Details

Time bar (total: 10.8s)

sample165.0ms

Algorithm
intervals
Results
36.0ms78×body5120valid
24.0ms445×body80nan
19.0ms55×body2560valid
13.0ms22×body10240exit
11.0ms208×body80valid
9.0ms31×body1280valid
3.0ms13×body640valid
1.0ms9×body320valid
0.0ms3×body160valid

simplify102.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06026
130425
2346225
3500325

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.6b

localize22.0ms

Local error

Found 4 expressions with local error:

15.5b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.5b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.5b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
28.5b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite710.0ms

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:
40.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
41.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
39.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
580.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
88.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
88.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
229.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify124.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
05942246
138771589
250011584

prune382.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 30.8b

localize4.0ms

Local error

Found 1 expressions with local error:

5.7b
(* (/ c0 (* 2.0 w)) 0)

rewrite26.0ms

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:
25.0ms
(* (/ c0 (* 2.0 w)) 0)

series1.0ms

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

simplify285.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 2 (281.0ms)

IterNodesCost
017840
1186124
2500114

prune74.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 29.7b

localize2.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune21.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 29.7b

localize27.0ms

Local error

Found 4 expressions with local error:

15.5b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
28.5b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
28.5b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
28.5b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
73×add-exp-log add-cbrt-cube
39×prod-exp cbrt-unprod
15×cbrt-undiv fma-def div-exp
13×*-un-lft-identity
10×add-log-exp
7×add-sqr-sqrt add-cube-cbrt
6×sqrt-div frac-add
4×pow1 expm1-log1p-u times-frac log1p-expm1-u div-inv
3×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ distribute-lft-out
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 108
Calls
4 calls:
41.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
573.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
575.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
570.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series758.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
226.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
219.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
226.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify153.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (129.0ms)

IterNodesCost
05942538
138772127
250012112

prune496.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 29.7b

regimes425.0ms

Accuracy

0% (2.2b remaining)

Error of 33.2b against oracle of 31.0b and baseline of 33.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050
180
280

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.0s2326×body5120valid
735.0ms12967×body80nan
586.0ms1702×body2560valid
397.0ms6868×body80valid
291.0ms612×body10240exit
244.0ms856×body1280valid
99.0ms447×body640valid
37.0ms233×body320valid
15.0ms122×body160valid