Details

Time bar (total: 27.5s)

sample369.0ms

Algorithm
intervals
Results
216.0ms1281×body80nan
87.0ms417×body80valid

simplify199.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize30.0ms

Local error

Found 4 expressions with local error:

7.0b
(* (* (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))))
10.3b
(pow (/ d h) (/ 1.0 2.0))
11.5b
(pow (/ d l) (/ 1.0 2.0))
13.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 176
Calls
4 calls:
33.0ms
(* (* (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))
4.0ms
(pow (/ d l) (/ 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:
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))))
65.0ms
(pow (/ d h) (/ 1.0 2.0))
67.0ms
(pow (/ d l) (/ 1.0 2.0))
710.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify46.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012282042
150011847

prune719.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.7b

localize47.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* M D) (* 2.0 d))
7.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
11.5b
(pow (/ d l) (/ 1.0 2.0))
13.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite253.0ms

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×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in 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 → 260
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
197.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
4.0ms
(pow (/ d l) (/ 1.0 2.0))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.4s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
633.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))
721.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify75.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
016425552
150025211

prune731.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.5b

localize60.0ms

Local error

Found 4 expressions with local error:

2.3b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
3.4b
(/ (* M D) (* 2.0 d))
7.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite561.0ms

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
32×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
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1229
Calls
4 calls:
6.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
321.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
172.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
26.0ms
(/ (* M D) (* 2.0 d))
973.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
720.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify362.0ms

Algorithm
egg-herbie
Counts
1241 → 1241
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0500145012

prune1.3s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.7b

localize60.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* M D) (* 2.0 d))
4.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
7.0b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
9.6b
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

rewrite677.0ms

Algorithm
rewrite-expression-head
Rules
7251×add-exp-log
5438×prod-exp
2642×pow-exp
1681×div-exp
794×pow-to-exp
232×rec-exp 1-exp
87×add-cbrt-cube
58×cbrt-unprod
26×associate-*r*
22×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity times-frac
17×cbrt-undiv
14×pow1
11×associate-*l*
9×cbrt-prod
6×unpow-prod-down pow-prod-down
4×add-log-exp
3×associate-*r/ associate-*l/ *-commutative div-inv unswap-sqr
2×distribute-rgt-in sub-neg distribute-lft-in sqr-pow
1×frac-times flip3-- frac-2neg clear-num associate-/r* flip-- associate-/l*
Counts
4 → 1269
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
318.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
127.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

series2.4s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
439.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
977.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
950.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

simplify417.0ms

Algorithm
egg-herbie
Counts
1281 → 1281
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500151815

prune1.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.9b

regimes1.4s

Accuracy

-5.2% (5.7b remaining)

Error of 14.4b against oracle of 8.7b and baseline of 14.1b

bsearch1.0s

Steps
ItersRangePoint
9
2.4244612197935837e-258
8.133353268825726e-250
3.370654506630173e-256
9
-7.125592805154627e-211
-7.029844283738286e-218
-7.133079929021998e-218

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07767
17767

end0.0ms

sample10.7s

Algorithm
intervals
Results
6.3s38288×body80nan
2.7s12882×body80valid