Details

Time bar (total: 7.5s)

analyze243.0ms

Algorithm
search
sampling

Space saved by range analysis: 71.925324%

Space saved by search: 71.925324%

Guaranteed chance to sample good point: 97.259521%

sample38.0ms

Algorithm
intervals
Results
11.0ms204×body80valid
5.0ms12×body1280valid
5.0ms256×pre80true
4.0ms20×body640valid
2.0ms14×body320valid
1.0ms6×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: 26.6b

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))
2.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.7b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite64.0ms

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:
21.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
27.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
12.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series156.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
79.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
16.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify91.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06811905
136221789
250011789

prune234.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1128120
Fresh000
Picked101
Done000
Total1138121

Merged error: 6.0b

Counts
121 → 8

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)))
4.1b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite106.0ms

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))
38.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
24.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series195.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
35.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
62.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
81.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify69.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010804781
150014605

prune559.0ms

Filtered
199 candidates to 307 candidates (-54.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3016307
Fresh437
Picked101
Done000
Total3069315

Merged error: 6.0b

Counts
315 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.1b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.6b
(* (+ alpha beta) (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
4.1b
(+ (* (+ alpha beta) (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
1713×times-frac
1199×*-un-lft-identity
879×add-sqr-sqrt
658×add-cube-cbrt
272×associate-*r*
170×distribute-lft-out
110×associate-/r*
99×distribute-lft-out-- difference-of-squares
76×associate-/r/
62×add-exp-log
43×div-inv
37×flip3-+ flip-+
33×div-exp
32×add-cbrt-cube
15×cbrt-undiv
10×prod-exp
7×pow1 associate-/l* unswap-sqr
6×rec-exp 1-exp add-log-exp
4×associate-*l* cbrt-unprod
2×frac-times frac-2neg associate-*l/ clear-num associate-/l/
1×+-commutative pow-flip associate-*r/ pow-prod-down sum-log un-div-inv *-commutative inv-pow
Counts
4 → 833
Calls
4 calls:
19.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
32.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
79.0ms
(* (+ alpha beta) (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
36.0ms
(+ (* (+ alpha beta) (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series215.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
38.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
61.0ms
(* (+ alpha beta) (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
86.0ms
(+ (* (+ alpha beta) (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify196.0ms

Algorithm
egg-herbie
Counts
845 → 845
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0229316042
1500315314

prune2.3s

Filtered
460 candidates to 845 candidates (-83.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New8450845
Fresh088
Picked011
Done000
Total8459854

Merged error: 6.0b

Counts
854 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)))
4.1b
(+ (* (+ 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:
26.0ms
(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
29.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
36.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
27.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series437.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
78.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
61.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
80.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify53.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09763078
150022920

prune346.0ms

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

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1826188
Fresh437
Picked011
Done011
Total18611197

Merged error: 6.0b

Counts
197 → 11

regimes527.0ms

Accuracy

75.7% (1.5b remaining)

Error of 7.3b against oracle of 5.8b and baseline of 12.1b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05138
15138

end0.0ms

analyze241.0ms

Algorithm
search
sampling

Space saved by range analysis: 71.925324%

Space saved by search: 71.925324%

Guaranteed chance to sample good point: 97.259521%

sample1.0s

Algorithm
intervals
Results
344.0ms6391×body80valid
162.0ms8000×pre80true
138.0ms500×body1280valid
127.0ms555×body640valid
58.0ms355×body320valid
21.0ms199×body160valid

Profiling

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