Details

Time bar (total: 10.7s)

sample47.0ms

Algorithm
intervals
Results
20.0ms286×body80valid
7.0ms100×body80nan

simplify56.0ms

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: 14.1b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.7b
(/ (* M D) (* 2.0 d))
10.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite31.0ms

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)))))
3.0ms
(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))

series1.6s

Counts
4 → 12
Calls
4 calls:
430.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
385.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
35.0ms
(/ (* M D) (* 2.0 d))
700.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06091075
12742997
25001994

prune383.0ms

Filtered
125 candidates to 81 candidates (64.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1178125
Fresh000
Picked101
Done000
Total1188126

Merged error: 7.2b

Counts
126 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

4.2b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.2b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.7b
(/ (* M D) (* 2.0 d))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
5.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
8.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms
(/ (* M D) (* 2.0 d))

series1.9s

Counts
4 → 12
Calls
4 calls:
390.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
766.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
730.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
29.0ms
(/ (* M D) (* 2.0 d))

simplify77.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0560828
12559746
25001744

prune303.0ms

Filtered
108 candidates to 70 candidates (64.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1053108
Fresh167
Picked101
Done000
Total1079116

Merged error: 6.8b

Counts
116 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.2b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
6.7b
(/ (* M D) (* 2.0 d))
6.7b
(/ (* M D) (* 2.0 d))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
39×add-cbrt-cube
16×pow-to-exp
14×add-sqr-sqrt
12×cbrt-unprod
11×cbrt-undiv
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×sqr-pow
1×*-commutative
Counts
4 → 150
Calls
4 calls:
8.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
15.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))

series1.6s

Counts
4 → 12
Calls
4 calls:
761.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
732.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
34.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))

simplify84.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
08361701
131181278
250011274

prune347.0ms

Filtered
162 candidates to 72 candidates (44.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1602162
Fresh268
Picked011
Done000
Total1629171

Merged error: 6.5b

Counts
171 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.4b
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
6.7b
(/ (* M D) (* 2.0 d))
6.7b
(/ (* M D) (* 2.0 d))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
98×add-exp-log
34×div-exp prod-exp
33×add-cbrt-cube
16×add-sqr-sqrt unpow-prod-down
15×pow-exp
14×times-frac
11×add-cube-cbrt *-un-lft-identity associate-/l*
10×cbrt-undiv cbrt-unprod
9×associate-*l*
6×div-inv
4×pow1 add-log-exp sqr-pow
3×pow-to-exp frac-2neg associate-*r* clear-num associate-/r* unswap-sqr
1×*-commutative
Counts
4 → 118
Calls
4 calls:
8.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
10.0ms
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(/ (* M D) (* 2.0 d))

series1.3s

Counts
4 → 12
Calls
4 calls:
769.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
501.0ms
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
29.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))

simplify66.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05411098
12335967
25001961

prune405.0ms

Filtered
130 candidates to 81 candidates (62.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1300130
Fresh077
Picked011
Done011
Total1309139

Merged error: 6.5b

Counts
139 → 9

regimes948.0ms

Accuracy

0.9% (1.3b remaining)

Error of 8.6b against oracle of 7.3b and baseline of 8.6b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04131
14131

end0.0ms

sample1.3s

Algorithm
intervals
Results
659.0ms9296×body80valid
213.0ms2974×body80nan

Profiling

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