Details

Time bar (total: 7.4s)

sample40.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
5.0ms256×pre80true

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 53.5b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.1b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
12.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
25.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
41.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
346.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
55.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify78.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012495670
150015161

prune436.0ms

Filtered
143 candidates to 212 candidates (-48.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2066212
Fresh000
Picked101
Done000
Total2076213

Merged error: 36.0b

Counts
213 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
36.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
264×times-frac
191×add-sqr-sqrt
178×*-un-lft-identity
110×add-cube-cbrt
96×associate-*r*
74×add-exp-log add-cbrt-cube
42×associate-*l*
40×associate-/r/
35×cbrt-undiv div-exp
30×difference-of-squares
21×flip3-+ flip-+
20×div-inv
19×distribute-lft-out
17×prod-exp cbrt-unprod
15×sqrt-prod distribute-lft-out--
13×associate-/l*
10×associate-/r*
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 304
Calls
4 calls:
20.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
95.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
397.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
16.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify101.0ms

Algorithm
egg-herbie
Counts
316 → 316
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015818513
150017655

prune934.0ms

Filtered
210 candidates to 316 candidates (-50.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3106316
Fresh325
Picked101
Done000
Total3148322

Merged error: 36.0b

Counts
322 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
36.1b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
223×times-frac
185×add-sqr-sqrt
147×*-un-lft-identity
117×sqrt-prod
99×add-cube-cbrt associate-*r*
42×associate-*l*
30×associate-/r/ difference-of-squares
27×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
15×div-inv distribute-lft-out--
9×cbrt-undiv div-exp associate-/r* distribute-lft-out
8×unswap-sqr
7×associate-/l*
6×pow1 prod-exp cbrt-unprod associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×sqrt-div
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 256
Calls
4 calls:
99.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
417.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
16.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
27.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify88.0ms

Algorithm
egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013306992
150026588

prune1.2s

Filtered
190 candidates to 268 candidates (-41.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2680268
Fresh077
Picked011
Done000
Total2688276

Merged error: 36.0b

Counts
276 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.5b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.5b
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
36.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
427×*-un-lft-identity
351×times-frac
168×add-sqr-sqrt add-cube-cbrt
148×distribute-lft-out
105×sqrt-prod
51×associate-/r*
17×associate-/r/
15×add-exp-log add-cbrt-cube associate-/l*
14×sqrt-div
11×flip3-+ flip-+
9×div-inv
6×cbrt-undiv div-exp associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
Counts
4 → 330
Calls
4 calls:
7.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
27.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
13.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
14.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series142.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
57.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
26.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
33.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify84.0ms

Algorithm
egg-herbie
Counts
342 → 342
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011646463
150016193

prune845.0ms

Filtered
176 candidates to 342 candidates (-94.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3402342
Fresh246
Picked101
Done011
Total3437350

Merged error: 2.0b

Counts
350 → 7

regimes219.0ms

Accuracy

44.4% (9.2b remaining)

Error of 11.4b against oracle of 2.2b and baseline of 18.7b

bsearch14.0ms

Steps
ItersRangePoint
4
1.0229035522097926e+115
1.5982727422379901e+115
1.5802924550496089e+115

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05578
15578

end0.0ms

sample1.1s

Algorithm
intervals
Results
644.0ms8000×body80valid
163.0ms8000×pre80true

Profiling

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