Details

sample149.0ms

Algorithm

intervals

Results

93.0ms	120×	body	1280	valid
26.0ms	56×	body	640	valid
8.0ms	27×	body	320	valid
4.0ms	44×	body	80	valid
2.0ms	9×	body	160	valid

simplify50.0ms

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	1817	10
6	5001	10

prune3.0ms

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: 4.5b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
30×	`associate-l`
28×	`add-cube-cbrt`
26×	`times-frac` `sqrt-prod`
22×	`unpow-prod-down`
14×	`associate-*l/`
11×	`add-exp-log`
10×	`distribute-lft-out`
9×	`pow1` `add-cbrt-cube` `hypot-def`
8×	`associate-/r*` `sqr-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `clear-num` `*-commutative` `div-inv`

Counts

4 → 131

Calls

4 calls:

18.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
109.0ms	(pow (sin ky) 2.0)
106.0ms	(pow (sin kx) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	432	1124
1	1824	1047
2	5001	1046

prune392.0ms

Filtered

143 candidates to 102 candidates (71.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	135	8	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	8	144

Merged error: 0.0b

Counts

144 → 8

localize23.0ms

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

0.2b

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

1.0ms

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

4.0ms

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

8.0ms

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

series978.0ms

Counts

3 → 9

Calls

3 calls:

249.0ms

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

372.0ms

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

357.0ms

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

simplify43.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	307	1166
1	1336	1040
2	5001	1039

prune264.0ms

Filtered

90 candidates to 72 candidates (80.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	91	7	98

Merged error: 0b

Counts

98 → 7

localize15.0ms

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))))

0.3b

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

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))))

9.0ms

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

series1.1s

Counts

3 → 9

Calls

3 calls:

337.0ms

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

348.0ms

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

383.0ms

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

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	305	1162
1	1248	1037
2	5001	1036

prune264.0ms

Filtered

92 candidates to 72 candidates (78.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	92	7	99

Merged error: 0b

Counts

99 → 7

localize15.0ms

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

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

0.2b

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r/` `associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`hypot-udef`

Counts

3 → 119

Calls

3 calls:

1.0ms

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

4.0ms

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

8.0ms

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

series1.1s

Counts

3 → 9

Calls

3 calls:

443.0ms

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

304.0ms

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

341.0ms

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

simplify59.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	446	2170
1	1800	2030
2	5002	2028

prune381.0ms

Filtered

128 candidates to 105 candidates (82.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	128	7	135

Merged error: 0b

Counts

135 → 7

regimes322.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	11
1	15	11

end0.0ms

sample4.6s

Algorithm

intervals

Results

3.0s	3723×	body	1280	valid
979.0ms	1983×	body	640	valid
232.0ms	714×	body	320	valid
128.0ms	1279×	body	80	valid
61.0ms	301×	body	160	valid