Details

Time bar (total: 1.2m)

sample372.0ms

Algorithm
intervals
Results
208.0ms1221×body80nan
100.0ms404×body80valid

simplify187.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize31.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2.0 d))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.1b
(pow (/ d l) (/ 1.0 2.0))
11.5b
(pow (/ d h) (/ 1.0 2.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
26×unpow-prod-down pow-unpow
24×pow-exp
14×cbrt-unprod
13×associate-*r*
9×cbrt-undiv
8×pow1
6×pow-to-exp div-inv
4×add-log-exp
3×associate-*l/
2×pow-pow sqr-pow
1×frac-times frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 159
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
22.0ms
(* (* (/ 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))

series874.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
716.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d l) (/ 1.0 2.0))
66.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify102.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
010711320
147091160
250011160

prune626.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.4b

localize39.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (* (* (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))))
5.2b
(/ (* M D) (* 2.0 d))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.1b
(pow (/ d l) (/ 1.0 2.0))

rewrite206.0ms

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×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 → 292
Calls
4 calls:
150.0ms
(* (* (* (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))))
7.0ms
(/ (* M D) (* 2.0 d))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
842.0ms
(* (* (* (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))))
27.0ms
(/ (* M D) (* 2.0 d))
905.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
66.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify81.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
018025799
150015527

prune719.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.4b

localize57.0ms

Local error

Found 4 expressions with local error:

2.1b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
4.3b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
5.2b
(/ (* M D) (* 2.0 d))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite569.0ms

Algorithm
rewrite-expression-head
Rules
8121×add-exp-log
6369×prod-exp
3426×pow-exp
1900×div-exp
967×pow-to-exp
592×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 → 1525
Calls
4 calls:
6.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
287.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
4.0ms
(/ (* M D) (* 2.0 d))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
179.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
840.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
27.0ms
(/ (* M D) (* 2.0 d))
724.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify435.0ms

Algorithm
egg-herbie
Counts
1537 → 1537
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0500150973

prune1.2s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 5.8b

localize71.0ms

Local error

Found 4 expressions with local error:

1.8b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.3b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 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))))
5.2b
(/ (* M D) (* 2.0 d))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite3.6s

Algorithm
rewrite-expression-head
Rules
70141×add-exp-log
56907×prod-exp
30907×pow-exp
18551×div-exp
8147×pow-to-exp
6906×1-exp
4242×rec-exp
66×add-cbrt-cube
37×times-frac
36×cbrt-unprod
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
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 → 9852
Calls
4 calls:
6.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
1.1s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 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))))
4.0ms
(/ (* M D) (* 2.0 d))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
181.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
1.2s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 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))))
31.0ms
(/ (* M D) (* 2.0 d))
709.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify3.8s

Algorithm
egg-herbie
Counts
9864 → 9864
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
08374478981

prune42.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 5.7b

regimes979.0ms

Accuracy

12.3% (4.6b remaining)

Error of 14.3b against oracle of 9.7b and baseline of 15.0b

bsearch161.0ms

Steps
ItersRangePoint
5
-6.610555522884768e+74
-1.8889592155002539e+74
-4.3643534339022127e+74

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06283
16283

end0.0ms

sample10.6s

Algorithm
intervals
Results
6.1s37972×body80nan
2.9s12773×body80valid