Details

Time bar (total: 16.6s)

sample38.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
5.0ms256×pre80true

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune5.0ms

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: 56.8b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.0b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.1b
(/ (/ (* (* 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))
49.0b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 189
Calls
4 calls:
8.0ms
(* i (+ (+ alpha beta) i))
12.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.0ms
(/ (/ (* (* 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))
23.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
25.0ms
(* i (+ (+ alpha beta) i))
122.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
769.0ms
(/ (/ (* (* 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))
188.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify76.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012085419
150014944

prune1.4s

Filtered
201 candidates to 138 candidates (31.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1947201
Fresh000
Picked101
Done000
Total1957202

Merged error: 32.4b

Counts
202 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
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))))
33.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
213×times-frac
175×add-sqr-sqrt
145×*-un-lft-identity
101×associate-*r*
92×add-cube-cbrt
67×add-exp-log add-cbrt-cube
45×associate-*l*
30×cbrt-undiv div-exp difference-of-squares
28×associate-/r/
17×prod-exp cbrt-unprod
16×flip3-+ flip-+
15×sqrt-prod distribute-lft-out--
14×div-inv
12×distribute-lft-out
8×pow1
7×unswap-sqr
6×associate-/r*
5×associate-*r/
4×associate-/l/ associate-/l* add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative
1×distribute-rgt-in frac-times flip3-- distribute-lft-in associate-*l/ flip--
Counts
4 → 260
Calls
4 calls:
8.0ms
(* i (+ (+ alpha beta) i))
97.0ms
(* (/ (/ (* 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)))

series2.8s

Counts
4 → 12
Calls
4 calls:
25.0ms
(* i (+ (+ alpha beta) i))
2.6s
(* (/ (/ (* 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))))
98.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
133.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify91.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015247165
150016394

prune2.7s

Filtered
272 candidates to 176 candidates (35.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2666272
Fresh426
Picked101
Done000
Total2718279

Merged error: 32.3b

Counts
279 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.4b
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.4b
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
34.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
117×times-frac
106×add-sqr-sqrt
76×add-cube-cbrt
60×sqrt-prod
39×distribute-lft-out
36×associate-*r*
24×associate-*l*
22×add-exp-log add-cbrt-cube
15×associate-/r*
11×associate-/l*
10×associate-/r/
9×unswap-sqr
8×sqrt-div
7×cbrt-undiv flip3-+ div-exp flip-+
6×pow1
5×div-inv
4×prod-exp cbrt-unprod associate-/l/ add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 218
Calls
4 calls:
36.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
7.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
13.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
205.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
181.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
134.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify116.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
09183163
145882914
250012824

prune2.5s

Filtered
230 candidates to 147 candidates (36.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2282230
Fresh257
Picked011
Done000
Total2308238

Merged error: 2.3b

Counts
238 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (+ alpha beta) (* 2.0 i)))
0.4b
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.4b
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.4b
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
134×*-un-lft-identity
108×times-frac
100×add-sqr-sqrt
69×add-cube-cbrt
63×sqrt-prod
39×distribute-lft-out
36×associate-*r*
24×associate-*l*
20×add-exp-log add-cbrt-cube
12×associate-/r*
10×sqrt-div
9×unswap-sqr
8×associate-/r/ associate-/l*
7×pow1
6×cbrt-undiv flip3-+ div-exp flip-+
4×prod-exp cbrt-unprod div-inv add-log-exp
2×frac-2neg clear-num associate-/l/
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 202
Calls
4 calls:
5.0ms
(sqrt (+ (+ alpha beta) (* 2.0 i)))
34.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
8.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
13.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))

series697.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (+ (+ alpha beta) (* 2.0 i)))
208.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
203.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
179.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))

simplify99.0ms

Algorithm
egg-herbie
Counts
214 → 214
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07972818
138312604
250012509

prune2.2s

Filtered
214 candidates to 133 candidates (37.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2104214
Fresh156
Picked101
Done011
Total21210222

Merged error: 2.1b

Counts
222 → 10

regimes342.0ms

Accuracy

38.4% (10.1b remaining)

Error of 12.1b against oracle of 2.0b and baseline of 18.4b

bsearch168.0ms

Steps
ItersRangePoint
4
1.7726761728158861e+146
2.7340940993108444e+146
1.8653840498378631e+146
4
7.301259794649873e+76
1.314993598117883e+77
8.725316479657627e+76
8
4.5061418184413155e+64
1.2689435492989146e+67
1.258186985671555e+67

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
070110
170110

end0.0ms

sample887.0ms

Algorithm
intervals
Results
415.0ms8000×body80valid
159.0ms8000×pre80true

Profiling

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