Details

Time bar (total: 8.2s)

sample32.0ms

Algorithm
intervals
Results
8.0ms209×body80valid
4.0ms256×pre80true
3.0ms20×body640valid
2.0ms12×body1280valid
1.0ms9×body320valid
0.0ms6×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize12.0ms

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))
2.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite488.0ms

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:
95.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
356.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
28.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series564.0ms

Counts
3 → 9
Calls
3 calls:
219.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
269.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
76.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify97.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07011971
137401800
250011782

prune528.0ms

Filtered
168 candidates to 131 candidates (78.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

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))
11.2b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite134.0ms

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:
25.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
98.0ms
(/ (/ (- 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)

series508.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
162.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
267.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify94.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07273112
132592892
250022876

prune596.0ms

Filtered
190 candidates to 135 candidates (71.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
11.2b
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
151×*-un-lft-identity
107×add-sqr-sqrt
77×add-cube-cbrt
22×distribute-lft-out
21×associate-/l*
15×distribute-lft-out-- difference-of-squares
12×cbrt-prod associate-/r/
10×add-exp-log add-cbrt-cube
6×unpow-prod-down flip3-+ cube-prod flip-+ div-inv
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow div-exp
2×cube-mult unpow3 div-sub sqr-pow
1×pow-to-exp pow-pow frac-2neg pow1/3 pow-exp clear-num rem-cbrt-cube fma-udef associate-/l/ rem-cube-cbrt
Counts
4 → 187
Calls
4 calls:
1.0ms
(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
99.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0ms
(cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
0.0ms
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
734.0ms
(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
164.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
266.0ms
(cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
266.0ms
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify105.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
08013653
138283410
250013396

prune628.0ms

Filtered
199 candidates to 130 candidates (65.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
11.2b
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
11.2b
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
11.2b
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 43
Calls
4 calls:
1.0ms
(cbrt (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
0.0ms
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
0.0ms
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
0.0ms
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
426.0ms
(cbrt (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
264.0ms
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
264.0ms
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
266.0ms
(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify73.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0217911
1669795
22928775
35001746

prune302.0ms

Filtered
55 candidates to 52 candidates (94.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

regimes254.0ms

Accuracy

16.1% (5.8b remaining)

Error of 11.5b against oracle of 5.7b and baseline of 12.6b

bsearch60.0ms

Steps
ItersRangePoint
6
3.2734834716934437e+101
4.803158087880582e+102
4.026667996136292e+102

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05242
15242

end0.0ms

sample835.0ms

Algorithm
intervals
Results
254.0ms6347×body80valid
133.0ms8000×pre80true
108.0ms531×body1280valid
97.0ms589×body640valid
41.0ms349×body320valid
15.0ms184×body160valid