Details

Time bar (total: 8.1s)

sample29.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

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: 3.4b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
4×associate-/l/
3×pow1 frac-2neg clear-num add-log-exp
Counts
3 → 450
Calls
3 calls:
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
18.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series375.0ms

Counts
3 → 9
Calls
3 calls:
140.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
81.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify146.0ms

Algorithm
egg-herbie
Counts
459 → 459
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0143912925
1500212452

prune1.3s

Filtered
459 candidates to 269 candidates (58.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4518459
Fresh000
Picked101
Done000
Total4528460

Merged error: 1.4b

Counts
460 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.6b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.5b
(* (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
2.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
157×times-frac
136×*-un-lft-identity
130×add-sqr-sqrt
84×add-cube-cbrt
75×add-exp-log
59×sqrt-prod
45×add-cbrt-cube
38×div-exp
30×associate-*r*
24×associate-*l*
23×distribute-lft-out
21×cbrt-undiv
20×associate-/r/
16×prod-exp associate-/r* associate-/l*
15×unswap-sqr
11×flip3-+ flip-+
10×div-inv
8×pow1 sqrt-div cbrt-unprod
5×rec-exp 1-exp
4×add-log-exp
3×pow-flip frac-2neg clear-num associate-/l/
1×frac-times sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 268
Calls
4 calls:
36.0ms
(/ (/ (* (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
8.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
37.0ms
(* (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series501.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (/ (* (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
144.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
82.0ms
(* (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
114.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify82.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011975743
150015060

prune804.0ms

Filtered
280 candidates to 161 candidates (57.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2791280
Fresh167
Picked011
Done000
Total2808288

Merged error: 1.4b

Counts
288 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

3.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.1b
(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
20×cbrt-prod
14×cbrt-div
11×add-sqr-sqrt add-cube-cbrt
10×flip3-+ flip-+
9×add-exp-log
8×associate-/r/
7×times-frac associate-/l*
6×add-cbrt-cube
5×distribute-lft-out
4×pow1 frac-times add-log-exp
3×pow1/3
2×cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/l/
1×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 81
Calls
4 calls:
6.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
6.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
6.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
26.0ms
(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))

series680.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
256.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
64.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
300.0ms
(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))

simplify59.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05861440
120821369
250011345

prune485.0ms

Filtered
93 candidates to 81 candidates (87.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New93093
Fresh066
Picked011
Done011
Total938101

Merged error: 1.4b

Counts
101 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))) (/ (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
655×times-frac
493×*-un-lft-identity
283×add-sqr-sqrt
271×add-cube-cbrt
258×associate-*r*
243×cbrt-prod
111×distribute-lft-out
40×associate-/r/
23×flip3-+ flip-+
22×add-exp-log
20×div-inv
16×add-cbrt-cube
12×associate-/l*
9×pow1 associate-/r*
8×cbrt-div
6×prod-exp cbrt-unprod associate-/l/
5×cbrt-undiv frac-times div-exp associate-*l/ unswap-sqr
4×add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
1×associate-*l* *-commutative
Counts
4 → 394
Calls
4 calls:
121.0ms
(* (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))) (/ (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
17.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))) (/ (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
81.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify163.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0179915490
1500115011

prune1.5s

Filtered
406 candidates to 263 candidates (64.8%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New4060406
Fresh055
Picked011
Done022
Total4068414

Merged error: 1.4b

Counts
414 → 8

regimes132.0ms

Accuracy

49.8% (1.5b remaining)

Error of 2.7b against oracle of 1.2b and baseline of 4.2b

bsearch64.0ms

Steps
ItersRangePoint
7
4.157937891073609e+213
6.513651957020406e+215
1.5796751234839218e+214

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05350
15350

end0.0ms

sample693.0ms

Algorithm
intervals
Results
355.0ms8000×body80valid
116.0ms8000×pre80true

Profiling

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