Details

Time bar (total: 7.6s)

analyze131.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14

sample36.0ms

Algorithm
intervals
Results
12.0ms218×body80valid
6.0ms256×pre80true
3.0ms15×body640valid
3.0ms9×body1280valid
2.0ms10×body320valid
0.0ms4×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0544629

prune11.0ms

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: 16.1b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
1.9b
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
2.2b
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
15.0b
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
22×associate-*r*
21×add-sqr-sqrt flip3-+ flip-+
20×add-exp-log add-cbrt-cube
16×associate-/r/
14×frac-times
11×add-cube-cbrt
10×times-frac
8×pow1 associate-*l* associate-*l/
7×associate-*r/
6×prod-exp cbrt-unprod add-log-exp
5×distribute-lft-out associate-/l*
4×cbrt-undiv div-exp
3×distribute-lft-out-- difference-of-squares
2×pow-prod-down *-commutative div-inv associate-/l/ unswap-sqr
1×+-commutative distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub clear-num associate-/r* sum-log flip--
Counts
4 → 120
Calls
4 calls:
13.0ms
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
19.0ms
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
21.0ms
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
16.0ms
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

series209.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
83.0ms
(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
65.0ms
(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
41.0ms
(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
055223306

prune274.0ms

Filtered
106 candidates to 132 candidates (-24.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1266132
Fresh101
Picked101
Done000
Total1286134

Merged error: 4.4b

Counts
134 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.1b
(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
1.9b
(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)
2.2b
(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
123×*-un-lft-identity
75×add-sqr-sqrt
69×times-frac
60×add-exp-log
37×distribute-lft-out
36×add-cube-cbrt add-cbrt-cube
32×associate-*r*
25×prod-exp
22×associate-*l*
17×div-exp
13×cbrt-unprod
11×pow1 distribute-lft-out-- difference-of-squares
10×frac-times
9×cbrt-undiv
8×flip3-+ flip-+
7×associate-*r/
6×associate-*l/ associate-/r/ add-log-exp unswap-sqr
5×associate-/r* associate-/l*
4×rec-exp 1-exp pow-prod-down
3×div-inv
2×*-commutative associate-/l/
1×+-commutative flip3-- frac-2neg div-sub clear-num sum-log flip--
Counts
4 → 182
Calls
4 calls:
11.0ms
(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
30.0ms
(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
24.0ms
(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)
22.0ms
(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))

series212.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
39.0ms
(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
85.0ms
(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)
70.0ms
(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))

simplify73.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
051434381

prune285.0ms

Filtered
120 candidates to 194 candidates (-61.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1913194
Fresh235
Picked011
Done000
Total1937200

Merged error: 4.4b

Counts
200 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
0.4b
(/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
2.2b
(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))))
6.3b
(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))) 1.0)

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
945×*-un-lft-identity
768×times-frac
490×sqrt-prod
453×add-sqr-sqrt
295×distribute-lft-out
291×add-cube-cbrt
81×distribute-lft-out-- difference-of-squares
64×add-exp-log
51×associate-/l*
40×add-cbrt-cube
25×prod-exp
22×sqrt-div div-exp associate-/r/
16×flip3-+ associate-/r* flip-+
13×cbrt-undiv cbrt-unprod
11×div-inv
9×pow1 frac-times
6×associate-*r/ add-log-exp
5×associate-*l/
4×associate-*l*
3×rec-exp 1-exp div-sub pow-prod-down associate-/l/
2×frac-2neg clear-num
1×+-commutative flip3-- associate-*r* sum-log *-commutative flip--
Counts
4 → 567
Calls
4 calls:
28.0ms
(/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
12.0ms
(/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
55.0ms
(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))))
53.0ms
(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))) 1.0)

series813.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
42.0ms
(/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
446.0ms
(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))))
238.0ms
(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))) 1.0)

simplify194.0ms

Algorithm
egg-herbie
Counts
579 → 579
Iterations

Useful iterations: 0 (99.0ms)

IterNodesCost
0526119202

prune747.0ms

Filtered
178 candidates to 579 candidates (-225.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New5772579
Fresh145
Picked101
Done011
Total5797586

Merged error: 4.4b

Counts
586 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ alpha beta) (+ alpha (+ beta (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
0.3b
(/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
0.4b
(/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
5.8b
(+ (* (/ (+ alpha beta) (+ alpha (+ beta (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
1770×*-un-lft-identity
1499×times-frac
930×sqrt-prod
889×add-sqr-sqrt
560×distribute-lft-out
544×add-cube-cbrt
374×associate-*r*
145×distribute-lft-out-- difference-of-squares
51×associate-/l*
42×associate-/r/
40×sqrt-div
32×add-exp-log add-cbrt-cube
22×flip3-+ associate-*l* flip-+
21×div-inv
16×associate-/r*
14×unswap-sqr
13×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod add-log-exp
3×div-sub associate-/l/
2×frac-2neg clear-num
1×+-commutative frac-times flip3-- associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip--
Counts
4 → 955
Calls
4 calls:
164.0ms
(* (/ (+ alpha beta) (+ alpha (+ beta (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
29.0ms
(/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
15.0ms
(/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
47.0ms
(+ (* (/ (+ alpha beta) (+ alpha (+ beta (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

series793.0ms

Counts
4 → 12
Calls
4 calls:
440.0ms
(* (/ (+ alpha beta) (+ alpha (+ beta (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
84.0ms
(/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
38.0ms
(/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
231.0ms
(+ (* (/ (+ alpha beta) (+ alpha (+ beta (* 2.0 i)))) (/ (/ (- beta alpha) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

simplify241.0ms

Algorithm
egg-herbie
Counts
967 → 967
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
0499431252
1499431252

prune1.2s

Filtered
276 candidates to 967 candidates (-250.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New9625967
Fresh145
Picked101
Done011
Total96410974

Merged error: 4.4b

Counts
974 → 10

regimes327.0ms

Accuracy

0% (6.3b remaining)

Error of 12.5b against oracle of 6.2b and baseline of 12.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04031
14031

end0.0ms

sample1.1s

Algorithm
intervals
Results
374.0ms6336×body80valid
181.0ms8000×pre80true
155.0ms526×body1280valid
134.0ms574×body640valid
60.0ms350×body320valid
24.0ms214×body160valid

Profiling

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