Details

Time bar (total: 6.0s)

sample71.0ms

Algorithm
intervals
Results
27.0ms303×body80valid
10.0ms131×body80nan

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
0520618

prune16.0ms

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:

2.8b
(* 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))))
6.9b
(/ (* M D) (* 2.0 d))
11.0b
(* (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)))))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series544.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
148.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
214.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify32.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
052151965

prune231.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1196125
Fresh101
Picked101
Done000
Total1216127

Merged error: 10.1b

Counts
127 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (/ D d) (/ M 2.0))
4.9b
(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
5.1b
(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)
5.2b
(* h (pow (* (/ D d) (/ M 2.0)) 2.0))

rewrite31.0ms

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:
10.0ms
(* (/ D d) (/ M 2.0))
4.0ms
(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))

series380.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ D d) (/ M 2.0))
108.0ms
(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
169.0ms
(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)
96.0ms
(* h (pow (* (/ D d) (/ M 2.0)) 2.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
051701740

prune227.0ms

Filtered
96 candidates to 132 candidates (-37.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1302132
Fresh145
Picked101
Done000
Total1326138

Merged error: 8.7b

Counts
138 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (/ D d) (/ M 2.0))
4.9b
(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
5.1b
(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
5.2b
(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
361×add-exp-log
180×prod-exp
125×div-exp
80×pow-exp
41×add-sqr-sqrt
27×add-cbrt-cube
25×*-un-lft-identity times-frac
23×add-cube-cbrt
18×associate-*r*
16×pow-to-exp associate-*l*
8×cbrt-unprod
7×pow1 cbrt-undiv
6×unswap-sqr
5×sqrt-prod
4×add-log-exp
3×associate-/r* div-inv
2×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 → 170
Calls
4 calls:
10.0ms
(* (/ D d) (/ M 2.0))
4.0ms
(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
12.0ms
(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
6.0ms
(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ D d) (/ M 2.0))
123.0ms
(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
169.0ms
(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
95.0ms
(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))

simplify50.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
052222909

prune285.0ms

Filtered
95 candidates to 182 candidates (-91.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1793182
Fresh235
Picked101
Done000
Total1826188

Merged error: 8.0b

Counts
188 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (/ D d) (/ M 2.0))
4.4b
(/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l)
4.9b
(sqrt (- 1.0 (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l))))
5.2b
(* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
47×add-sqr-sqrt
37×times-frac
31×add-cube-cbrt *-un-lft-identity
20×add-cbrt-cube
19×div-exp prod-exp
18×associate-*r*
16×associate-*l*
10×pow-exp
7×pow1
6×unswap-sqr sqr-pow
5×cbrt-undiv unpow-prod-down cbrt-unprod associate-/l*
4×add-log-exp
3×associate-/r* sqrt-prod div-inv
2×pow-to-exp sqrt-div *-commutative
1×frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num flip--
Counts
4 → 132
Calls
4 calls:
10.0ms
(* (/ D d) (/ M 2.0))
5.0ms
(/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l)
2.0ms
(sqrt (- 1.0 (* (* 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)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* (/ D d) (/ M 2.0))
175.0ms
(/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l)
108.0ms
(sqrt (- 1.0 (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l))))
96.0ms
(* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))

simplify50.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049832193
149832193

prune301.0ms

Filtered
110 candidates to 144 candidates (-30.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1440144
Fresh055
Picked011
Done000
Total1446150

Merged error: 8.0b

Counts
150 → 6

regimes1.0s

Accuracy

0% (1.5b remaining)

Error of 8.3b against oracle of 6.9b and baseline of 8.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02432
12432

end0.0ms

sample1.7s

Algorithm
intervals
Results
688.0ms9296×body80valid
240.0ms3081×body80nan

Profiling

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