Details

Time bar (total: 24.2s)

sample241.0ms

Algorithm
intervals
Results
122.0ms1185×body80nan
54.0ms392×body80valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
272017
3500117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize33.0ms

Local error

Found 4 expressions with local error:

6.8b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.5b
(pow (/ d h) (/ 1.0 2.0))
13.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
14.5b
(pow (/ d l) (/ 1.0 2.0))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
40×pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×cbrt-undiv distribute-rgt-in distribute-lft-in div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 190
Calls
4 calls:
40.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
25.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
643.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
66.0ms
(pow (/ d h) (/ 1.0 2.0))
724.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
61.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012872382
150012125

prune799.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.3b

localize46.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (* M D) (* 2.0 d))
6.8b
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.5b
(pow (/ d h) (/ 1.0 2.0))
13.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 274
Calls
4 calls:
5.0ms
(/ (* M D) (* 2.0 d))
171.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
8.0ms
(pow (/ d h) (/ 1.0 2.0))
25.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
639.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
65.0ms
(pow (/ d h) (/ 1.0 2.0))
732.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify85.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
017806072
150025729

prune865.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.3b

localize58.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
6.5b
(/ (* M D) (* 2.0 d))
6.8b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite613.0ms

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
34×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv cbrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1243
Calls
4 calls:
7.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
342.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
28.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
177.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
27.0ms
(/ (* M D) (* 2.0 d))
873.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
742.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify375.0ms

Algorithm
egg-herbie
Counts
1255 → 1255
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0500145189

prune1.5s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.5b

localize64.0ms

Local error

Found 4 expressions with local error:

5.9b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
6.5b
(/ (* M D) (* 2.0 d))
6.6b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.8b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

rewrite622.0ms

Algorithm
rewrite-expression-head
Rules
6936×add-exp-log
5237×prod-exp
2607×pow-exp
1610×div-exp
787×pow-to-exp
232×rec-exp 1-exp
60×add-cbrt-cube
30×prod-diff
29×cbrt-unprod
24×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
17×distribute-rgt-in distribute-lft-in
11×pow1
10×cbrt-undiv
8×times-frac associate-*r* div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
2×sub-neg frac-2neg associate-*r/ associate-*l* clear-num associate-/r* *-commutative associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 1220
Calls
4 calls:
16.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
4.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
356.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

series2.6s

Counts
4 → 12
Calls
4 calls:
726.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
29.0ms
(/ (* M D) (* 2.0 d))
752.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.1s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

simplify388.0ms

Algorithm
egg-herbie
Counts
1232 → 1232
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500146250

prune835.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 8.2b

regimes1.7s

Accuracy

-19.8% (7.8b remaining)

Error of 17.4b against oracle of 9.5b and baseline of 16.1b

bsearch560.0ms

Steps
ItersRangePoint
9
-2.7296408488674618e-146
-1.8716528914051566e-154
-6.325905308635602e-151
9
-8.427232839923008e+166
-3.344454949308258e+161
-3.839735720487782e+164

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
088111
188111

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.0s38836×body80nan
1.8s12933×body80valid