Details

Time bar (total: 5.3s)

sample42.0ms

Algorithm
intervals
Results
11.0ms203×body80valid
6.0ms256×pre80true
4.0ms19×body640valid
4.0ms14×body1280valid
2.0ms11×body320valid
1.0ms9×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune7.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 25.4b

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))
2.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite66.0ms

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))
28.0ms
(+ (/ (/ (* (+ 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)))

series161.0ms

Counts
3 → 9
Calls
3 calls:
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)
18.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify93.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250011789

prune269.0ms

Filtered
120 candidates to 89 candidates (25.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10812120
Fresh000
Picked101
Done000
Total10912121

Merged error: 6.7b

Counts
121 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.9b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.2b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite112.0ms

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)))
19.0ms
(/ (/ (- 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)))
25.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series199.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
40.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
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)

simplify74.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010804781
150014605

prune575.0ms

Filtered
307 candidates to 199 candidates (35.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New3016307
Fresh6511
Picked101
Done000
Total30811319

Merged error: 6.7b

Counts
319 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
1.9b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.2b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
306×times-frac
275×*-un-lft-identity
196×add-sqr-sqrt
133×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
27×distribute-lft-out-- difference-of-squares
22×associate-/r/
21×associate-/l*
18×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×cbrt-prod
11×div-inv
6×pow1 cbrt-undiv div-exp add-log-exp
4×associate-*l* associate-/r*
3×unpow-prod-down cube-prod prod-exp cbrt-unprod unswap-sqr
2×cube-div frac-times cbrt-div div-sub associate-*l/
1×+-commutative cube-mult frac-2neg pow1/3 unpow3 associate-*r/ pow-prod-down clear-num sum-log *-commutative rem-cbrt-cube associate-/l/ sqr-pow
Counts
4 → 278
Calls
4 calls:
18.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
25.0ms
(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)

series267.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
80.0ms
(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)))
84.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify71.0ms

Algorithm
egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011244978
150014845

prune712.0ms

Filtered
290 candidates to 186 candidates (35.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2819290
Fresh6410
Picked101
Done000
Total28813301

Merged error: 6.7b

Counts
301 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (pow (+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.2b
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
39×*-un-lft-identity associate-*r*
36×add-sqr-sqrt
30×add-cbrt-cube
28×times-frac
25×add-cube-cbrt
22×prod-exp
12×cbrt-prod cbrt-unprod
11×pow1 frac-times div-exp associate-*l/
10×flip3-+ flip-+
6×cbrt-undiv add-log-exp
5×associate-*l*
4×associate-*r/ pow-prod-down associate-/r/ distribute-lft-out
3×unpow-prod-down rec-exp 1-exp cube-prod distribute-lft-out-- difference-of-squares
2×cube-div cbrt-div *-commutative div-inv unswap-sqr
1×+-commutative cube-mult pow1/3 unpow3 sum-log un-div-inv rem-cbrt-cube sqr-pow
Counts
4 → 138
Calls
4 calls:
24.0ms
(cbrt (pow (+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
25.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series244.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(cbrt (pow (+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
17.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
64.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
82.0ms
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify47.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08602233
150012050

prune235.0ms

Filtered
150 candidates to 96 candidates (36.0%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1482150
Fresh11112
Picked101
Done000
Total15013163

Merged error: 6.7b

Counts
163 → 13

regimes588.0ms

Accuracy

73.1% (1.7b remaining)

Error of 7.5b against oracle of 5.8b and baseline of 12.2b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06386
16386

end0.0ms

sample1.2s

Algorithm
intervals
Results
368.0ms6385×body80valid
165.0ms8000×pre80true
140.0ms506×body1280valid
125.0ms562×body640valid
59.0ms358×body320valid
21.0ms189×body160valid

Profiling

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