Details

Time bar (total: 8.7s)

sample34.0ms

Algorithm
intervals
Results
7.0ms193×body80valid
5.0ms25×body1280valid
4.0ms256×pre80true
3.0ms23×body640valid
1.0ms10×body320valid
0.0ms5×body160valid

simplify54.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214
done500214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite870.0ms

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-exp-log add-cbrt-cube
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
5×add-log-exp
4×frac-times
3×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 159
Calls
3 calls:
177.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
628.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
58.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series621.0ms

Counts
3 → 9
Calls
3 calls:
243.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
292.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
86.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify96.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07011971
137401800
250011782
done50011782

prune539.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.0b
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.6b
(fma (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
33×add-sqr-sqrt
32×times-frac
23×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
7×add-exp-log associate-/r* add-cbrt-cube
5×distribute-lft-out-- difference-of-squares
4×associate-/l/
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 → 93
Calls
3 calls:
19.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
132.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series413.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
91.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
247.0ms
(fma (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify48.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0418956
11604879
25001868
done5001868

prune332.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.2b
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.9b
(fma (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite512.0ms

Algorithm
rewrite-expression-head
Rules
614×times-frac
573×*-un-lft-identity
389×add-sqr-sqrt
352×sqrt-prod
261×add-cube-cbrt
92×distribute-lft-out
64×distribute-lft-out-- difference-of-squares
50×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 add-log-exp
3×frac-2neg div-sub clear-num
1×flip3-- flip-- fma-udef
Counts
4 → 466
Calls
4 calls:
19.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
323.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
136.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms
(fma (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series565.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
91.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
135.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
264.0ms
(fma (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify142.0ms

Counts
478 → 478
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0109110148
142479096
250019078
done50019078

prune905.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize169.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
0.3b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.9b
(fma (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite518.0ms

Algorithm
rewrite-expression-head
Rules
704×times-frac
631×*-un-lft-identity
431×add-sqr-sqrt
352×sqrt-prod
303×add-cube-cbrt
100×distribute-lft-out
64×distribute-lft-out-- difference-of-squares
49×associate-/l*
32×associate-/r*
29×associate-/r/
22×add-exp-log
20×sqrt-div
16×add-cbrt-cube
15×div-inv
14×flip3-+ flip-+
11×div-exp
7×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg div-sub clear-num associate-/l/
2×rec-exp 1-exp
1×flip3-- pow-flip flip-- fma-udef inv-pow
Counts
4 → 529
Calls
4 calls:
324.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
17.0ms
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
136.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms
(fma (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series421.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
118.0ms
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
136.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
79.0ms
(fma (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify112.0ms

Counts
541 → 541
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0129910893
150019772
done50019772

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

regimes241.0ms

Accuracy

18.5% (5.5b remaining)

Error of 11.4b against oracle of 5.9b and baseline of 12.7b

bsearch69.0ms

Steps
ItersRangePoint
9
2.57588219440865e+170
5.648441501904801e+176
5.127844411711004e+176

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04125
14525
24525
done4525

end0.0ms

sample829.0ms

Algorithm
intervals
Results
233.0ms6330×body80valid
108.0ms8000×pre80true
101.0ms523×body1280valid
94.0ms576×body640valid
42.0ms391×body320valid
13.0ms180×body160valid