Details

Time bar (total: 9.6s)

sample40.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
6.0ms256×pre80true

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0495453
1495453

prune15.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 49.2b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
0.3b
(/ i (+ alpha (+ beta (* i 2.0))))
3.4b
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
48.6b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
29×*-un-lft-identity
22×add-sqr-sqrt
21×frac-times
20×prod-exp cbrt-unprod
19×add-cube-cbrt associate-*r*
18×times-frac associate-/r/
15×flip3-+ flip-+
13×associate-*l/
12×cbrt-undiv div-exp
11×pow1 associate-*r/
9×flip3-- flip--
6×distribute-rgt-in distribute-lft-in associate-/l*
5×associate-*l* associate-/r* distribute-lft-out
4×pow-prod-down associate--l+ add-log-exp
3×div-inv
2×sub-neg frac-2neg clear-num *-commutative associate-/l/
1×difference-of-squares unswap-sqr
Counts
4 → 155
Calls
4 calls:
16.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
6.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
38.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
24.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
13.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
306.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
163.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify75.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050325217

prune333.0ms

Filtered
119 candidates to 167 candidates (-40.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1616167
Fresh101
Picked101
Done000
Total1636169

Merged error: 37.3b

Counts
169 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ i (+ alpha (+ beta (* i 2.0))))
0.6b
(/ 1 (/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0))))
3.4b
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ 1 (/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0)))))
43.8b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
2298×times-frac
1435×*-un-lft-identity
1359×add-sqr-sqrt
831×add-cube-cbrt
380×associate-*r*
352×difference-of-squares
214×distribute-lft-out
155×add-exp-log
137×associate-/r*
88×unpow-prod-down distribute-lft-out-- unpow2 sqr-pow
72×div-exp
71×add-cbrt-cube
69×associate-/r/
50×prod-exp
39×div-inv
30×cbrt-undiv
29×flip3-- flip--
20×cbrt-unprod
12×rec-exp 1-exp
10×pow1
9×frac-times associate-/l*
7×associate-*l/
6×flip3-+ flip-+
5×associate-*r/
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
2×associate-/l/
1×pow-flip associate-*l* un-div-inv *-commutative inv-pow
Counts
4 → 1057
Calls
4 calls:
6.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
42.0ms
(/ 1 (/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0))))
92.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ 1 (/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0)))))
17.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0))

series435.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
69.0ms
(/ 1 (/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0))))
305.0ms
(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ 1 (/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0)))))
47.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (pow (+ alpha (+ beta (* i 2.0))) 2) 1.0))

simplify345.0ms

Algorithm
egg-herbie
Counts
1069 → 1069
Iterations

Useful iterations: 0 (130.0ms)

IterNodesCost
0497152345
1497152345

prune3.8s

Filtered
558 candidates to 1069 candidates (-91.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New106541069
Fresh325
Picked101
Done000
Total106961075

Merged error: 36.3b

Counts
1075 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))
0.3b
(/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
0.3b
(/ i (+ alpha (+ beta (* i 2.0))))
39.3b
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
321×*-un-lft-identity
276×times-frac
203×add-sqr-sqrt
127×add-cube-cbrt
72×distribute-lft-out
43×associate-/r*
38×distribute-lft-out-- difference-of-squares
19×sqrt-prod
18×cbrt-prod
17×associate-/r/
16×associate-/l*
15×add-exp-log
14×add-cbrt-cube
9×div-inv
6×cbrt-undiv flip3-- div-exp flip--
4×pow1 frac-2neg flip3-+ clear-num flip-+ associate-/l/ add-log-exp
Counts
4 → 291
Calls
4 calls:
9.0ms
(/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))
23.0ms
(/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
6.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
19.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))

series136.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))
74.0ms
(/ (+ alpha (+ beta (* i 2.0))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
13.0ms
(/ i (+ alpha (+ beta (* i 2.0))))
34.0ms
(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))

simplify89.0ms

Algorithm
egg-herbie
Counts
303 → 303
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0534011038

prune1.0s

Filtered
179 candidates to 303 candidates (-69.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3003303
Fresh145
Picked011
Done000
Total3018309

Merged error: 6.3b

Counts
309 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ i (+ alpha beta)) (* (cbrt 1) (/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))))
0.2b
(/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))
0.3b
(/ (+ alpha (+ beta (* i 2.0))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))
0.3b
(/ i (+ alpha (+ beta (* i 2.0))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
54×times-frac
42×add-sqr-sqrt add-cube-cbrt
32×distribute-lft-out
19×add-exp-log
18×cbrt-prod
15×add-cbrt-cube
13×associate-/l*
12×associate-/r*
9×pow1
6×flip3-+ associate-/r/ flip-+
5×associate-*l* prod-exp cbrt-unprod
4×cbrt-undiv associate-*r/ div-exp add-log-exp
3×frac-2neg pow-prod-down clear-num div-inv
2×frac-times associate-*l/ associate-/l/
1×associate-*r* *-commutative
Counts
4 → 150
Calls
4 calls:
20.0ms
(* (+ i (+ alpha beta)) (* (cbrt 1) (/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))))
9.0ms
(/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))
11.0ms
(/ (+ alpha (+ beta (* i 2.0))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))
6.0ms
(/ i (+ alpha (+ beta (* i 2.0))))

series79.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (+ i (+ alpha beta)) (* (cbrt 1) (/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))))
15.0ms
(/ (cbrt 1) (+ alpha (+ (+ beta (* i 2.0)) (sqrt 1.0))))
28.0ms
(/ (+ alpha (+ beta (* i 2.0))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))
13.0ms
(/ i (+ alpha (+ beta (* i 2.0))))

simplify56.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049653381
149653381

prune559.0ms

Filtered
112 candidates to 162 candidates (-44.6%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1557162
Fresh066
Picked101
Done011
Total15614170

Merged error: 6.2b

Counts
170 → 14

regimes341.0ms

Accuracy

0% (7.4b remaining)

Error of 13.4b against oracle of 6.0b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04652
14652

end0.0ms

sample1.1s

Algorithm
intervals
Results
630.0ms8000×body80valid
179.0ms8000×pre80true

Profiling

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