Details

Time bar (total: 8.9s)

sample44.0ms

Algorithm
intervals
Results
12.0ms189×body80valid
6.0ms256×pre80true
5.0ms20×body1280valid
4.0ms21×body640valid
3.0ms20×body320valid
1.0ms6×body160valid

simplify50.0ms

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: 27.9b

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))
1.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite72.0ms

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))
34.0ms
(+ (/ (/ (* (+ 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)))

series592.0ms

Counts
3 → 9
Calls
3 calls:
233.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
277.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
82.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify103.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06811905
136221789
250031789

prune345.0ms

Filtered
120 candidates to 89 candidates (74.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10911120
Fresh000
Picked101
Done000
Total11011121

Merged error: 7.4b

Counts
121 → 11

localize12.0ms

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))
1.2b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.5b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite122.0ms

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:
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
40.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
32.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series756.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
161.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
236.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
281.0ms
(+ (* (+ 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 (28.0ms)

IterNodesCost
010804781
150014605

prune706.0ms

Filtered
307 candidates to 200 candidates (65.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2989307
Fresh5510
Picked101
Done000
Total30414318

Merged error: 7.4b

Counts
318 → 14

localize16.0ms

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))
1.2b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.5b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite142.0ms

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:
28.0ms
(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
33.0ms
(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)))
31.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
743.0ms
(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
279.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
240.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
285.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify56.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09733074
150012918

prune530.0ms

Filtered
188 candidates to 119 candidates (63.3%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1799188
Fresh7613
Picked011
Done000
Total18616202

Merged error: 7.4b

Counts
202 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

3.7b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
3.7b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
3.7b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
11.5b
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (* (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)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
49×add-sqr-sqrt *-un-lft-identity
45×times-frac
31×add-cube-cbrt
9×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×cbrt-div pow1/3 div-inv
1×+-commutative sum-log
Counts
4 → 101
Calls
4 calls:
9.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
9.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
9.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
78.0ms
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (* (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)

series1.5s

Counts
4 → 12
Calls
4 calls:
382.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
379.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
379.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
333.0ms
(+ (* (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (* (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)

simplify59.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03601991
111441740
250011706

prune533.0ms

Filtered
113 candidates to 96 candidates (85.0%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1085113
Fresh41014
Picked101
Done011
Total11316129

Merged error: 7.4b

Counts
129 → 16

regimes483.0ms

Accuracy

76.4% (1.6b remaining)

Error of 7.6b against oracle of 6.0b and baseline of 12.6b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05239
15239

end0.0ms

sample1.0s

Algorithm
intervals
Results
314.0ms6329×body80valid
182.0ms8000×pre80true
131.0ms520×body1280valid
113.0ms576×body640valid
54.0ms374×body320valid
21.0ms201×body160valid