Details

sample156.0ms

Algorithm

intervals

Results

91.0ms	120×	body	1280	valid
34.0ms	59×	body	640	valid
10.0ms	32×	body	320	valid
4.0ms	37×	body	80	valid
2.0ms	8×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	39	10
2	67	10
3	153	10
4	439	10
5	1830	10
6	5001	10

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 4.6b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
22×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`hypot-def`
8×	`add-exp-log` `associate-/r*` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 117

Calls

4 calls:

11.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
109.0ms	(pow (sin ky) 2.0)
103.0ms	(pow (sin kx) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	341	1065
1	1159	981
2	5001	976

prune433.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	119	10	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	10	130

Merged error: 0.0b

Counts

130 → 10

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.1b

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

0.2b

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

1.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

7.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

4.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series985.0ms

Counts

3 → 9

Calls

3 calls:

253.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

349.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

383.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	295	1114
1	1091	988
2	5001	986

prune329.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 0b

Counts

92 → 9

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.2b

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

0.2b

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

1.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

4.0ms

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

8.0ms

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series956.0ms

Counts

3 → 9

Calls

3 calls:

253.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

331.0ms

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

371.0ms

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	291	1109
1	1164	984
2	5001	983

prune346.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	82	9	91

Merged error: 0b

Counts

91 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.1b	(* (/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))) (sin th))
0.2b	(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))
0.2b	(/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-l`
36×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 191

Calls

4 calls:

1.0ms	(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
13.0ms	(* (/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))) (sin th))
4.0ms	(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))
6.0ms	(/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

series1.2s

Counts

4 → 12

Calls

4 calls:

248.0ms	(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
356.0ms	(* (/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))) (sin th))
283.0ms	(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))
286.0ms	(/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

simplify88.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	693	3162
1	3134	2842
2	5001	2742

prune779.0ms

Filtered

203 candidates to 137 candidates (67.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	203	9	212

Merged error: 0b

Counts

212 → 9

regimes273.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	11

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.1s	3743×	body	1280	valid
951.0ms	1949×	body	640	valid
244.0ms	741×	body	320	valid
130.0ms	1282×	body	80	valid
85.0ms	285×	body	160	valid