Details

Time bar (total: 12.1s)

sample46.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 75.154745%

Results
11.0ms210×body80valid
6.0ms256×pre80true
4.0ms16×body1280valid
4.0ms17×body640valid
2.0ms10×body320valid
0.0ms3×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.7b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
13.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series166.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
84.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify94.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06811905
136221789
250011789

prune251.0ms

Filtered
89 candidates to 120 candidates (-34.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1119120
Fresh000
Picked101
Done000
Total1129121

Merged error: 4.0b

Counts
121 → 9

localize13.0ms

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)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.6b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
45×add-sqr-sqrt
35×times-frac
26×add-cube-cbrt
21×associate-*r*
20×add-exp-log add-cbrt-cube
8×flip3-+ flip-+
7×associate-/r* associate-/l/ distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod distribute-lft-out
3×div-inv
2×frac-2neg associate-*r/ clear-num unswap-sqr
1×+-commutative flip3-- div-sub pow-prod-down sum-log *-commutative flip--
Counts
4 → 129
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
24.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series177.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
63.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
82.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify92.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06571569
135541429
250021429

prune233.0ms

Filtered
101 candidates to 141 candidates (-39.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1338141
Fresh628
Picked101
Done000
Total14010150

Merged error: 4.0b

Counts
150 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
1.6b
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
2.2b
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
32×add-sqr-sqrt
24×times-frac
21×associate-*r*
19×add-exp-log add-cube-cbrt add-cbrt-cube
14×unpow-prod-down cube-prod
8×distribute-lft-out add-log-exp
7×pow1
6×flip3-+ associate-/r/ flip-+
5×cbrt-undiv div-exp
4×associate-*l* pow-exp prod-exp cbrt-unprod distribute-lft-out-- rem-cube-cbrt difference-of-squares
3×pow-unpow div-inv
2×frac-times associate-*l/ unswap-sqr
1×+-commutative cube-div cube-mult pow-to-exp sub-neg flip3-- pow-pow diff-log unpow3 associate-*r/ pow-prod-down sum-log sum-cubes *-commutative flip-- sqr-pow
Counts
4 → 120
Calls
4 calls:
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
21.0ms
(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
26.0ms
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
11.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series4.6s

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.7s
(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
2.8s
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
57.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify115.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07711892
141751722
250021718

prune462.0ms

Filtered
85 candidates to 132 candidates (-55.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1293132
Fresh099
Picked101
Done000
Total13012142

Merged error: 4.0b

Counts
142 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.6b
(+ (* (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 2) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (pow 1.0 3))
2.2b
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
42×*-un-lft-identity associate-*r*
32×times-frac
24×add-cube-cbrt
14×add-exp-log add-cbrt-cube
8×pow1 associate-*l* add-log-exp
7×flip3-+ flip-+ distribute-lft-out-- difference-of-squares
4×frac-times associate-*l/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
2×cbrt-undiv associate-*r/ div-exp pow-prod-down *-commutative div-inv distribute-lft-out
1×+-commutative sub-neg flip3-- diff-log pow3 sum-log sum-cubes flip-- unpow2
Counts
4 → 116
Calls
4 calls:
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
18.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
31.0ms
(+ (* (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 2) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (pow 1.0 3))
12.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series3.1s

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
19.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
3.0s
(+ (* (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 2) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (pow 1.0 3))
54.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify79.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05411704
128321471
250021471

prune594.0ms

Filtered
94 candidates to 128 candidates (-36.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1271128
Fresh01111
Picked101
Done000
Total12812140

Merged error: 4.0b

Counts
140 → 12

regimes399.0ms

Accuracy

14.3% (5.6b remaining)

Error of 11.7b against oracle of 6.0b and baseline of 12.6b

bsearch50.0ms

Steps
ItersRangePoint
9
9.018248224096775e+192
1.981144790306819e+198
3.880399077369057e+195

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066114
166114

end0.0ms

sample1.2s

Algorithm
intervals
sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 75.154745%

Results
349.0ms6322×body80valid
177.0ms8000×pre80true
158.0ms551×body1280valid
126.0ms585×body640valid
59.0ms365×body320valid
19.0ms177×body160valid

Profiling

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