Details

Time bar (total: 24.7s)

sample35.0ms

Algorithm
intervals
Results
9.0ms215×body80valid
6.0ms14×body1280valid
4.0ms256×pre80true
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
110314
245414
3212714
4500114

prune2.0ms

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

localize13.0ms

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)))

rewrite528.0ms

Algorithm
rewrite-expression-head
Rules
4111×*-un-lft-identity
2228×distribute-lft-out
1938×times-frac
818×associate-*l*
781×add-sqr-sqrt
493×add-cube-cbrt
360×associate-*r*
141×associate-/l*
72×*-commutative distribute-lft-out-- difference-of-squares unswap-sqr
49×associate-/l/
22×associate-/r* associate-/r/
19×flip3-+ flip-+
18×add-exp-log add-cbrt-cube
15×add-log-exp
11×div-inv
8×frac-times
7×cbrt-undiv div-exp sum-log
6×associate-+l+ flip3-- flip--
4×pow1 +-commutative associate-*r/ associate-*l/
3×frac-2neg clear-num
2×prod-exp cbrt-unprod
Counts
4 → 1243
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
67.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
277.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
234.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
277.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
88.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify248.0ms

Algorithm
egg-herbie
Counts
1255 → 1255
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0149421786
1500121650

prune1.1s

Filtered
1255 candidates to 290 candidates (23.1%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New124961255
Fresh000
Picked101
Done000
Total125061256

Merged error: 3.5b

Counts
1256 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.3b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.8b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite3.2s

Algorithm
rewrite-expression-head
Rules
29091×*-un-lft-identity
20833×times-frac
13716×distribute-lft-out
7607×add-sqr-sqrt
5511×add-cube-cbrt
2988×associate-*l*
1048×distribute-lft-out-- difference-of-squares
654×associate-/r/
567×associate-/r*
516×div-inv
151×flip3-+ flip-+
131×associate-/l*
56×associate-/l/
41×add-exp-log
32×add-cbrt-cube
28×div-exp
23×frac-2neg clear-num
19×cbrt-undiv flip3-- flip--
6×add-log-exp
4×pow1
3×1-exp
1×+-commutative div-sub sum-log
Counts
4 → 6526
Calls
4 calls:
14.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
39.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
200.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.5s
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

series735.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
145.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
230.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
286.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify1.6s

Algorithm
egg-herbie
Counts
6538 → 6538
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
05001153436

prune4.1s

Filtered
6538 candidates to 896 candidates (13.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New653446538
Fresh415
Picked011
Done000
Total653866544

Merged error: 3.5b

Counts
6544 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
3.0b
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite413.0ms

Algorithm
rewrite-expression-head
Rules
2069×*-un-lft-identity
1328×frac-times
1049×distribute-lft-out
799×associate-/r*
449×add-sqr-sqrt
448×associate-/l*
328×associate-*r/
293×flip3-+ flip-+
288×associate-*l*
269×add-cube-cbrt
140×times-frac
134×associate-*r*
122×clear-num
106×frac-2neg
98×associate-/l/
86×distribute-lft-out--
70×difference-of-squares
50×add-exp-log
49×flip3-- flip--
48×un-div-inv
46×associate-*l/
32×add-cbrt-cube
22×prod-exp
19×unswap-sqr
12×div-exp cbrt-unprod
11×pow1
8×associate-/r/
7×cbrt-undiv
6×add-log-exp
5×div-inv
4×pow-prod-down
3×rec-exp 1-exp *-commutative
1×+-commutative div-sub sum-log
Counts
4 → 1167
Calls
4 calls:
14.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
32.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
92.0ms
(* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
145.0ms
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

series679.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
77.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
242.0ms
(* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
283.0ms
(+ (* (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify269.0ms

Algorithm
egg-herbie
Counts
1179 → 1179
Iterations

Useful iterations: 1 (63.0ms)

IterNodesCost
0306719609
1500219113

prune1.5s

Filtered
1179 candidates to 355 candidates (30.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New117811179
Fresh134
Picked011
Done011
Total117961185

Merged error: 3.5b

Counts
1185 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
8905×*-un-lft-identity
4400×distribute-lft-out
2754×times-frac
2720×frac-times
2424×add-sqr-sqrt
2259×associate-*r*
2053×sqrt-prod
1972×associate-/r*
1686×associate-/l*
1387×add-cube-cbrt
1237×associate-*l*
1178×associate-/l/
445×associate-*r/
388×flip3-+ flip-+
363×distribute-lft-out--
344×difference-of-squares
220×clear-num
200×frac-2neg
137×unswap-sqr
90×associate-/r/
77×add-exp-log
61×un-div-inv
57×flip3-- flip--
55×associate-*l/
47×add-cbrt-cube
46×div-inv
42×*-commutative
30×div-exp
26×prod-exp
17×cbrt-undiv
14×cbrt-unprod
8×pow1 sqrt-div
6×add-log-exp
5×rec-exp 1-exp
3×pow-flip
1×+-commutative sqrt-pow1 pow1/2 pow-prod-down sum-log inv-pow
Counts
4 → 3692
Calls
4 calls:
443.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
64.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
16.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
868.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series974.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
315.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
132.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
282.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify831.0ms

Algorithm
egg-herbie
Counts
3704 → 3704
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0500277849

prune4.7s

Filtered
3704 candidates to 1000 candidates (27.0%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New370133704
Fresh213
Picked101
Done022
Total370463710

Merged error: 3.5b

Counts
3710 → 6

regimes146.0ms

Accuracy

16.8% (5.4b remaining)

Error of 11.2b against oracle of 5.8b and baseline of 12.3b

bsearch80.0ms

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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04826
14826

end0.0ms

sample871.0ms

Algorithm
intervals
Results
281.0ms6361×body80valid
133.0ms8000×pre80true
114.0ms531×body1280valid
94.0ms560×body640valid
43.0ms345×body320valid
17.0ms203×body160valid