Details

Time bar (total: 7.5s)

sample32.0ms

Algorithm
intervals
Results
8.0ms215×body80valid
4.0ms256×pre80true
3.0ms14×body1280valid
2.0ms14×body640valid
1.0ms6×body320valid
1.0ms7×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: 21.7b

Counts
2 → 1

localize12.0ms

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))
1.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite85.0ms

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:
8.0ms
(+ (+ (+ 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))
36.0ms
(+ (/ (/ (* (+ 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)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
225.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
267.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
78.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify109.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07582073
142381870
250011858

prune582.0ms

Filtered
191 candidates to 149 candidates (78.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1838191
Fresh000
Picked101
Done000
Total1848192

Merged error: 3.5b

Counts
192 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
0.3b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
5.0b
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
87×add-exp-log
70×times-frac
52×add-sqr-sqrt add-cube-cbrt
49×add-cbrt-cube
48×sqrt-prod
36×prod-exp
29×div-exp
27×associate-*l*
20×distribute-lft-out
18×cbrt-unprod
15×cbrt-undiv
14×associate-/r*
11×pow1
7×associate-/l*
6×rec-exp sqrt-div 1-exp associate-/r/ add-log-exp
5×frac-times flip3-+ associate-*r/ flip-+
4×expm1-log1p-u log1p-expm1-u
3×pow-flip pow-prod-down associate-*l/ div-inv
2×frac-2neg clear-num associate-/l/
1×+-commutative fma-def sqrt-pow1 pow1/2 associate-*r* sum-log *-commutative inv-pow
Counts
4 → 201
Calls
4 calls:
35.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
13.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
36.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

series753.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
134.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
119.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
275.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

simplify125.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08973539
147403012
250012990

prune550.0ms

Filtered
213 candidates to 116 candidates (54.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2103213
Fresh257
Picked101
Done000
Total2138221

Merged error: 3.5b

Counts
221 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.6b
(/ (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
5.9b
(+ (* (/ (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
834×sqrt-prod
748×times-frac
550×*-un-lft-identity
376×add-sqr-sqrt add-cube-cbrt
87×distribute-lft-out
54×sqrt-div
43×associate-/l*
28×associate-/r/
27×associate-/r*
20×sqrt-pow1
19×add-exp-log
18×pow1
16×flip3-+ flip-+
14×pow-flip div-inv
13×add-cbrt-cube
10×pow1/2 pow-div
9×div-exp
6×add-log-exp
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num associate-/l/
2×rec-exp 1-exp inv-pow
1×+-commutative fma-def sum-log
Counts
4 → 575
Calls
4 calls:
17.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
13.0ms
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
31.0ms
(/ (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
68.0ms
(+ (* (/ (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

series703.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
169.0ms
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
120.0ms
(/ (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
279.0ms
(+ (* (/ (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

simplify146.0ms

Algorithm
egg-herbie
Counts
587 → 587
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0144113960
1500112227

prune1.0s

Filtered
587 candidates to 180 candidates (30.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New5861587
Fresh167
Picked101
Done000
Total5887595

Merged error: 3.5b

Counts
595 → 7

localize14.0ms

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)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
9.5b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite49.0ms

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:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
13.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
18.0ms
(/ (/ (- 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)

series506.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
73.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
156.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
255.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify102.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07843185
137052969
250022951

prune644.0ms

Filtered
213 candidates to 154 candidates (72.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2094213
Fresh246
Picked101
Done000
Total2128220

Merged error: 3.5b

Counts
220 → 8

regimes206.0ms

Accuracy

18% (5.5b remaining)

Error of 11.2b against oracle of 5.7b and baseline of 12.4b

bsearch78.0ms

Steps
ItersRangePoint
8
2.911341738631546e+214
3.8498885149509344e+217
2.9093475849372547e+217

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14625
24625

end0.0ms

sample828.0ms

Algorithm
intervals
Results
248.0ms6361×body80valid
126.0ms8000×pre80true
112.0ms531×body1280valid
95.0ms560×body640valid
43.0ms345×body320valid
16.0ms203×body160valid