Details

Time bar (total: 1.9m)

sample100.0ms

Algorithm
intervals
Results
38.0ms213×body80valid
16.0ms19×body1280valid
14.0ms256×pre80true
5.0ms11×body320valid
5.0ms7×body640valid
2.0ms6×body160valid

simplify178.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
178.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize57.0ms

Local error

Found 3 expressions with local error:

19.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.6b
(+ (/ (/ (* (+ 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))

rewrite886.0ms

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
614.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
198.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
70.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series798.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
416.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
290.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
92.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify33.1s

Counts
169 → 171
Calls
169 calls:
Slowest
765.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
687.0ms
(/ (* (* (/ (* (+ 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)))
682.0ms
(/ (* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
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))))
663.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize39.0ms

Local error

Found 4 expressions with local error:

1.6b
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
1.6b
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.3b
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
0.2b
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))

rewrite73.0ms

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
39.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
28.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))
3.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series564.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
160.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
135.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
88.0ms
(/ (+ beta alpha) (fma 2 i (+ beta alpha)))

simplify9.6s

Counts
107 → 127
Calls
107 calls:
Slowest
617.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
471.0ms
(+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha)))))
329.0ms
(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)))))
299.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
287.0ms
(log (sqrt (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize60.0ms

Local error

Found 4 expressions with local error:

4.9b
(log (log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
1.6b
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
1.6b
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.3b
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
29×add-sqr-sqrt
20×times-frac
19×add-cube-cbrt
11×log-prod
9×log-pow
7×pow1 add-exp-log
6×exp-prod add-cbrt-cube distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
2×rem-log-exp associate-/r/ fma-udef associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-sub div-exp exp-sum flip-+ div-inv flip--
Counts
4 → 98
Calls
4 calls:
Slowest
23.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
4.0ms
(log (log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
4.0ms
(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)

series902.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
334.0ms
(log (log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))
215.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
199.0ms
(fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
155.0ms
(/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

simplify10.8s

Counts
82 → 110
Calls
82 calls:
Slowest
455.0ms
(+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha)))))
335.0ms
(log (* (cbrt (log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))) (cbrt (log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))))))
311.0ms
(- (+ (* 1.5 (/ 1 (pow beta 2))) (log 2.0)) (* 1.0 (/ 1 beta)))
282.0ms
(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)))))
280.0ms
(log (exp (fma (/ (- beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize41.0ms

Local error

Found 3 expressions with local error:

9.5b
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite305.0ms

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
229.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
69.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
1.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series569.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
246.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
205.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
118.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify42.6s

Counts
252 → 193
Calls
252 calls:
Slowest
941.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
882.0ms
(/ (/ (* (* (- 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)))
783.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
769.0ms
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
765.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

regimes411.0ms

Accuracy

16.4% (5.3b remaining)

Error of 11.0b against oracle of 5.7b and baseline of 12.1b

bsearch168.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s6408×body80valid
716.0ms497×body1280valid
378.0ms8000×pre80true
345.0ms566×body640valid
139.0ms340×body320valid
72.0ms189×body160valid