Details

Time bar (total: 9.4s)

analyze2.4s

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
5.1%94.6%0.3%13
7%92.7%0.3%14

sample86.0ms

Algorithm
intervals
Results
17.0ms256×body80valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
0490418
1490418

prune17.0ms

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: 13.0b

Counts
2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

1.7b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.3b
(/ (* M D) (* 2.0 d))
9.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
7.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series577.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
157.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
225.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify36.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
053731965

prune250.0ms

Filtered
85 candidates to 125 candidates (-47.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1178125
Fresh101
Picked011
Done000
Total1189127

Merged error: 7.7b

Counts
127 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
4.5b
(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)
5.0b
(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
5.6b
(* (/ D d) (/ M 2.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
41×add-sqr-sqrt
26×prod-exp
25×*-un-lft-identity times-frac
23×add-cube-cbrt add-cbrt-cube
20×div-exp
18×associate-*r*
16×associate-*l*
10×pow-exp
7×pow1
6×cbrt-undiv cbrt-unprod unswap-sqr
5×sqrt-prod
4×add-log-exp
3×associate-/r* div-inv
2×pow-to-exp sqrt-div *-commutative sqr-pow
1×frac-times unpow-prod-down rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 120
Calls
4 calls:
6.0ms
(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
6.0ms
(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)
6.0ms
(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
10.0ms
(* (/ D d) (/ M 2.0))

series399.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
178.0ms
(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)
100.0ms
(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
7.0ms
(* (/ D d) (/ M 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
053041740

prune240.0ms

Filtered
92 candidates to 132 candidates (-43.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1293132
Fresh257
Picked101
Done101
Total1338141

Merged error: 6.8b

Counts
141 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
5.3b
(* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))
5.6b
(* (/ D d) (/ M 2.0))
5.6b
(* (/ D d) (/ M 2.0))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
63×add-sqr-sqrt
47×times-frac
39×add-cbrt-cube
36×add-cube-cbrt *-un-lft-identity
31×associate-*r*
29×associate-*l*
16×pow-to-exp
12×cbrt-unprod
11×cbrt-undiv
10×unswap-sqr
8×pow1
5×div-inv
4×add-log-exp
3×associate-/r* *-commutative
2×frac-times associate-*r/ pow-prod-down associate-*l/ sqr-pow
1×unpow-prod-down frac-2neg clear-num associate-/l*
Counts
4 → 203
Calls
4 calls:
12.0ms
(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
6.0ms
(* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))
12.0ms
(* (/ D d) (/ M 2.0))
10.0ms
(* (/ D d) (/ M 2.0))

series296.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
101.0ms
(* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))
7.0ms
(* (/ D d) (/ M 2.0))
7.0ms
(* (/ D d) (/ M 2.0))

simplify70.0ms

Algorithm
egg-herbie
Counts
215 → 215
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050142901

prune366.0ms

Filtered
117 candidates to 215 candidates (-83.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2132215
Fresh077
Picked011
Done000
Total21310223

Merged error: 6.8b

Counts
223 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (* (/ D d) (* (/ (cbrt M) (sqrt 2.0)) (cbrt M))) (/ (cbrt M) (sqrt 2.0))) (/ 2.0 2))) l)
4.8b
(* (/ D d) (* (/ (cbrt M) (sqrt 2.0)) (cbrt M)))
5.3b
(* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))
5.6b
(* (/ D d) (/ M 2.0))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
1106×add-exp-log
620×prod-exp
354×div-exp
210×pow-exp
44×add-sqr-sqrt
42×add-cbrt-cube
34×times-frac
29×add-cube-cbrt *-un-lft-identity associate-*l*
26×pow-to-exp
19×associate-*r*
18×cbrt-unprod
12×cbrt-undiv
11×pow1
6×unswap-sqr
4×pow-prod-down associate-*l/ div-inv add-log-exp
3×associate-/r* *-commutative
2×frac-times associate-*r/ sqr-pow
1×unpow-prod-down frac-2neg clear-num associate-/l*
Counts
4 → 272
Calls
4 calls:
18.0ms
(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (* (/ D d) (* (/ (cbrt M) (sqrt 2.0)) (cbrt M))) (/ (cbrt M) (sqrt 2.0))) (/ 2.0 2))) l)
12.0ms
(* (/ D d) (* (/ (cbrt M) (sqrt 2.0)) (cbrt M)))
6.0ms
(* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))
11.0ms
(* (/ D d) (/ M 2.0))

series390.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (* (/ D d) (* (/ (cbrt M) (sqrt 2.0)) (cbrt M))) (/ (cbrt M) (sqrt 2.0))) (/ 2.0 2))) l)
33.0ms
(* (/ D d) (* (/ (cbrt M) (sqrt 2.0)) (cbrt M)))
100.0ms
(* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))
7.0ms
(* (/ D d) (/ M 2.0))

simplify112.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
050206936

prune364.0ms

Filtered
108 candidates to 284 candidates (-163.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2840284
Fresh088
Picked011
Done011
Total28410294

Merged error: 6.8b

Counts
294 → 10

regimes894.0ms

Accuracy

0% (1.6b remaining)

Error of 9.4b against oracle of 7.8b and baseline of 9.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06732
16732

end0.0ms

sample2.5s

Algorithm
intervals
Results
552.0ms8000×body80valid

Profiling

Loading profile data...