Details

Time bar (total: 6.2s)

sample33.0ms

Algorithm
intervals
Results
9.0ms214×body80valid
4.0ms256×pre80true
3.0ms16×body1280valid
3.0ms16×body640valid
1.0ms7×body320valid
0.0ms3×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.5b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
87×*-un-lft-identity
45×add-sqr-sqrt add-cube-cbrt fma-def
24×associate-/r/
21×distribute-lft-out
18×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
15×add-log-exp
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* sum-log
4×pow1 expm1-log1p-u frac-times log1p-expm1-u
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 179
Calls
4 calls:
12.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
33.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
15.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
228.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
270.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify109.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
07582073
142381870
250011858

prune519.0ms

Filtered
191 candidates to 149 candidates (78.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1847191
Fresh000
Picked101
Done000
Total1857192

Merged error: 4.5b

Counts
192 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (fma 2.0 i 2.0))
0.0b
(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
0.0b
(/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0)))
0.6b
(fma (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
93×*-un-lft-identity
40×times-frac
37×add-sqr-sqrt
31×distribute-lft-out
27×add-cube-cbrt
9×associate-/r* associate-/l* add-log-exp
8×add-exp-log add-cbrt-cube
5×distribute-lft-out-- difference-of-squares
4×pow1 expm1-log1p-u fma-def flip3-+ associate-/r/ flip-+ log1p-expm1-u associate-/l/
3×sum-log
2×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
1×+-commutative associate-+l+ associate-+r+ flip3-- div-sub flip--
Counts
4 → 127
Calls
4 calls:
10.0ms
(+ (+ alpha beta) (fma 2.0 i 2.0))
8.0ms
(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
10.0ms
(/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0)))
1.0ms
(fma (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

series426.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (+ alpha beta) (fma 2.0 i 2.0))
80.0ms
(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
75.0ms
(/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0)))
247.0ms
(fma (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

simplify63.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04821027
11960957
25003953

prune356.0ms

Filtered
139 candidates to 95 candidates (68.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1390139
Fresh066
Picked011
Done000
Total1397146

Merged error: 4.5b

Counts
146 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.0b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
166×*-un-lft-identity
120×add-sqr-sqrt
82×add-cube-cbrt
26×associate-/l*
23×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
13×add-log-exp
11×add-exp-log add-cbrt-cube
8×flip3-+ flip-+
7×associate-/r* div-inv
6×sum-log
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-def div-sub associate-/l/
2×frac-2neg clear-num
1×+-commutative associate-+l+ flip3-- flip-- fma-udef
Counts
4 → 201
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
19.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series543.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
72.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
167.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify110.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07843185
137052969
250022951

prune576.0ms

Filtered
213 candidates to 154 candidates (72.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2121213
Fresh055
Picked011
Done011
Total2128220

Merged error: 4.5b

Counts
220 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.5b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.5b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
10.0b
(fma (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+
1×fma-udef
Counts
4 → 55
Calls
4 calls:
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
1.0ms
(fma (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series942.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
163.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
163.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
457.0ms
(fma (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify80.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0242782
1714703
23079693
35002682

prune259.0ms

Filtered
67 candidates to 63 candidates (94.0%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New63467
Fresh055
Picked101
Done022
Total641175

Merged error: 4.5b

Counts
75 → 11

regimes269.0ms

Accuracy

19.9% (5.3b remaining)

Error of 10.8b against oracle of 5.5b and baseline of 12.1b

bsearch72.0ms

Steps
ItersRangePoint
8
8.186102315163911e+158
4.460963336559458e+161
2.213273507034204e+161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
14425
24425

end0.0ms

sample885.0ms

Algorithm
intervals
Results
285.0ms6384×body80valid
131.0ms8000×pre80true
118.0ms546×body1280valid
106.0ms579×body640valid
40.0ms314×body320valid
15.0ms177×body160valid