-squares
12×associate-/r/
10×add-exp-log
9×add-cbrt-cube
6×pow1 log-prod flip3-+ flip-+ div-inv
4×expm1-log1p-u exp-prod associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp exp-sum
2×div-sub log-pow
1×clear-num frac-2neg rem-log-exp fma-udef rem-exp-log associate-/l/
Counts
4 → 174
Calls
4 calls:
Slowest
155.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
3.0ms
(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
1.0ms
(log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
0.0ms
(fma (+ 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
429.0ms
(log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
230.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
220.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
202.0ms
(exp (log (fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))

simplify43.3s

Counts
224 → 186
Calls
224 calls:
Slowest
875.0ms
(/ (/ (* (* (- 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)))
777.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
776.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
772.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
749.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.2b

regimes694.0ms

Accuracy

15.3% (5.4b remaining)

Error of 11.5b against oracle of 6.1b and baseline of 12.5b

bsearch173.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s6351×body80valid
462.0ms514×body1280valid
370.0ms552×body640valid
350.0ms8000×pre80true
213.0ms371×body320valid
82.0ms212×body160valid