Details

sample81.0ms

Algorithm

intervals

Results

31.0ms	92×	body	1280	valid
14.0ms	69×	body	640	valid
13.0ms	256×	body	80	valid
6.0ms	44×	body	320	valid
2.0ms	18×	body	160	valid

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	15	4
1	28	4
2	56	4
3	102	4
4	153	4
5	334	4
6	924	4
7	1912	4
8	5001	4

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: 0.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (cosh x) (/ (sin y) y))
0.0b	(cosh x)
0.1b	(/ (sin y) y)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 93

Calls

3 calls:

10.0ms	(* (cosh x) (/ (sin y) y))
1.0ms	(cosh x)
5.0ms	(/ (sin y) y)

series195.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(* (cosh x) (/ (sin y) y))
56.0ms	(cosh x)
44.0ms	(/ (sin y) y)

simplify98.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	355	559
1	1467	511
2	5001	473

prune211.0ms

Filtered

102 candidates to 77 candidates (75.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	9	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	9	103

Merged error: 0.0b

Counts

103 → 9

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (/ (sin y) 1/2) (cosh x))
0.1b	(/ (* (/ (sin y) 1/2) (cosh x)) (* 2 y))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

416×	`times-frac`
326×	`add-sqr-sqrt`
254×	`associate-l`
208×	`add-cube-cbrt` `*-un-lft-identity`
114×	`associate-r`
52×	`unswap-sqr`
38×	`*-commutative`
35×	`associate-/l*`
29×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
21×	`cosh-def`
19×	`associate-/l/`
18×	`frac-times` `associate-*l/`
15×	`div-inv`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
5×	`pow1` `frac-2neg` `clear-num`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`associate-*r/`
1×	`pow-prod-down`

Counts

3 → 416

Calls

3 calls:

1.0ms	(cosh x)
9.0ms	(* (/ (sin y) 1/2) (cosh x))
31.0ms	(/ (* (/ (sin y) 1/2) (cosh x)) (* 2 y))

series266.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(cosh x)
94.0ms	(* (/ (sin y) 1/2) (cosh x))
110.0ms	(/ (* (/ (sin y) 1/2) (cosh x)) (* 2 y))

simplify145.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 1 (91.0ms)

Iter	Nodes	Cost
0	2025	4583
1	5001	4431

prune919.0ms

Filtered

425 candidates to 318 candidates (74.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	420	5	425
Fresh	7	1	8
Picked	0	1	1
Done	0	0	0
Total	427	7	434

Merged error: 0b

Counts

434 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (cosh x)) (* (sqrt 2) y))
0.3b	(* (/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2)) (/ (sqrt (cosh x)) (* (sqrt 2) y)))
0.4b	(* (sqrt 2) y)
0.4b	(/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2))

rewrite633.0ms

Algorithm

rewrite-expression-head

Rules

2251×	`add-sqr-sqrt`
1708×	`frac-times`
1301×	`associate-/l*`
1264×	`associate-/r*`
1150×	`*-un-lft-identity`
1149×	`add-cube-cbrt`
1132×	`times-frac`
1124×	`sqrt-prod`
1118×	`associate-l`
590×	`associate-/l/`
553×	`associate-r`
479×	`unswap-sqr`
338×	`cosh-def` `sqrt-div`
308×	`associate-*l/`
143×	`clear-num`
142×	`frac-2neg`
112×	`*-commutative`
74×	`add-exp-log` `add-cbrt-cube`
54×	`associate-*r/`
44×	`div-inv`
26×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `un-div-inv`

Counts

4 → 2322

Calls

4 calls:

13.0ms	(/ (sqrt (cosh x)) (* (sqrt 2) y))
328.0ms	(* (/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2)) (/ (sqrt (cosh x)) (* (sqrt 2) y)))
6.0ms	(* (sqrt 2) y)
23.0ms	(/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2))

series815.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (sqrt (cosh x)) (* (sqrt 2) y))
310.0ms	(* (/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2)) (/ (sqrt (cosh x)) (* (sqrt 2) y)))
53.0ms	(* (sqrt 2) y)
238.0ms	(/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2))

simplify495.0ms

Algorithm

egg-herbie

Counts

2334 → 2334

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5001	42834

prune5.7s

Filtered

2334 candidates to 1378 candidates (59.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	2331	3	2334
Fresh	5	0	5
Picked	0	1	1
Done	0	1	1
Total	2336	5	2341

Merged error: 0b

Counts

2341 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt 2)) y)
0.3b	(* (/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2)) (/ (sqrt (cosh x)) (sqrt (sqrt 2))))
0.4b	(/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2))
1.0b	(/ (sqrt (cosh x)) (sqrt (sqrt 2)))

rewrite454.0ms

Algorithm

rewrite-expression-head

Rules

1650×	`add-sqr-sqrt`
1428×	`sqrt-prod`
1253×	`frac-times`
1063×	`associate-/l*`
971×	`times-frac`
941×	`*-un-lft-identity`
940×	`add-cube-cbrt`
774×	`associate-/r*`
610×	`associate-l`
457×	`associate-/l/`
268×	`cosh-def` `sqrt-div` `unswap-sqr`
259×	`associate-r`
245×	`associate-*l/`
122×	`clear-num`
121×	`frac-2neg`
49×	`add-exp-log` `add-cbrt-cube`
40×	`associate-*r/`
37×	`div-inv`
35×	`*-commutative`
17×	`cbrt-undiv` `div-exp`
15×	`prod-exp` `cbrt-unprod`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `un-div-inv`
1×	`sqrt-undiv`

Counts

4 → 1827

Calls

4 calls:

7.0ms	(* (sqrt (sqrt 2)) y)
222.0ms	(* (/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2)) (/ (sqrt (cosh x)) (sqrt (sqrt 2))))
23.0ms	(/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2))
9.0ms	(/ (sqrt (cosh x)) (sqrt (sqrt 2)))

series962.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (sqrt (sqrt 2)) y)
442.0ms	(* (/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2)) (/ (sqrt (cosh x)) (sqrt (sqrt 2))))
240.0ms	(/ (* (/ (sin y) 1/2) (sqrt (cosh x))) (sqrt 2))
188.0ms	(/ (sqrt (cosh x)) (sqrt (sqrt 2)))

simplify375.0ms

Algorithm

egg-herbie

Counts

1839 → 1839

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5001	32835

prune4.7s

Filtered

1839 candidates to 1085 candidates (59.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1839	0	1839
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1839	5	1844

Merged error: 0b

Counts

1844 → 5

regimes76.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

end0.0ms

sample2.3s

Algorithm

intervals

Results

899.0ms	2972×	body	1280	valid
452.0ms	2428×	body	640	valid
377.0ms	8529×	body	80	valid
171.0ms	1281×	body	320	valid
56.0ms	612×	body	160	valid