Details

Time bar (total: 19.0s)

sample325.0ms

Algorithm
intervals
Results
161.0ms1161×body80nan
67.0ms385×body80valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
0540135

prune19.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 25.8b

Counts
2 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (* (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))))
10.7b
(pow (/ d l) (/ 1.0 2.0))
11.3b
(pow (/ d h) (/ 1.0 2.0))
12.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite49.0ms

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:
16.0ms
(* (* (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 l) (/ 1.0 2.0))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series542.0ms

Counts
4 → 12
Calls
4 calls:
279.0ms
(* (* (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))))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
13.0ms
(pow (/ d h) (/ 1.0 2.0))
237.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify53.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
054413792

prune554.0ms

Filtered
110 candidates to 188 candidates (-70.9%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New16523188
Fresh101
Picked101
Done000
Total16723190

Merged error: 11.0b

Counts
190 → 23

localize41.0ms

Local error

Found 4 expressions with local error:

5.9b
(/ (* M D) (* 2.0 d))
6.2b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
10.7b
(pow (/ d l) (/ 1.0 2.0))
12.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite79.0ms

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:
6.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
15.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series534.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
278.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
237.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify79.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049897893
149897893

prune531.0ms

Filtered
93 candidates to 272 candidates (-192.5%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New2639272
Fresh51722
Picked101
Done000
Total26926295

Merged error: 10.5b

Counts
295 → 26

localize53.0ms

Local error

Found 4 expressions with local error:

2.4b
(pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0))
5.9b
(/ (* M D) (* 2.0 d))
6.2b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
12.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite289.0ms

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
19×pow1 add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
16×associate-*r*
13×pow-unpow
9×cbrt-undiv
6×pow-pow
5×pow-prod-down
4×add-log-exp
3×associate-*r/ associate-*l/ div-inv
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×pow2 frac-times unpow-prod-down flip3-- frac-2neg pow-plus clear-num associate-/r* pow-sqr pow-prod-up flip-- associate-/l* sqr-pow
Counts
4 → 984
Calls
4 calls:
15.0ms
(pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
76.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series554.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
276.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
240.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify283.0ms

Algorithm
egg-herbie
Counts
996 → 996
Iterations

Useful iterations: 0 (92.0ms)

IterNodesCost
0509639522

prune738.0ms

Filtered
82 candidates to 996 candidates (-1114.6%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New9915996
Fresh42125
Picked101
Done000
Total996261022

Merged error: 9.5b

Counts
1022 → 26

localize47.0ms

Local error

Found 4 expressions with local error:

2.0b
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
5.9b
(/ (* M D) (* 2.0 d))
6.2b
(* (* (* (pow (/ (cbrt d) (cbrt h)) (* (/ 1.0 2.0) 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
12.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
3071×add-exp-log
2281×prod-exp
1067×pow-exp
676×div-exp
424×pow-to-exp
55×add-cbrt-cube
27×cbrt-unprod
19×pow1 add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
16×associate-*r*
13×pow-unpow
9×cbrt-undiv
6×pow-pow
5×pow-prod-down
4×add-log-exp
3×associate-*r/ associate-*l/ div-inv
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×pow2 frac-times unpow-prod-down flip3-- frac-2neg pow-plus clear-num associate-/r* pow-sqr pow-prod-up flip-- associate-/l* sqr-pow
Counts
4 → 636
Calls
4 calls:
14.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
9.0ms
(/ (* M D) (* 2.0 d))
63.0ms
(* (* (* (pow (/ (cbrt d) (cbrt h)) (* (/ 1.0 2.0) 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
15.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series556.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
281.0ms
(* (* (* (pow (/ (cbrt d) (cbrt h)) (* (/ 1.0 2.0) 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
240.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify188.0ms

Algorithm
egg-herbie
Counts
648 → 648
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
0504426013

prune352.0ms

Filtered
83 candidates to 648 candidates (-680.7%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New6453648
Fresh22325
Picked101
Done000
Total64826674

Merged error: 9.5b

Counts
674 → 26

regimes1.8s

Accuracy

0.4% (6.9b remaining)

Error of 16.9b against oracle of 10.0b and baseline of 16.9b

bsearch740.0ms

Steps
ItersRangePoint
9
1.5053543950693137e+273
4.710771477570216e+279
4.614840620336055e+279
10
3.096340579999169e-162
2.265454961338096e-152
3.272686059279945e-155
9
-2.4861764467990342e-33
-7.510291037781001e-41
-3.503234114470326e-38

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0185224
1185224

end0.0ms

sample10.4s

Algorithm
intervals
Results
5.3s37982×body80nan
2.3s12725×body80valid

Profiling

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