Details

Time bar (total: 9.3s)

sample51.0ms

Algorithm
intervals
Results
21.0ms290×body80valid
8.0ms110×body80nan

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

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: 14.7b

Counts
2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

2.4b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.6b
(/ (* M D) (* 2.0 d))
9.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite31.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 → 121
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
418.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
376.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
34.0ms
(/ (* M D) (* 2.0 d))
699.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify75.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06301135
127791057
250021054

prune586.0ms

Filtered
133 candidates to 89 candidates (66.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1258133
Fresh000
Picked101
Done000
Total1268134

Merged error: 8.4b

Counts
134 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

2.4b
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
4.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
4.9b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
5.6b
(/ (* M D) (* 2.0 d))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
179×add-exp-log
88×prod-exp
52×div-exp
28×add-cbrt-cube
25×pow-exp
23×add-sqr-sqrt
14×cbrt-unprod
12×associate-*l*
11×add-cube-cbrt *-un-lft-identity associate-*r*
8×cbrt-undiv unswap-sqr
7×pow1 unpow-prod-down sqrt-prod
6×times-frac
5×pow-to-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r/ div-inv sqr-pow
2×flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 137
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
16.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
3.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
6.0ms
(/ (* M D) (* 2.0 d))

series1.3s

Counts
4 → 12
Calls
4 calls:
407.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
533.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
366.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
31.0ms
(/ (* M D) (* 2.0 d))

simplify95.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
08002280
134272054
250021991

prune452.0ms

Filtered
149 candidates to 82 candidates (55.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1445149
Fresh257
Picked101
Done000
Total14710157

Merged error: 7.8b

Counts
157 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
5.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
5.6b
(/ (* M D) (* 2.0 d))
5.6b
(/ (* M D) (* 2.0 d))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
189×add-exp-log
91×prod-exp
56×div-exp
38×add-cbrt-cube
25×pow-exp
17×cbrt-unprod
16×add-sqr-sqrt
12×cbrt-undiv
9×associate-*l*
8×add-cube-cbrt *-un-lft-identity
7×unpow-prod-down times-frac
6×unswap-sqr
5×pow1 pow-to-exp associate-*r*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×sqrt-prod sqr-pow
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 134
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
16.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))

series969.0ms

Counts
4 → 12
Calls
4 calls:
377.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
537.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
28.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify91.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07562049
132211812
250031751

prune466.0ms

Filtered
146 candidates to 78 candidates (53.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1451146
Fresh189
Picked011
Done000
Total14610156

Merged error: 7.8b

Counts
156 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (* M D) (* 2.0 d))
5.6b
(/ (* M D) (* 2.0 d))
7.2b
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
7.2b
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log add-cbrt-cube
8×cbrt-undiv div-exp prod-exp cbrt-unprod
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
2×flip3-- frac-2neg times-frac pow1/3 clear-num associate-/r* flip-- div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
7.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
3.0ms
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
3.0ms
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

series575.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))
257.0ms
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
254.0ms
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
02761560
113931388
250021370

prune459.0ms

Filtered
88 candidates to 64 candidates (72.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New87188
Fresh088
Picked101
Done011
Total881098

Merged error: 7.8b

Counts
98 → 10

regimes738.0ms

Accuracy

-20.3% (2.3b remaining)

Error of 10.1b against oracle of 7.8b and baseline of 9.7b

bsearch90.0ms

Steps
ItersRangePoint
8
-3.0806074236375943e-243
-2.2401259385727792e-246
-2.3090407106292327e-243

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04645
14645

end0.0ms

sample1.4s

Algorithm
intervals
Results
697.0ms9345×body80valid
256.0ms3247×body80nan