Details

Time bar (total: 31.4s)

sample473.0ms

Algorithm
intervals
Results
288.0ms1271×body80nan
120.0ms390×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: 24.9b

localize29.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* (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))))
11.3b
(pow (/ d l) (/ 1.0 2.0))
11.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.7b
(pow (/ d h) (/ 1.0 2.0))

rewrite79.0ms

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:
35.0ms
(* (* (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))))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
24.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
614.0ms
(* (* (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 l) (/ 1.0 2.0))
713.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
65.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012872382
150012125

prune722.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.0b

localize40.0ms

Local error

Found 4 expressions with local error:

5.4b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt 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))))
11.3b
(pow (/ d l) (/ 1.0 2.0))
11.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
818×add-exp-log
567×prod-exp
280×pow-exp
187×div-exp
94×pow-to-exp
46×add-cbrt-cube
32×rec-exp 1-exp
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 → 306
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
159.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt 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 l) (/ 1.0 2.0))
27.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
840.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt 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))))
65.0ms
(pow (/ d l) (/ 1.0 2.0))
720.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify88.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
018766250
150025934

prune816.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.3b

localize55.0ms

Local error

Found 4 expressions with local error:

2.5b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
5.4b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (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))))
11.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite706.0ms

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:
6.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
323.0ms
(* (* (* (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))))
27.0ms
(* (* (/ 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))
28.0ms
(/ (* M D) (* 2.0 d))
861.0ms
(* (* (* (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))))
721.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify379.0ms

Algorithm
egg-herbie
Counts
1255 → 1255
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0500145189

prune1.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 6.6b

localize55.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
5.4b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (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)))
7.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

rewrite589.0ms

Algorithm
rewrite-expression-head
Rules
6964×add-exp-log
5245×prod-exp
2612×pow-exp
1626×div-exp
788×pow-to-exp
232×rec-exp 1-exp
57×add-cbrt-cube
42×prod-diff
36×add-sqr-sqrt *-un-lft-identity
34×add-cube-cbrt
27×cbrt-unprod
23×distribute-rgt-in distribute-lft-in
22×times-frac
11×pow1
10×cbrt-undiv
8×associate-*r* div-inv
4×expm1-log1p-u pow-prod-down associate-*l/ associate-/r* log1p-expm1-u add-log-exp
2×sub-neg frac-2neg associate-*r/ associate-*l* clear-num *-commutative associate-/l*
1×flip3-- flip-- associate-/l/ distribute-lft-out-- difference-of-squares
Counts
4 → 1242
Calls
4 calls:
23.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
4.0ms
(/ (* M D) (* 2.0 d))
337.0ms
(* (* (* (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)))
23.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

series2.4s

Counts
4 → 12
Calls
4 calls:
737.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
33.0ms
(/ (* M D) (* 2.0 d))
854.0ms
(* (* (* (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)))
745.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

simplify402.0ms

Algorithm
egg-herbie
Counts
1254 → 1254
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0500148586

prune1.3s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 6.4b

regimes1.2s

Accuracy

6.8% (6.1b remaining)

Error of 15.5b against oracle of 9.4b and baseline of 15.9b

bsearch798.0ms

Steps
ItersRangePoint
9
5.019943360880153e-133
3.947628775452049e-127
4.5669509591709906e-130
6
-4.6694182989135773e+98
-3.733707963051749e+97
-3.83023767151277e+97

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07284
17284

end0.0ms

sample14.7s

Algorithm
intervals
Results
8.9s39199×body80nan
4.0s13003×body80valid