Details

Time bar (total: 6.6s)

sample62.0ms

Algorithm
intervals
Results
23.0ms288×body80valid
7.0ms84×body80nan

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0520618

prune21.0ms

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: 14.8b

Counts
2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b
(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
3.9b
(* M (/ D (* 2.0 d)))
4.9b
(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
12.3b
(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
55×add-exp-log
34×add-sqr-sqrt
26×associate-*r*
25×prod-exp
20×add-cbrt-cube
19×add-cube-cbrt *-un-lft-identity
14×times-frac
12×div-exp
11×associate-*l*
9×pow1
8×pow-exp
7×sqrt-prod cbrt-unprod unswap-sqr
4×sqrt-div associate-*r/ add-log-exp
3×cbrt-undiv *-commutative sqr-pow
2×pow-to-exp flip3-- pow-prod-down flip-- div-inv
1×unpow-prod-down rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 111
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
8.0ms
(* M (/ D (* 2.0 d)))
3.0ms
(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
9.0ms
(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

series603.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
6.0ms
(* M (/ D (* 2.0 d)))
164.0ms
(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
235.0ms
(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

simplify28.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
054411864

prune262.0ms

Filtered
82 candidates to 123 candidates (-50.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1167123
Fresh101
Picked101
Done000
Total1187125

Merged error: 9.1b

Counts
125 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

3.9b
(* M (/ D (* 2.0 d)))
4.9b
(sqrt (- 1.0 (* (* h (pow (* M (/ D (* 2.0 d))) 2.0)) (/ 1 l))))
5.2b
(* h (pow (* M (/ D (* 2.0 d))) 2.0))
5.3b
(* (* h (pow (* M (/ D (* 2.0 d))) 2.0)) (/ 1 l))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
137×add-exp-log
82×prod-exp
27×add-cbrt-cube
26×div-exp
25×associate-*r*
23×add-sqr-sqrt
20×pow-exp
17×add-cube-cbrt *-un-lft-identity
12×times-frac
11×cbrt-unprod
9×pow1
7×rec-exp 1-exp associate-*l*
5×pow-to-exp
4×cbrt-undiv add-log-exp
3×sqrt-prod *-commutative unswap-sqr
2×sqrt-div associate-*r/ pow-prod-down div-inv sqr-pow
1×unpow-prod-down rem-sqrt-square flip3-- sqrt-pow1 pow1/2 un-div-inv flip--
Counts
4 → 124
Calls
4 calls:
10.0ms
(* M (/ D (* 2.0 d)))
3.0ms
(sqrt (- 1.0 (* (* h (pow (* M (/ D (* 2.0 d))) 2.0)) (/ 1 l))))
6.0ms
(* h (pow (* M (/ D (* 2.0 d))) 2.0))
11.0ms
(* (* h (pow (* M (/ D (* 2.0 d))) 2.0)) (/ 1 l))

series431.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* M (/ D (* 2.0 d)))
134.0ms
(sqrt (- 1.0 (* (* h (pow (* M (/ D (* 2.0 d))) 2.0)) (/ 1 l))))
103.0ms
(* h (pow (* M (/ D (* 2.0 d))) 2.0))
187.0ms
(* (* h (pow (* M (/ D (* 2.0 d))) 2.0)) (/ 1 l))

simplify33.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
052981854

prune235.0ms

Filtered
77 candidates to 136 candidates (-76.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1342136
Fresh246
Picked101
Done000
Total1376143

Merged error: 9.1b

Counts
143 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (/ M d) D)
4.9b
(sqrt (- 1.0 (* (* h (pow (* 0.5 (* (/ M d) D)) 2.0)) (/ 1 l))))
5.2b
(* h (pow (* 0.5 (* (/ M d) D)) 2.0))
5.3b
(* (* h (pow (* 0.5 (* (/ M d) D)) 2.0)) (/ 1 l))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
133×add-exp-log
85×prod-exp
31×add-sqr-sqrt
23×add-cbrt-cube
22×add-cube-cbrt *-un-lft-identity
21×associate-*r*
20×div-exp pow-exp
19×times-frac
17×associate-*l*
9×pow1 cbrt-unprod
7×rec-exp 1-exp
5×pow-to-exp
4×add-log-exp unswap-sqr
3×cbrt-undiv sqrt-prod *-commutative
2×sqrt-div pow-prod-down div-inv sqr-pow
1×unpow-prod-down rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ associate-*l/ un-div-inv flip--
Counts
4 → 129
Calls
4 calls:
7.0ms
(* (/ M d) D)
3.0ms
(sqrt (- 1.0 (* (* h (pow (* 0.5 (* (/ M d) D)) 2.0)) (/ 1 l))))
7.0ms
(* h (pow (* 0.5 (* (/ M d) D)) 2.0))
12.0ms
(* (* h (pow (* 0.5 (* (/ M d) D)) 2.0)) (/ 1 l))

series418.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (/ M d) D)
118.0ms
(sqrt (- 1.0 (* (* h (pow (* 0.5 (* (/ M d) D)) 2.0)) (/ 1 l))))
101.0ms
(* h (pow (* 0.5 (* (/ M d) D)) 2.0))
190.0ms
(* (* h (pow (* 0.5 (* (/ M d) D)) 2.0)) (/ 1 l))

simplify48.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049951832
149951832

prune229.0ms

Filtered
83 candidates to 141 candidates (-69.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1401141
Fresh055
Picked101
Done000
Total1416147

Merged error: 8.9b

Counts
147 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (/ M d) D)
4.9b
(sqrt (- 1.0 (* (* (* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (/ 1 l))))
5.3b
(* (* (* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (/ 1 l))
6.8b
(* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
985×add-exp-log
757×prod-exp
212×pow-exp
140×div-exp
53×pow-to-exp
43×rec-exp 1-exp
32×add-cbrt-cube
31×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×associate-*r*
19×times-frac
17×associate-*l*
15×cbrt-unprod
9×pow1
4×cbrt-undiv add-log-exp unswap-sqr
3×sqrt-prod *-commutative
2×sqrt-div pow-prod-down div-inv sqr-pow
1×unpow-prod-down rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ associate-*l/ un-div-inv flip--
Counts
4 → 275
Calls
4 calls:
7.0ms
(* (/ M d) D)
3.0ms
(sqrt (- 1.0 (* (* (* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (/ 1 l))))
22.0ms
(* (* (* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (/ 1 l))
7.0ms
(* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2)))

series626.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ M d) D)
120.0ms
(sqrt (- 1.0 (* (* (* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (/ 1 l))))
392.0ms
(* (* (* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2))) (/ 1 l))
108.0ms
(* h (pow (* 0.5 (* (/ M d) D)) (/ 2.0 2)))

simplify78.0ms

Algorithm
egg-herbie
Counts
287 → 287
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049704810
149704810

prune254.0ms

Filtered
88 candidates to 287 candidates (-226.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2861287
Fresh145
Picked011
Done000
Total2876293

Merged error: 8.5b

Counts
293 → 6

regimes1.1s

Accuracy

-23% (2.1b remaining)

Error of 9.4b against oracle of 7.3b and baseline of 9.0b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04670
14670

end0.0ms

sample1.9s

Algorithm
intervals
Results
752.0ms9345×body80valid
252.0ms3190×body80nan

Profiling

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