Details

Time bar (total: 7.4s)

sample34.0ms

Algorithm
intervals
Results
9.0ms213×body80valid
5.0ms256×pre80true
3.0ms17×body1280valid
2.0ms13×body640valid
1.0ms11×body320valid
0.0ms2×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite459.0ms

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:
90.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
336.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
27.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series614.0ms

Counts
3 → 9
Calls
3 calls:
243.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
287.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
84.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify99.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07011971
137401800
250011782

prune552.0ms

Filtered
168 candidates to 131 candidates (78.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

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))
0.4b
(fma (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite80.0ms

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:
7.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
69.0ms
(/ (- 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)

series403.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
89.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
248.0ms
(fma (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify54.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0418956
11604879
25001868

prune339.0ms

Filtered
102 candidates to 74 candidates (72.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.3b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite130.0ms

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-exp-log add-cbrt-cube
7×flip3-+ associate-/r* flip-+ div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num
1×flip3-- flip-- fma-udef
Counts
3 → 181
Calls
3 calls:
23.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
95.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series517.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
169.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
273.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify101.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07273112
132592892
250022876

prune635.0ms

Filtered
190 candidates to 135 candidates (71.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.4b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
10.2b
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
490×times-frac
410×*-un-lft-identity
284×add-sqr-sqrt
228×add-cube-cbrt
156×sqrt-prod
63×distribute-lft-out
42×associate-/l*
28×distribute-lft-out-- difference-of-squares
22×associate-/r/
19×div-inv
18×add-exp-log
17×associate-/r*
16×add-cbrt-cube
11×flip3-+ flip-+
9×div-exp
7×cbrt-undiv
4×pow1 expm1-log1p-u sqrt-div log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg div-sub clear-num
1×flip3-- 1-exp flip-- fma-udef
Counts
4 → 402
Calls
4 calls:
22.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
97.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
76.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series692.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
234.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
138.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
239.0ms
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify88.0ms

Algorithm
egg-herbie
Counts
414 → 414
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012837520
150026956

prune1.1s

Filtered
414 candidates to 212 candidates (51.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

regimes230.0ms

Accuracy

11.2% (5.6b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 12.2b

bsearch76.0ms

Steps
ItersRangePoint
9
3.088617839269422e+142
1.495088011218417e+148
1.4714840476837656e+148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04327
14727
24727

end0.0ms

sample845.0ms

Algorithm
intervals
Results
265.0ms6396×body80valid
129.0ms8000×pre80true
109.0ms499×body1280valid
90.0ms574×body640valid
46.0ms341×body320valid
16.0ms190×body160valid