Details

Time bar (total: 9.9s)

sample51.0ms

Algorithm
intervals
Results
23.0ms295×body80valid
7.0ms97×body80nan

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

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: 13.8b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

2.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b
(/ (* M D) (* 2.0 d))
10.5b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite29.0ms

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:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
425.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
380.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms
(/ (* M D) (* 2.0 d))
714.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify78.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06091075
12742997
25001994

prune386.0ms

Filtered
125 candidates to 81 candidates (64.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11510125
Fresh000
Picked101
Done000
Total11610126

Merged error: 8.0b

Counts
126 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.9b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.5b
(/ (* M D) (* 2.0 d))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 128
Calls
4 calls:
12.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
2.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* M D) (* 2.0 d))

series1.9s

Counts
4 → 12
Calls
4 calls:
730.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
379.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
758.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
29.0ms
(/ (* M D) (* 2.0 d))

simplify90.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07521136
134601014
250021001

prune331.0ms

Filtered
140 candidates to 74 candidates (52.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1373140
Fresh189
Picked101
Done000
Total13911150

Merged error: 8.0b

Counts
150 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

4.8b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.9b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
14×add-sqr-sqrt
12×div-exp
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 pow-exp
4×add-log-exp
3×times-frac associate-*r* sqrt-prod div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 88
Calls
4 calls:
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
2.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
6.0ms
(/ (* M D) (* 2.0 d))
9.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
747.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
374.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
28.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify57.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0442889
11993783
25001782

prune316.0ms

Filtered
100 candidates to 65 candidates (65.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New991100
Fresh1910
Picked101
Done000
Total10110111

Merged error: 8.0b

Counts
111 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))
7.4b
(cbrt (pow (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l)))) 3))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log add-cbrt-cube
18×cbrt-prod
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×sqrt-prod
8×cbrt-undiv div-exp prod-exp cbrt-unprod
6×unpow-prod-down cube-prod
5×pow1
4×sqrt-div add-log-exp
2×cube-div cbrt-div flip3-- frac-2neg times-frac clear-num associate-/r* flip-- div-inv associate-/l*
1×cube-mult rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 86
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(cbrt (pow (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l)))) 3))

series811.0ms

Counts
4 → 12
Calls
4 calls:
376.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
28.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))
379.0ms
(cbrt (pow (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l)))) 3))

simplify60.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03541328
116691255
250011255

prune270.0ms

Filtered
98 candidates to 56 candidates (57.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New98098
Fresh099
Picked011
Done000
Total9810108

Merged error: 8.0b

Counts
108 → 10

regimes1.2s

Accuracy

38% (2.2b remaining)

Error of 9.1b against oracle of 7.0b and baseline of 10.5b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05130
15130

end0.0ms

sample1.4s

Algorithm
intervals
Results
673.0ms9311×body80valid
231.0ms3084×body80nan

Profiling

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