Details

sample6.0s

Algorithm

intervals

Results

5.7s	1708×	body	10240	exit
86.0ms	82×	body	1280	valid
46.0ms	63×	body	640	valid
18.0ms	86×	body	80	valid
15.0ms	21×	body	320	valid
1.0ms	4×	body	160	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(pow (/ (* 2.0 l) Om) 2.0)
1.8b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
11.8b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite56.0ms

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:

1.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (/ (* 2.0 l) Om) 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)))))

series865.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (sin ky) 2.0)
83.0ms	(pow (/ (* 2.0 l) Om) 2.0)
373.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
302.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	515	957
1	2069	914
2	5001	914

prune467.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize28.0ms

Local error

Found 4 expressions with local error:

2.1b	(exp (fma (log (/ (* 2.0 l) Om)) 2.0 (log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.4b	(log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
11.8b	(sqrt (+ 1.0 (exp (fma (log (/ (* 2.0 l) Om)) 2.0 (log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
14.9b	(log (/ (* 2.0 l) Om))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `log-prod`
11×	`add-exp-log`
9×	`add-cube-cbrt`
7×	`pow1`
5×	`add-log-exp`
4×	`expm1-log1p-u` `rem-log-exp` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-div` `exp-prod` `times-frac` `distribute-lft-out`
2×	`unpow-prod-down` `flip3-+` `sqrt-div` `div-exp` `log-pow` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-sum` `prod-exp` `fma-udef` `hypot-def` `div-inv` `rem-exp-log`

Counts

4 → 72

Calls

4 calls:

1.0ms	(exp (fma (log (/ (* 2.0 l) Om)) 2.0 (log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms	(sqrt (+ 1.0 (exp (fma (log (/ (* 2.0 l) Om)) 2.0 (log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
2.0ms	(log (/ (* 2.0 l) Om))

series681.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(exp (fma (log (/ (* 2.0 l) Om)) 2.0 (log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
69.0ms	(log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
339.0ms	(sqrt (+ 1.0 (exp (fma (log (/ (* 2.0 l) Om)) 2.0 (log (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
52.0ms	(log (/ (* 2.0 l) Om))

simplify92.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	371	916
1	1017	861
2	3727	848
3	5001	847

prune459.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(exp (fma (log (/ (* 2.0 l) Om)) 2.0 (fma 1/3 (- (pow kx 2) (pow ky 2)) (* 2 (log ky)))))
1.7b	(sqrt (+ 1.0 (exp (fma (log (/ (* 2.0 l) Om)) 2.0 (fma 1/3 (- (pow kx 2) (pow ky 2)) (* 2 (log ky)))))))
3.3b	(- (pow kx 2) (pow ky 2))
14.9b	(log (/ (* 2.0 l) Om))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

64×	`prod-diff`
61×	`add-sqr-sqrt` `unpow-prod-down`
48×	`*-un-lft-identity`
42×	`add-cube-cbrt`
25×	`unpow2` `sqr-pow`
16×	`difference-of-squares`
10×	`add-exp-log`
8×	`fma-neg`
7×	`log-prod` `add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod` `times-frac` `rem-log-exp`
2×	`sqrt-div` `div-exp` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `log-div` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `exp-sum` `prod-exp` `log-pow` `flip--` `flip-+` `fma-udef` `hypot-def` `div-inv` `rem-exp-log` `distribute-lft-out`

Counts

4 → 158

Calls

4 calls:

1.0ms	(exp (fma (log (/ (* 2.0 l) Om)) 2.0 (fma 1/3 (- (pow kx 2) (pow ky 2)) (* 2 (log ky)))))
6.0ms	(sqrt (+ 1.0 (exp (fma (log (/ (* 2.0 l) Om)) 2.0 (fma 1/3 (- (pow kx 2) (pow ky 2)) (* 2 (log ky)))))))
14.0ms	(- (pow kx 2) (pow ky 2))
2.0ms	(log (/ (* 2.0 l) Om))

series530.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(exp (fma (log (/ (* 2.0 l) Om)) 2.0 (fma 1/3 (- (pow kx 2) (pow ky 2)) (* 2 (log ky)))))
272.0ms	(sqrt (+ 1.0 (exp (fma (log (/ (* 2.0 l) Om)) 2.0 (fma 1/3 (- (pow kx 2) (pow ky 2)) (* 2 (log ky)))))))
30.0ms	(- (pow kx 2) (pow ky 2))
53.0ms	(log (/ (* 2.0 l) Om))

simplify60.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	663	1892
1	1830	1365
2	5001	1344

prune555.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes278.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample3.3m

Algorithm

intervals

Results

3.2m	56042×	body	10240	exit
2.9s	2662×	body	1280	valid
1.4s	1842×	body	640	valid
453.0ms	793×	body	320	valid
402.0ms	2358×	body	80	valid
134.0ms	345×	body	160	valid