Details

sample42.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	16
1	131	16
2	342	16
3	1202	16
4	5002	16

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ (* 2.0 l) Om) 2.0)
0.3b	(pow (sin kx) 2.0)
2.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`add-sqr-sqrt` `unpow-prod-down`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`associate-l`
7×	`pow1` `pow-exp` `prod-exp`
6×	`pow-unpow` `times-frac` `add-cbrt-cube`
5×	`associate-r`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `sqrt-prod` `unswap-sqr`
2×	`pow-pow` `flip3-+` `sqrt-div` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

4.0ms	(pow (/ (* 2.0 l) Om) 2.0)
1.0ms	(pow (sin kx) 2.0)
41.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series932.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow (/ (* 2.0 l) Om) 2.0)
139.0ms	(pow (sin kx) 2.0)
386.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
322.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	514	957
1	2069	914
2	5001	914

prune495.0ms

Filtered

112 candidates to 79 candidates (70.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.5b

localize30.0ms

Local error

Found 4 expressions with local error:

6.9b	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 69

Calls

4 calls:

2.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
309.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
318.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
317.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	135	1217
1	432	1159
2	2357	1157
3	5001	1157

prune473.0ms

Filtered

81 candidates to 65 candidates (80.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.5b

localize41.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

316.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
436.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
306.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
310.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	111	1092
1	402	1048
2	2306	1048
3	5001	1048

prune528.0ms

Filtered

80 candidates to 64 candidates (80.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ (* 2.0 l) Om) 2.0)
0.3b	(pow (sin kx) 2.0)
0.7b	(log1p (expm1 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`unpow-prod-down`
18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`associate-l`
7×	`pow-exp` `prod-exp`
6×	`pow1` `pow-unpow` `times-frac` `add-cbrt-cube`
5×	`associate-r`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `unswap-sqr`
2×	`pow-pow` `associate-*r/` `div-inv` `distribute-lft-out`
1×	`distribute-rgt-in` `log1p-udef` `distribute-lft-in` `flip3-+` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 94

Calls

4 calls:

4.0ms	(pow (/ (* 2.0 l) Om) 2.0)
2.0ms	(pow (sin kx) 2.0)
0.0ms	(log1p (expm1 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
45.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

86.0ms	(pow (/ (* 2.0 l) Om) 2.0)
105.0ms	(pow (sin kx) 2.0)
475.0ms	(log1p (expm1 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
384.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	466	858
1	1882	789
2	5002	789

prune498.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.5b

regimes484.0ms

Accuracy

0% (0.3b remaining)

Error of 1.6b against oracle of 1.2b and baseline of 1.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	72
1	36	72

end0.0ms

sample1.0s

Algorithm

intervals

Results

796.0ms

8000×

body

valid