Details

Time bar (total: 9.4s)

sample33.0ms

Algorithm
intervals
Results
8.0ms212×body80valid
4.0ms256×pre80true
4.0ms19×body1280valid
2.0ms15×body640valid
1.0ms8×body320valid
0.0ms2×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize13.0ms

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))
1.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite761.0ms

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:
173.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
533.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
51.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series754.0ms

Counts
3 → 9
Calls
3 calls:
213.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
470.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
70.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify94.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06811905
136221789
250031789

prune329.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.4b

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))
2.2b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
3.3b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite680.0ms

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:
42.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
173.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
95.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
353.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series675.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
147.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
248.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
212.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify73.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010804781
150014605

prune732.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.5b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.5b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
8.5b
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite862.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 distribute-lft-out
1×+-commutative sum-log
Counts
4 → 53
Calls
4 calls:
56.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
56.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
56.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
692.0ms
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series776.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
160.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
162.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
298.0ms
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify43.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03191262
110811150
250011142

prune291.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.5b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.5b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
8.5b
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite865.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 distribute-lft-out
1×+-commutative sum-log
Counts
4 → 53
Calls
4 calls:
56.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
56.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
56.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
695.0ms
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series765.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
158.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
158.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
290.0ms
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify45.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03191262
110811150
250011142

prune327.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.4b

regimes184.0ms

Accuracy

15.9% (5.6b remaining)

Error of 11.2b against oracle of 5.7b and baseline of 12.3b

bsearch109.0ms

Steps
ItersRangePoint
9
3.6722806727149755e+159
5.762254725775896e+165
2.956513572083282e+162

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
059165
159165

end0.0ms

sample880.0ms

Algorithm
intervals
Results
256.0ms6404×body80valid
126.0ms8000×pre80true
98.0ms487×body1280valid
95.0ms590×body640valid
42.0ms337×body320valid
14.0ms182×body160valid