Details

Time bar (total: 20.9s)

sample246.0ms

Algorithm
intervals
Results
122.0ms1250×body80nan
56.0ms410×body80valid

simplify29.0ms

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

localize30.0ms

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))))
11.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.6b
(pow (/ d l) (/ 1.0 2.0))
11.8b
(pow (/ d h) (/ 1.0 2.0))

rewrite75.0ms

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:
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))))
25.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d l) (/ 1.0 2.0))
4.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
617.0ms
(* (* (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))))
706.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
62.0ms
(pow (/ d l) (/ 1.0 2.0))
64.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012872382
150012125

prune730.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.1b

localize42.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (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))))
11.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.6b
(pow (/ d l) (/ 1.0 2.0))

rewrite245.0ms

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:
4.0ms
(/ (* M D) (* 2.0 d))
192.0ms
(* (* (* (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))))
25.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ (* M D) (* 2.0 d))
617.0ms
(* (* (* (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))))
716.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
66.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
017106060
150015717

prune844.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.4b

localize59.0ms

Local error

Found 4 expressions with local error:

1.9b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
3.1b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
11.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite529.0ms

Algorithm
rewrite-expression-head
Rules
5947×add-exp-log
4317×prod-exp
1997×pow-exp
1387×div-exp
643×pow-to-exp
55×add-cbrt-cube
27×cbrt-unprod
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×times-frac
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv
6×prod-diff
5×distribute-rgt-in unpow-prod-down 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 → 997
Calls
4 calls:
8.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
334.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
115.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
33.0ms
(/ (* M D) (* 2.0 d))
622.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
741.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify491.0ms

Algorithm
egg-herbie
Counts
1009 → 1009
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0416938921
1500137861

prune952.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.8b

localize59.0ms

Local error

Found 4 expressions with local error:

1.9b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
3.1b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
6.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite551.0ms

Algorithm
rewrite-expression-head
Rules
6247×add-exp-log
4488×prod-exp
2027×pow-exp
1477×div-exp
649×pow-to-exp
79×add-cbrt-cube
54×cbrt-unprod
21×cbrt-undiv
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×pow-unpow
12×pow1 times-frac
8×associate-*r*
6×prod-diff
5×distribute-rgt-in unpow-prod-down 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 → 1043
Calls
4 calls:
9.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
334.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
37.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series1.3s

Counts
4 → 12
Calls
4 calls:
117.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
28.0ms
(/ (* M D) (* 2.0 d))
628.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
562.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify391.0ms

Algorithm
egg-herbie
Counts
1055 → 1055
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0445649216
1500248020

prune928.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 8.3b

regimes1.5s

Accuracy

0% (4.2b remaining)

Error of 14.9b against oracle of 10.7b and baseline of 14.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04768
14768

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.8s39394×body80nan
1.7s12703×body80valid