Details

Time bar (total: 19.6s)

sample70.0ms

Algorithm
intervals
Results
17.0ms204×body80valid
12.0ms12×body640valid
9.0ms256×pre80true
7.0ms17×body1280valid
4.0ms16×body320valid
1.0ms7×body160valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5000
42315
3458
299
132
016

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
0.0b
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
12.5b
(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
16.9b
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×*-un-lft-identity
18×add-cube-cbrt
15×times-frac
11×pow1
8×add-cbrt-cube add-exp-log
5×associate-/l*
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×associate-/r* swap-sqr associate-*r* associate-*l*
2×associate-/l/
1×pow2 distribute-rgt-in cbrt-undiv clear-num frac-2neg distribute-lft-in pow-plus flip3-- div-sub div-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod div-inv flip-- unswap-sqr
Counts
4 → 93
Calls
4 calls:
0.0ms
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
6.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
0.0ms
(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
12.0ms
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
86.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
301.0ms
(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
233.0ms
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify2.4s

Counts
105 → 105
Iterations
IterNodes
done5000
33884
21077
1377
0168

prune721.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.3b
(/ (- beta alpha) (fma i 2 (+ beta alpha)))
1.8b
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
4.3b
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
33×add-sqr-sqrt
31×times-frac
25×add-cube-cbrt
10×distribute-lft-out
9×add-exp-log associate-/l*
8×add-cbrt-cube
7×associate-/r*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares associate-/l/
3×log-prod
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+ div-inv
1×flip3-- div-sub rem-log-exp log-pow fma-udef flip--
Counts
4 → 110
Calls
4 calls:
36.0ms
(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
25.0ms
(/ (- beta alpha) (fma i 2 (+ beta alpha)))
0.0ms
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
3.0ms
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))

series762.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
94.0ms
(/ (- beta alpha) (fma i 2 (+ beta alpha)))
215.0ms
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)
337.0ms
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))

simplify1.4s

Counts
122 → 122
Iterations
IterNodes
done5000
21246
1438
0195

prune910.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- beta alpha) (fma i 2 (+ beta alpha)))
0.3b
(/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
4.3b
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0))
6.9b
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
67×*-un-lft-identity
43×times-frac
41×add-sqr-sqrt
33×add-cube-cbrt
20×sqrt-prod
13×distribute-lft-out
10×associate-/r*
9×add-exp-log associate-/l*
8×add-cbrt-cube
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares associate-/l/
3×log-prod
2×cbrt-undiv clear-num frac-2neg flip3-+ sqrt-div div-exp associate-/r/ flip-+ div-inv
1×flip3-- div-sub rem-log-exp log-pow fma-udef flip--
Counts
4 → 125
Calls
4 calls:
27.0ms
(/ (- beta alpha) (fma i 2 (+ beta alpha)))
34.0ms
(/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
2.0ms
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0))
1.0ms
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

series869.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (- beta alpha) (fma i 2 (+ beta alpha)))
169.0ms
(/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
386.0ms
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0))
212.0ms
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

simplify2.1s

Counts
137 → 137
Iterations
IterNodes
done5000
34274
21246
1490
0231

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ beta alpha))
0.5b
(cbrt (+ beta alpha))
4.3b
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (* (/ (* (cbrt (+ beta alpha)) (cbrt (+ beta alpha))) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (cbrt (+ beta alpha)) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0))
10.3b
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (* (/ (* (cbrt (+ beta alpha)) (cbrt (+ beta alpha))) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (cbrt (+ beta alpha)) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
5×pow1 add-exp-log
4×expm1-log1p-u cbrt-div add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×log-prod
2×flip3-+ pow1/3 flip-+ distribute-lft-out
1×rem-log-exp log-pow fma-udef
Counts
4 → 60
Calls
4 calls:
5.0ms
(cbrt (+ beta alpha))
5.0ms
(cbrt (+ beta alpha))
3.0ms
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (* (/ (* (cbrt (+ beta alpha)) (cbrt (+ beta alpha))) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (cbrt (+ beta alpha)) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0))
1.0ms
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (* (/ (* (cbrt (+ beta alpha)) (cbrt (+ beta alpha))) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (cbrt (+ beta alpha)) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
169.0ms
(cbrt (+ beta alpha))
162.0ms
(cbrt (+ beta alpha))
745.0ms
(log (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (* (/ (* (cbrt (+ beta alpha)) (cbrt (+ beta alpha))) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (cbrt (+ beta alpha)) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0))
221.0ms
(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (* (/ (* (cbrt (+ beta alpha)) (cbrt (+ beta alpha))) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (cbrt (+ beta alpha)) (sqrt (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

simplify1.7s

Counts
72 → 72
Iterations
IterNodes
done5000
31853
2658
1253
0118

prune628.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.0b

regimes476.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 12.8b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done25
125
023

end0.0ms

sample2.1s

Algorithm
intervals
Results
623.0ms6317×body80valid
447.0ms8000×pre80true
310.0ms521×body1280valid
290.0ms597×body640valid
102.0ms368×body320valid
34.0ms197×body160valid