Details

Time bar (total: 7.6s)

sample39.0ms

Algorithm
intervals
Results
9.0ms196×body80valid
6.0ms256×pre80true
4.0ms19×body1280valid
4.0ms22×body640valid
2.0ms15×body320valid
0.0ms4×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

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: 25.3b

Counts
2 → 1

localize12.0ms

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))
1.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
50×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-exp-log add-cbrt-cube
15×add-log-exp
14×associate-/r/
12×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* sum-log div-inv
4×pow1 frac-times
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 126
Calls
4 calls:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
33.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
14.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series580.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
219.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
262.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
78.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify106.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07322016
141081891
250021891

prune362.0ms

Filtered
138 candidates to 102 candidates (73.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New12612138
Fresh000
Picked101
Done000
Total12712139

Merged error: 8.8b

Counts
139 → 12

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))
2.3b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite117.0ms

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)))
24.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
37.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
30.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series919.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
157.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
426.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
266.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify78.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
010804781
150014605

prune661.0ms

Filtered
307 candidates to 200 candidates (65.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New3016307
Fresh5611
Picked101
Done000
Total30712319

Merged error: 8.8b

Counts
319 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.3b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.9b
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
3.5b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
134×*-un-lft-identity
99×add-sqr-sqrt
90×associate-*r*
66×add-cube-cbrt
22×distribute-lft-out
14×add-exp-log
13×add-cbrt-cube
12×distribute-lft-out-- difference-of-squares
10×flip3-+ associate-/r/ flip-+
8×pow1
6×log-prod add-log-exp
5×div-inv
4×log-div exp-prod associate-*l*
3×cbrt-undiv div-exp exp-sum prod-exp cbrt-unprod unswap-sqr
2×frac-times exp-diff associate-*l/ log-pow
1×+-commutative associate-*r/ rem-log-exp pow-prod-down sum-log *-commutative rem-exp-log
Counts
4 → 159
Calls
4 calls:
27.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
43.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
24.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
31.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.0s

Counts
4 → 12
Calls
4 calls:
267.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
224.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
269.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
275.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify49.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09282698
150022523

prune450.0ms

Filtered
171 candidates to 114 candidates (66.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1674171
Fresh3811
Picked101
Done000
Total17112183

Merged error: 6.0b

Counts
183 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.5b
(* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
2.3b
(* (+ alpha beta) (/ (* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
10.0b
(+ (* (+ alpha beta) (/ (* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
84×add-exp-log
37×prod-exp
35×add-cbrt-cube
30×div-exp
26×add-sqr-sqrt
20×*-un-lft-identity
19×cbrt-prod
17×cbrt-unprod
16×add-cube-cbrt associate-*r*
14×cbrt-undiv cbrt-div
13×pow1
11×flip3-+ flip-+
10×associate-*l*
7×pow1/3
6×frac-times swap-sqr add-log-exp
5×unswap-sqr
4×rec-exp times-frac 1-exp associate-*l/
3×associate-*r/ pow-prod-down
2×associate-/r/ pow-sqr *-commutative pow-prod-up distribute-lft-out
1×+-commutative pow2 pow-plus sum-log div-inv
Counts
4 → 125
Calls
4 calls:
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
15.0ms
(* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
41.0ms
(* (+ alpha beta) (/ (* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
41.0ms
(+ (* (+ alpha beta) (/ (* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series948.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
209.0ms
(* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))
256.0ms
(* (+ alpha beta) (/ (* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
327.0ms
(+ (* (+ alpha beta) (/ (* (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify126.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
09672869
146762454
250012391

prune357.0ms

Filtered
137 candidates to 94 candidates (68.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1352137
Fresh01111
Picked101
Done000
Total13613149

Merged error: 6.0b

Counts
149 → 13

regimes401.0ms

Accuracy

57.6% (3.3b remaining)

Error of 7.3b against oracle of 4.0b and baseline of 11.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05751
15751

end0.0ms

sample956.0ms

Algorithm
intervals
Results
300.0ms6443×body80valid
172.0ms8000×pre80true
117.0ms489×body1280valid
97.0ms516×body640valid
54.0ms350×body320valid
19.0ms202×body160valid

Profiling

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