Details

Time bar (total: 24.0s)

sample301.0ms

Algorithm
intervals
Results
164.0ms1228×body80nan
70.0ms404×body80valid

simplify199.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.9b

Counts
2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

8.1b
(* (* (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))))
8.4b
(pow (/ d h) (/ 1.0 2.0))
12.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
15.8b
(pow (/ d l) (/ 1.0 2.0))

rewrite48.0ms

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:
13.0ms
(* (* (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))))
8.0ms
(pow (/ d h) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
621.0ms
(* (* (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))
697.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012282042
150011847

prune678.0ms

Filtered
188 candidates to 109 candidates (58.0%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New16919188
Fresh000
Picked011
Done000
Total16920189

Merged error: 14.3b

Counts
189 → 20

localize41.0ms

Local error

Found 4 expressions with local error:

3.6b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
8.1b
(* (* (pow (/ d 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))))
8.4b
(pow (/ d h) (/ 1.0 2.0))
12.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
809×add-exp-log
563×prod-exp
282×pow-exp
184×div-exp
95×pow-to-exp
54×times-frac
46×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
35×unpow-prod-down
34×add-cbrt-cube
32×rec-exp 1-exp
26×pow-unpow
16×associate-*r* cbrt-unprod
10×pow1
9×cbrt-prod
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 → 318
Calls
4 calls:
8.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
28.0ms
(* (* (pow (/ d 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))))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
17.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
175.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
996.0ms
(* (* (pow (/ d 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))))
64.0ms
(pow (/ d h) (/ 1.0 2.0))
711.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify90.0ms

Algorithm
egg-herbie
Counts
330 → 330
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
019736098
150015693

prune830.0ms

Filtered
330 candidates to 119 candidates (36.1%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New3219330
Fresh51318
Picked101
Done101
Total32822350

Merged error: 13.0b

Counts
350 → 22

localize57.0ms

Local error

Found 4 expressions with local error:

2.8b
(/ (* M D) (* 2.0 d))
3.6b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
8.1b
(* (* (* (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))))
12.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite379.0ms

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
(/ (* M D) (* 2.0 d))
7.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
89.0ms
(* (* (* (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))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.0s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
377.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
841.0ms
(* (* (* (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))))
713.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify434.0ms

Algorithm
egg-herbie
Counts
1537 → 1537
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
0500150973

prune1.1s

Filtered
1537 candidates to 131 candidates (8.5%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New152981537
Fresh31821
Picked101
Done000
Total1533261559

Merged error: 11.4b

Counts
1559 → 26

localize57.0ms

Local error

Found 4 expressions with local error:

3.6b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.1b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
7.6b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
8.1b
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

rewrite378.0ms

Algorithm
rewrite-expression-head
Rules
8083×add-exp-log
6357×prod-exp
3421×pow-exp
1881×div-exp
966×pow-to-exp
592×rec-exp 1-exp
48×add-cbrt-cube
28×add-sqr-sqrt *-un-lft-identity times-frac
26×add-cube-cbrt
25×cbrt-unprod
22×unpow-prod-down
13×pow-unpow
12×pow1
9×cbrt-prod
8×associate-*r*
6×cbrt-undiv
4×pow-prod-down add-log-exp
3×div-inv
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ associate-*l* *-commutative
1×flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 1504
Calls
4 calls:
7.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
8.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
11.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
91.0ms
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

series2.5s

Counts
4 → 12
Calls
4 calls:
177.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
784.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
702.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
837.0ms
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

simplify460.0ms

Algorithm
egg-herbie
Counts
1516 → 1516
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500150905

prune945.0ms

Filtered
1516 candidates to 119 candidates (7.8%)
Pruning

28 alts after pruning (27 fresh and 1 done)

PrunedKeptTotal
New151331516
Fresh12425
Picked011
Done000
Total1514281542

Merged error: 10.9b

Counts
1542 → 28

regimes1.4s

Accuracy

15.6% (5.1b remaining)

Error of 15.2b against oracle of 10.2b and baseline of 16.2b

bsearch5.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
071117
171117

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.7s37983×body80nan
2.1s12761×body80valid

Profiling

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