Details

Time bar (total: 5.5s)

sample306.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 97.259521%

Results
11.0ms198×body80valid
7.0ms23×body1280valid
6.0ms256×pre80true
4.0ms17×body640valid
2.0ms10×body320valid
1.0ms8×body160valid

simplify52.0ms

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: 25.7b

Counts
2 → 1

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))
2.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite65.0ms

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:
19.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
29.0ms
(+ (/ (/ (* (+ 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)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
82.0ms
(+ (/ (/ (* (+ 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)))

simplify95.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250011789

prune234.0ms

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1137120
Fresh000
Picked101
Done000
Total1147121

Merged error: 5.0b

Counts
121 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

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))
1.6b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.7b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
18.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
39.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series203.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
39.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
64.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
85.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify71.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010804781
150014605

prune533.0ms

Filtered
200 candidates to 307 candidates (-53.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3007307
Fresh336
Picked101
Done000
Total30410314

Merged error: 5.0b

Counts
314 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
0.1b
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
1.6b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.7b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
137×*-un-lft-identity
102×add-sqr-sqrt
90×associate-*r*
69×add-cube-cbrt
22×distribute-lft-out
14×add-exp-log add-cbrt-cube
12×cbrt-prod distribute-lft-out-- difference-of-squares
10×flip3-+ associate-/r/ flip-+
7×pow1
6×unpow-prod-down cube-prod add-log-exp
5×div-inv
4×cube-div associate-*l*
3×cbrt-undiv pow-unpow div-exp prod-exp cbrt-unprod unswap-sqr
2×cube-mult frac-times cbrt-div unpow3 associate-*l/ sqr-pow
1×+-commutative pow-to-exp pow-pow pow1/3 associate-*r/ pow-prod-down pow-exp sum-log *-commutative rem-cbrt-cube rem-cube-cbrt
Counts
4 → 176
Calls
4 calls:
27.0ms
(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
26.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
40.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series452.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
82.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
64.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
83.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify59.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09733074
150012918

prune396.0ms

Filtered
119 candidates to 188 candidates (-58.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1844188
Fresh369
Picked011
Done000
Total18711198

Merged error: 5.0b

Counts
198 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.6b
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
6.9b
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
72×add-exp-log
39×add-cbrt-cube
28×prod-exp cbrt-unprod
27×cbrt-undiv div-exp
13×*-un-lft-identity
9×pow1 frac-times
8×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt flip3-+ flip-+
6×associate-*r/ add-log-exp
5×associate-*l/
4×cbrt-div associate-*l*
3×pow-prod-down distribute-lft-out
2×pow1/3
1×+-commutative associate-*r* sum-log *-commutative
Counts
4 → 91
Calls
4 calls:
7.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
69.0ms
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
62.0ms
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series230.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
40.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
65.0ms
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
86.0ms
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify101.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08043188
134812536
250032456

prune196.0ms

Filtered
60 candidates to 103 candidates (-71.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1021103
Fresh099
Picked101
Done101
Total10410114

Merged error: 5.0b

Counts
114 → 10

regimes429.0ms

Accuracy

75.4% (1.6b remaining)

Error of 7.0b against oracle of 5.5b and baseline of 11.9b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04937
14937

end0.0ms

sample1.4s

Algorithm
intervals
sampling

Space saved by range analysis: 71.884159%

Space saved by search: 71.884159%

Guaranteed chance to sample good point: 97.259521%

Results
365.0ms6432×body80valid
178.0ms8000×pre80true
149.0ms493×body1280valid
125.0ms561×body640valid
61.0ms340×body320valid
19.0ms174×body160valid

Profiling

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