Details

Time bar (total: 15.8s)

sample32.0ms

Algorithm
intervals
Results
8.0ms207×body80valid
4.0ms256×pre80true
3.0ms17×body1280valid
2.0ms13×body640valid
2.0ms13×body320valid
0.0ms6×body160valid

simplify592.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
01529
13129
210527
343326
4160026
done500026

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0b
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
2.2b
(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
31×add-sqr-sqrt times-frac
23×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
7×add-exp-log associate-/r* add-cbrt-cube
4×associate-/l/ distribute-lft-out-- difference-of-squares
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+ div-inv
1×flip3-- div-sub flip-- fma-udef
Counts
3 → 92
Calls
3 calls:
11.0ms
(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))
9.0ms
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.0ms
(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series379.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))
73.0ms
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
234.0ms
(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify626.0ms

Counts
101 → 101
Iterations

Useful iterations: done (623.0ms)

IterNodesCost
01761908
13951852
211561716
done50001715

prune290.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.2b
(/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
6.3b
(fma (/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
510×*-un-lft-identity
505×times-frac
288×sqrt-prod
238×add-sqr-sqrt
230×add-cube-cbrt
136×distribute-lft-out
43×associate-/l*
20×sqrt-div associate-/r/
17×associate-/r*
13×add-exp-log add-cbrt-cube
11×flip3-+ flip-+ div-inv
5×cbrt-undiv div-exp associate-/l/
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×frac-2neg clear-num
1×flip3-- div-sub flip-- fma-udef
Counts
4 → 405
Calls
4 calls:
11.0ms
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
29.0ms
(/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
12.0ms
(/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms
(fma (/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series519.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
72.0ms
(/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
134.0ms
(/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
240.0ms
(fma (/ (/ (+ alpha beta) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify980.0ms

Counts
417 → 417
Iterations

Useful iterations: done (962.0ms)

IterNodesCost
041915923
194513806
2251912967
done500012963

prune734.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.3b
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b
(/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
8.5b
(fma (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite388.0ms

Algorithm
rewrite-expression-head
Rules
1456×times-frac
1233×sqrt-prod
1226×*-un-lft-identity
830×add-sqr-sqrt
579×add-cube-cbrt
328×associate-*r*
310×distribute-lft-out
72×sqrt-div
63×unswap-sqr
52×add-exp-log
49×associate-/l*
38×associate-/r/
36×associate-*l*
32×add-cbrt-cube
23×div-exp
19×flip3-+ flip-+ div-inv
17×associate-/r*
13×cbrt-undiv
12×prod-exp
9×pow1
6×cbrt-unprod
5×pow-flip
4×expm1-log1p-u rec-exp sqrt-pow1 1-exp log1p-expm1-u add-log-exp
2×frac-2neg pow1/2 clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef associate-/l/ inv-pow
Counts
4 → 930
Calls
4 calls:
260.0ms
(* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
34.0ms
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
13.0ms
(/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.0ms
(fma (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series3.1s

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
2.6s
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
265.0ms
(/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
81.0ms
(fma (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.4s

Counts
942 → 942
Iterations

Useful iterations: done (1.4s)

IterNodesCost
071641863
1213236013
done500033693

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
0.3b
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.4b
(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
8.3b
(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite457.0ms

Algorithm
rewrite-expression-head
Rules
2106×sqrt-prod
1959×times-frac
1611×*-un-lft-identity
1058×add-sqr-sqrt
797×add-cube-cbrt
466×associate-*r*
394×distribute-lft-out
96×sqrt-div
65×unswap-sqr
52×add-exp-log
50×associate-/r/
49×associate-/l*
32×add-cbrt-cube
27×associate-*l*
25×flip3-+ flip-+ div-inv
23×div-exp
17×associate-/r*
13×cbrt-undiv
12×prod-exp
8×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×pow-flip
2×frac-2neg clear-num
1×frac-times sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef associate-/l/ inv-pow
Counts
4 → 1188
Calls
4 calls:
291.0ms
(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
40.0ms
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
7.0ms
(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms
(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series509.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
141.0ms
(/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
120.0ms
(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
82.0ms
(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (/ (+ alpha beta) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.5s

Counts
1200 → 1200
Iterations

Useful iterations: done (1.4s)

IterNodesCost
079055155
1242346158
done500044783

prune1.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.0b

regimes109.0ms

Accuracy

16.9% (5.5b remaining)

Error of 11.0b against oracle of 5.5b and baseline of 12.1b

bsearch56.0ms

Steps
ItersRangePoint
7
1.4116812876132222e+209
2.791389625835243e+210
1.5371929371909745e+209

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02958
13258
done3258

end0.0ms

sample824.0ms

Algorithm
intervals
Results
255.0ms6387×body80valid
131.0ms8000×pre80true
109.0ms532×body1280valid
82.0ms529×body640valid
40.0ms341×body320valid
19.0ms211×body160valid