Details

Time bar (total: 15.6s)

sample74.0ms

Algorithm
intervals
Results
26.0ms312×body80valid
9.0ms128×body80nan

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune6.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.1b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b
(/ (* M D) (* 2.0 d))
9.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite28.0ms

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))))
5.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
433.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
392.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
32.0ms
(/ (* M D) (* 2.0 d))
774.0ms
(* (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

prune837.0ms

Filtered
125 candidates to 81 candidates (35.2%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1196125
Fresh000
Picked101
Done000
Total1206126

Merged error: 7.7b

Counts
126 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.2b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.5b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.7b
(/ (* M D) (* 2.0 d))

rewrite32.0ms

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:
2.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
11.0ms
(* (* (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))

series2.1s

Counts
4 → 12
Calls
4 calls:
414.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
812.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
844.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
39.0ms
(/ (* M D) (* 2.0 d))

simplify85.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07521137
134601014
250021001

prune944.0ms

Filtered
140 candidates to 74 candidates (47.1%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1391140
Fresh055
Picked101
Done000
Total1406146

Merged error: 7.5b

Counts
146 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (* M D) (* 2.0 d))
11.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
33×add-cbrt-cube
30×prod-exp
28×add-sqr-sqrt
23×div-exp
15×times-frac
14×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
7×unpow-prod-down
6×unswap-sqr
5×pow1
4×div-inv add-log-exp
3×sqrt-prod sqr-pow
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 110
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.3s

Counts
4 → 12
Calls
4 calls:
404.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
33.0ms
(/ (* M D) (* 2.0 d))
40.0ms
(/ (* M D) (* 2.0 d))
795.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify73.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05761132
125821013
250011012

prune1.2s

Filtered
122 candidates to 77 candidates (36.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1220122
Fresh055
Picked011
Done000
Total1226128

Merged error: 7.5b

Counts
128 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l)))))
3.6b
(* (/ M 2.0) (/ D d))
4.5b
(sqrt (- 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l))))
9.9b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
55×add-sqr-sqrt
33×times-frac
32×associate-*r*
30×add-cube-cbrt *-un-lft-identity
27×prod-exp
23×add-cbrt-cube
21×associate-*l*
19×div-exp
10×pow-exp unswap-sqr
9×pow1
7×sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div associate-*r/ add-log-exp
3×*-commutative div-inv sqr-pow
2×pow-to-exp flip3-- pow-prod-down flip--
1×frac-times unpow-prod-down rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/
Counts
4 → 136
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l)))))
12.0ms
(* (/ M 2.0) (/ D d))
2.0ms
(sqrt (- 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l))))
9.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
421.0ms
(* w0 (sqrt (- 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l)))))
33.0ms
(* (/ M 2.0) (/ D d))
384.0ms
(sqrt (- 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l))))
766.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) (/ h l))

simplify76.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07381170
131371092
250011089

prune1.4s

Filtered
148 candidates to 99 candidates (33.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1453148
Fresh044
Picked101
Done011
Total1468154

Merged error: 7.0b

Counts
154 → 8

regimes2.3s

Accuracy

60.1% (1.6b remaining)

Error of 9.3b against oracle of 7.6b and baseline of 11.7b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04931
14931

end0.0ms

sample1.7s

Algorithm
intervals
Results
664.0ms9352×body80valid
230.0ms3202×body80nan

Profiling

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