Details

Time bar (total: 8.3s)

sample43.0ms

Algorithm
intervals
Results
17.0ms291×body80valid
6.0ms94×body80nan

simplify52.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize18.0ms

Local error

Found 4 expressions with local error:

3.1b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.2b
(/ (* M D) (* 2.0 d))
11.9b
(* (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:
396.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
370.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
35.0ms
(/ (* M D) (* 2.0 d))
692.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify68.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06091075
12742997
25003994

prune379.0ms

Filtered
125 candidates to 81 candidates (64.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize25.0ms

Local error

Found 4 expressions with local error:

3.1b
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
4.0b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
5.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
6.2b
(/ (* M D) (* 2.0 d))

rewrite34.0ms

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×sqrt-div 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 → 129
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))))))
2.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
14.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
6.0ms
(/ (* M D) (* 2.0 d))

series1.3s

Counts
4 → 12
Calls
4 calls:
394.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
391.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
527.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
27.0ms
(/ (* M D) (* 2.0 d))

simplify86.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07612167
133661977
250021950

prune650.0ms

Filtered
141 candidates to 73 candidates (51.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

localize24.0ms

Local error

Found 4 expressions with local error:

3.1b
(* w0 (sqrt (- 1.0 (* (* (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l))))))
4.0b
(sqrt (- 1.0 (* (* (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
6.2b
(/ (* M D) (* 2.0 d))
6.2b
(/ (* M D) (* 2.0 d))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp
7×pow1 sqrt-prod
6×associate-*r*
4×sqrt-div add-log-exp
3×associate-*l*
2×flip3-- frac-2neg times-frac associate-*r/ clear-num associate-/r* flip-- div-inv associate-/l* unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 81
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (* (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l))))))
2.0ms
(sqrt (- 1.0 (* (* (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))

series888.0ms

Counts
4 → 12
Calls
4 calls:
451.0ms
(* w0 (sqrt (- 1.0 (* (* (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l))))))
378.0ms
(sqrt (- 1.0 (* (* (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (fabs (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
31.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))

simplify61.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04501784
120161628
250011625

prune414.0ms

Filtered
93 candidates to 60 candidates (64.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

localize26.0ms

Local error

Found 4 expressions with local error:

6.2b
(/ (* M D) (* 2.0 d))
6.2b
(/ (* M D) (* 2.0 d))
6.2b
(/ (* M D) (* 2.0 d))
6.2b
(/ (* M D) (* 2.0 d))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
16×cbrt-undiv div-exp prod-exp cbrt-unprod
4×pow1 add-sqr-sqrt add-cube-cbrt frac-2neg *-un-lft-identity times-frac clear-num associate-/r* div-inv associate-/l* add-log-exp
Counts
4 → 84
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))

series121.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
40.0ms
(/ (* M D) (* 2.0 d))
26.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))

simplify30.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0166496
1953356
25001356

prune456.0ms

Filtered
96 candidates to 56 candidates (58.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.2b

regimes744.0ms

Accuracy

20.2% (1.2b remaining)

Error of 8.3b against oracle of 7.1b and baseline of 8.6b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04470
14470

end0.0ms

sample1.2s

Algorithm
intervals
Results
565.0ms9305×body80valid
197.0ms3133×body80nan