Details

Time bar (total: 22.3s)

sample260.0ms

Algorithm
intervals
Results
132.0ms1335×body80nan
57.0ms398×body80valid

simplify196.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize30.0ms

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))))
9.7b
(pow (/ d h) (/ 1.0 2.0))
13.2b
(pow (/ d l) (/ 1.0 2.0))
13.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite79.0ms

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:
36.0ms
(* (* (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))))
4.0ms
(pow (/ d h) (/ 1.0 2.0))
5.0ms
(pow (/ d l) (/ 1.0 2.0))
24.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
656.0ms
(* (* (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))))
68.0ms
(pow (/ d h) (/ 1.0 2.0))
63.0ms
(pow (/ d l) (/ 1.0 2.0))
753.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify47.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012282042
150011847

prune773.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.9b

localize44.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* 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))))
9.7b
(pow (/ d h) (/ 1.0 2.0))
13.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite223.0ms

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))
165.0ms
(* (* (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))))
4.0ms
(pow (/ d h) (/ 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:
28.0ms
(/ (* M D) (* 2.0 d))
649.0ms
(* (* (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))))
66.0ms
(pow (/ d h) (/ 1.0 2.0))
948.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify73.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
016745564
150015223

prune793.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.9b

localize46.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
6.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
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) (/ 1 l))))
9.7b
(pow (/ d h) (/ 1.0 2.0))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
990×add-exp-log
658×prod-exp
246×pow-exp
229×div-exp
84×pow-to-exp
54×add-cbrt-cube
29×cbrt-unprod
27×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
19×associate-*r*
16×rec-exp 1-exp
14×pow1
13×unpow-prod-down pow-unpow
7×cbrt-undiv associate-*l/
5×pow-prod-down
4×add-log-exp
3×associate-*r/ associate-*l* *-commutative div-inv
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-times flip3-- pow-pow un-div-inv flip-- sqr-pow
Counts
4 → 309
Calls
4 calls:
74.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
20.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
166.0ms
(* (* (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) (/ 1 l))))
5.0ms
(pow (/ d h) (/ 1.0 2.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
755.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
775.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
654.0ms
(* (* (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) (/ 1 l))))
69.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify82.0ms

Algorithm
egg-herbie
Counts
321 → 321
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
018536383
150026011

prune882.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 10.9b

localize48.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.8b
(* (* (* (pow (/ d h) (/ (/ 1.0 2.0) 2)) (pow (/ d h) (/ (/ 1.0 2.0) 2))) (* (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) (/ 1 l))))
9.8b
(pow (/ d h) (/ (/ 1.0 2.0) 2))
9.8b
(pow (/ d h) (/ (/ 1.0 2.0) 2))

rewrite419.0ms

Algorithm
rewrite-expression-head
Rules
2972×add-exp-log
2236×prod-exp
1056×pow-exp
640×div-exp
423×pow-to-exp
150×times-frac
90×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
86×pow-unpow
31×add-cbrt-cube
26×unpow-prod-down
18×cbrt-unprod
13×pow1
10×div-inv
6×associate-*r*
4×pow-prod-down add-log-exp
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*r/ associate-*l* associate-*l/ *-commutative sqr-pow
1×cbrt-undiv flip3-- flip--
Counts
4 → 687
Calls
4 calls:
20.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
283.0ms
(* (* (* (pow (/ d h) (/ (/ 1.0 2.0) 2)) (pow (/ d h) (/ (/ 1.0 2.0) 2))) (* (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) (/ 1 l))))
7.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
8.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))

series1.6s

Counts
4 → 12
Calls
4 calls:
783.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
662.0ms
(* (* (* (pow (/ d h) (/ (/ 1.0 2.0) 2)) (pow (/ d h) (/ (/ 1.0 2.0) 2))) (* (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) (/ 1 l))))
71.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))
75.0ms
(pow (/ d h) (/ (/ 1.0 2.0) 2))

simplify189.0ms

Algorithm
egg-herbie
Counts
699 → 699
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0275219551
1500118114

prune1.4s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 10.9b

regimes1.3s

Accuracy

21.2% (7.7b remaining)

Error of 18.7b against oracle of 11.0b and baseline of 20.7b

bsearch711.0ms

Steps
ItersRangePoint
9
1.8873145584877945e-156
4.721159578661076e-149
1.2122010728787284e-151
10
-2.706336275879294e-296
2.422548674844098e-306
6.643637581917233e-307
6
-5.087052211169612e-47
-1.038894416666328e-47
-3.842427574997273e-47

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
091100
191100

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.8s38398×body80nan
1.7s12747×body80valid