Details

Time bar (total: 8.6s)

sample193.0ms

Algorithm
intervals
Results
45.0ms78×body5120valid
35.0ms63×body2560valid
31.0ms399×body80nan
17.0ms205×body80valid
11.0ms16×body5120exit
9.0ms24×body1280valid
5.0ms16×body640valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify102.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06026
130425
2346225
3500325

prune12.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.2b

Counts
2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

17.8b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.8b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.8b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
30.9b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
211×add-exp-log add-cbrt-cube
117×prod-exp cbrt-unprod
45×cbrt-undiv div-exp
7×*-un-lft-identity
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt fma-def
4×pow1 expm1-log1p-u times-frac log1p-expm1-u div-inv
3×frac-2neg clear-num associate-/r* associate-/l*
2×sqrt-div frac-add
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 156
Calls
4 calls:
12.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
12.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
12.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
32.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series507.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
91.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
92.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
233.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify125.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
05942246
138771589
250011584

prune338.0ms

Filtered
168 candidates to 70 candidates (41.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1626168
Fresh101
Picked101
Done000
Total1646170

Merged error: 29.4b

Counts
170 → 6

localize5.0ms

Local error

Found 1 expressions with local error:

3.7b
(* (/ c0 (* 2.0 w)) 0)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log add-cbrt-cube
7×associate-*l*
6×add-sqr-sqrt
4×add-cube-cbrt *-un-lft-identity prod-exp cbrt-unprod
3×pow1 times-frac associate-*r*
2×cbrt-undiv div-exp
1×expm1-log1p-u mul0 pow-prod-down associate-*l/ *-commutative log1p-expm1-u div-inv add-log-exp unswap-sqr
Counts
1 → 30
Calls
1 calls:
6.0ms
(* (/ c0 (* 2.0 w)) 0)

series1.0ms

Counts
1 → 3
Calls
1 calls:
1.0ms
(* (/ c0 (* 2.0 w)) 0)

simplify287.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 2 (283.0ms)

IterNodesCost
017840
1186124
2500114

prune67.0ms

Filtered
33 candidates to 21 candidates (63.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New32133
Fresh055
Picked101
Done000
Total33639

Merged error: 28.3b

Counts
39 → 6

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune23.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New000
Fresh055
Picked011
Done000
Total066

Merged error: 28.3b

Counts
6 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

12.3b
(* (* w h) (* D D))
17.8b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.8b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
52.2b
(fma (* c0 (* d d)) (/ 1 (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
154×add-exp-log add-cbrt-cube
86×prod-exp cbrt-unprod
30×cbrt-undiv div-exp
16×pow1
8×pow-prod-down
4×add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity log1p-expm1-u add-log-exp
2×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
1×associate-*r* associate-*l* *-commutative fma-udef
Counts
4 → 124
Calls
4 calls:
7.0ms
(* (* w h) (* D D))
13.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
13.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
1.0ms
(fma (* c0 (* d d)) (/ 1 (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* w h) (* D D))
90.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
92.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
232.0ms
(fma (* c0 (* d d)) (/ 1 (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify93.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
04751510
130881011
250021011

prune256.0ms

Filtered
136 candidates to 55 candidates (40.4%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1360136
Fresh044
Picked011
Done011
Total1366142

Merged error: 28.3b

Counts
142 → 6

regimes355.0ms

Accuracy

0% (2.3b remaining)

Error of 33.5b against oracle of 31.2b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.3s2229×body5120valid
1.0s13127×body80nan
834.0ms1758×body2560valid
555.0ms6905×body80valid
360.0ms576×body5120exit
347.0ms897×body1280valid
135.0ms443×body640valid
54.0ms239×body320valid
17.0ms109×body160valid