Details

Time bar (total: 9.5s)

sample47.0ms

Algorithm
intervals
Results
20.0ms291×body80valid
6.0ms86×body80nan

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

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: 15.6b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

2.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.9b
(/ (* M D) (* 2.0 d))
11.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
409.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
348.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
30.0ms
(/ (* M D) (* 2.0 d))
734.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify94.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06091075
12742997
25001994

prune361.0ms

Filtered
125 candidates to 81 candidates (64.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1169125
Fresh000
Picked011
Done000
Total11610126

Merged error: 7.8b

Counts
126 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

3.9b
(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
4.2b
(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))
4.8b
(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))
4.9b
(/ (* M D) (* 2.0 d))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
210×add-exp-log
121×prod-exp
43×div-exp
33×add-cbrt-cube
31×associate-*r*
30×pow-exp
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity times-frac
19×cbrt-unprod
9×cbrt-prod
7×pow1 cbrt-undiv
6×pow-to-exp unpow-prod-down
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div associate-*l* *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* flip-- associate-/l*
Counts
4 → 142
Calls
4 calls:
11.0ms
(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
2.0ms
(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))
20.0ms
(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))
6.0ms
(/ (* M D) (* 2.0 d))

series1.4s

Counts
4 → 12
Calls
4 calls:
442.0ms
(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
282.0ms
(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))
608.0ms
(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))
28.0ms
(/ (* M D) (* 2.0 d))

simplify120.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
08861784
145191605
250011578

prune350.0ms

Filtered
154 candidates to 78 candidates (50.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1522154
Fresh358
Picked101
Done011
Total1568164

Merged error: 7.8b

Counts
164 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

4.2b
(sqrt (- 1.0 (* (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) l))))
4.8b
(* (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) l))
4.9b
(/ (* M D) (* 2.0 d))
4.9b
(/ (* M D) (* 2.0 d))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
38×add-cbrt-cube
24×add-sqr-sqrt
22×times-frac associate-*r*
18×add-cube-cbrt *-un-lft-identity
14×prod-exp cbrt-unprod
10×pow1 cbrt-undiv cbrt-prod div-exp
4×add-log-exp
3×pow-prod-down sqrt-prod div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ associate-*l* *-commutative flip--
Counts
4 → 102
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) l))))
11.0ms
(* (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) l))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))

series999.0ms

Counts
4 → 12
Calls
4 calls:
614.0ms
(sqrt (- 1.0 (* (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) l))))
324.0ms
(* (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))))) (/ (cbrt h) l))
33.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify90.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07041948
134061703
250021696

prune409.0ms

Filtered
114 candidates to 75 candidates (65.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1122114
Fresh156
Picked101
Done011
Total1148122

Merged error: 7.5b

Counts
122 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

4.2b
(sqrt (- 1.0 (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l)))))
4.9b
(/ (* M D) (* 2.0 d))
4.9b
(/ (* M D) (* 2.0 d))
7.1b
(* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
33×add-exp-log
32×add-cbrt-cube
28×add-sqr-sqrt
22×times-frac associate-*r*
19×add-cube-cbrt *-un-lft-identity
10×cbrt-prod prod-exp cbrt-unprod
9×cbrt-undiv div-exp
7×pow1
4×add-log-exp
3×associate-*l* sqrt-prod div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ pow-prod-down *-commutative flip--
Counts
4 → 99
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l)))))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
9.0ms
(* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))

series924.0ms

Counts
4 → 12
Calls
4 calls:
629.0ms
(sqrt (- 1.0 (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l)))))
27.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(/ (* M D) (* 2.0 d))
236.0ms
(* (fabs (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))

simplify79.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06411492
130821337
250011330

prune410.0ms

Filtered
111 candidates to 77 candidates (69.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1101111
Fresh066
Picked011
Done011
Total1109119

Merged error: 7.5b

Counts
119 → 9

regimes952.0ms

Accuracy

14.7% (1.8b remaining)

Error of 9.4b against oracle of 7.7b and baseline of 9.7b

bsearch130.0ms

Steps
ItersRangePoint
6
-3.1316829782388316e-266
-4.779045178500523e-267
-1.4420583403478956e-266
10
-inf.0
-1.5809500588112086e+294
-1.7771696287420844e+308

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03720
13720

end0.0ms

sample1.4s

Algorithm
intervals
Results
685.0ms9319×body80valid
235.0ms3131×body80nan

Profiling

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