Details

Time bar (total: 8.3s)

sample43.0ms

Algorithm
intervals
Results
16.0ms291×body80valid
5.0ms94×body80nan

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize14.0ms

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))

rewrite34.0ms

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:
10.0ms
(* 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))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
417.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
367.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
693.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06301135
127791057
250021054

prune434.0ms

Filtered
133 candidates to 89 candidates (66.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize21.0ms

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))

rewrite36.0ms

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))))))
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)))))
15.0ms
(* (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:
400.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
364.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
532.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
31.0ms
(/ (* M D) (* 2.0 d))

simplify104.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
08002279
134272053
250021990

prune517.0ms

Filtered
149 candidates to 81 candidates (54.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 → 89
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
3.0ms
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (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))

series1.0s

Counts
4 → 12
Calls
4 calls:
393.0ms
(* w0 (sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
356.0ms
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
224.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify55.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03301677
116521531
250011528

prune435.0ms

Filtered
101 candidates to 66 candidates (65.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

localize25.0ms

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))

rewrite28.0ms

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 expm1-log1p-u add-cube-cbrt frac-2neg *-un-lft-identity times-frac clear-num associate-/r* log1p-expm1-u div-inv associate-/l* add-log-exp
Counts
4 → 92
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))

series116.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(/ (* M D) (* 2.0 d))

simplify32.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0168528
1955388
25001388

prune491.0ms

Filtered
104 candidates to 64 candidates (61.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.2b

regimes767.0ms

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
04366
14366

end0.0ms

sample1.2s

Algorithm
intervals
Results
540.0ms9305×body80valid
190.0ms3133×body80nan