Details

Time bar (total: 22.0s)

sample255.0ms

Algorithm
intervals
Results
133.0ms1335×body80nan
53.0ms398×body80valid

simplify28.0ms

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: 25.8b

localize28.0ms

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))

rewrite81.0ms

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:
39.0ms
(* (* (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))
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:
645.0ms
(* (* (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))))
61.0ms
(pow (/ d h) (/ 1.0 2.0))
68.0ms
(pow (/ d l) (/ 1.0 2.0))
748.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify48.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012872382
150022125

prune802.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.9b

localize43.0ms

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))

rewrite232.0ms

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:
5.0ms
(/ (* M D) (* 2.0 d))
170.0ms
(* (* (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))))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
28.0ms
(* (* (/ 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))
827.0ms
(* (* (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))))
62.0ms
(pow (/ d h) (/ 1.0 2.0))
763.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify81.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
017806072
150025729

prune873.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.9b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
728×add-exp-log
483×prod-exp
216×pow-exp
168×div-exp
78×pow-to-exp
50×add-sqr-sqrt *-un-lft-identity
48×add-cube-cbrt
42×prod-diff
39×times-frac
36×add-cbrt-cube
23×distribute-rgt-in distribute-lft-in
16×cbrt-unprod
13×unpow-prod-down pow-unpow
9×pow1 div-inv
8×associate-*r*
6×cbrt-undiv
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×associate-/r*
2×sub-neg associate-*r/ associate-*l* pow-prod-down *-commutative
1×flip3-- pow-pow frac-2neg clear-num flip-- associate-/l/ associate-/l* distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 299
Calls
4 calls:
22.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
21.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
185.0ms
(* (* (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)))
5.0ms
(pow (/ d h) (/ 1.0 2.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
797.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
792.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
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)))
74.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify109.0ms

Algorithm
egg-herbie
Counts
311 → 311
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
019169165
150018092

prune918.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.9b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
140×add-exp-log
74×prod-exp
36×times-frac
34×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×div-exp
26×unpow-prod-down pow-unpow
24×pow-exp
22×add-cbrt-cube
10×pow1 cbrt-unprod
6×pow-to-exp associate-*r*
4×expm1-log1p-u associate-*l/ log1p-expm1-u div-inv add-log-exp
2×cbrt-undiv pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
Counts
4 → 148
Calls
4 calls:
26.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
21.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
5.0ms
(pow (/ d h) (/ 1.0 2.0))
5.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
789.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
796.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
73.0ms
(pow (/ d h) (/ 1.0 2.0))
66.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify65.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
06181222
123651096
250011096

prune1.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.7b

regimes1.5s

Accuracy

1.7% (9.2b remaining)

Error of 19.8b against oracle of 10.6b and baseline of 19.9b

bsearch882.0ms

Steps
ItersRangePoint
9
2.9763822268774595e+236
1.6614371998585104e+244
3.846423325806426e+236
10
1.357824392174745e-98
4.026405462094873e-81
3.4885049966384686e-81
8
-2.619469317643146e-07
-1.1636360205254454e-10
-3.2788073086762934e-10
6
-2.5966141019343266e+227
-1.9150714658838128e+226
-1.1622442629311353e+227

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093114
193114

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.9s38398×body80nan
1.7s12747×body80valid