Details

sample81.0ms

Algorithm

intervals

Results

28.0ms	90×	body	1280	valid
19.0ms	81×	body	640	valid
14.0ms	287×	body	80	valid
5.0ms	35×	body	320	valid
2.0ms	22×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	4
1	28	4
2	56	4
3	98	4
4	143	4
5	310	4
6	877	4
7	1824	4
8	5001	4

prune2.0ms

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

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 61

Calls

2 calls:

7.0ms	(* (cosh x) (/ (sin y) y))
4.0ms	(/ (sin y) y)

series103.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(* (cosh x) (/ (sin y) y))
26.0ms	(/ (sin y) y)

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	263	392
1	1063	349
2	5001	337

prune155.0ms

Filtered

67 candidates to 50 candidates (74.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	58	9	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	9	68

Merged error: 0.0b

Counts

68 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`cosh-def` `sqrt-div`
9×	`times-frac` `sqrt-prod`
6×	`associate-l`
5×	`frac-times` `associate-*r/` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-l/` `associate-/r` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`
1×	`frac-2neg` `associate-r` `clear-num` `*-commutative` `div-inv`

Counts

4 → 85

Calls

4 calls:

10.0ms	(* (sqrt (cosh x)) (* (sqrt (cosh x)) (/ (sin y) y)))
1.0ms	(sqrt (cosh x))
1.0ms	(sqrt (cosh x))
4.0ms	(/ (sin y) y)

series238.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sqrt (cosh x)) (* (sqrt (cosh x)) (/ (sin y) y)))
67.0ms	(sqrt (cosh x))
68.0ms	(sqrt (cosh x))
27.0ms	(/ (sin y) y)

simplify41.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	327	592
1	1177	496
2	5001	482

prune213.0ms

Filtered

97 candidates to 70 candidates (72.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	97	9	106

Merged error: 0.0b

Counts

106 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (cosh x)) (sin y))
0.3b	(/ (* (sqrt (+ (exp x) (exp (- x)))) (* (sqrt (cosh x)) (sin y))) (* (sqrt 2) y))
0.4b	(* (sqrt 2) y)
0.4b	(* (sqrt (+ (exp x) (exp (- x)))) (* (sqrt (cosh x)) (sin y)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt`
19×	`associate-l`
15×	`sqrt-div`
14×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
13×	`pow1`
12×	`add-cube-cbrt` `sqrt-prod`
11×	`associate-*l/`
7×	`cosh-def` `associate-r`
6×	`cbrt-undiv` `div-exp`
5×	`pow-prod-down` `associate-/l/`
4×	`frac-times` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`associate-*r/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `distribute-lft-out` `associate-/l`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* (sqrt (cosh x)) (sin y))
15.0ms	(/ (* (sqrt (+ (exp x) (exp (- x)))) (* (sqrt (cosh x)) (sin y))) (* (sqrt 2) y))
5.0ms	(* (sqrt 2) y)
12.0ms	(* (sqrt (+ (exp x) (exp (- x)))) (* (sqrt (cosh x)) (sin y)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (sqrt (cosh x)) (sin y))
201.0ms	(/ (* (sqrt (+ (exp x) (exp (- x)))) (* (sqrt (cosh x)) (sin y))) (* (sqrt 2) y))
39.0ms	(* (sqrt 2) y)
143.0ms	(* (sqrt (+ (exp x) (exp (- x)))) (* (sqrt (cosh x)) (sin y)))

simplify80.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	532	1168
1	2886	1014
2	5002	1014

prune323.0ms

Filtered

114 candidates to 73 candidates (64.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	116	7	123

Merged error: 0b

Counts

123 → 7

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (* (sin y) (/ 1 y)))
0.3b	(* (sin y) (/ 1 y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
18×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
14×	`associate-r`
13×	`prod-exp`
12×	`*-un-lft-identity`
11×	`add-cube-cbrt` `times-frac`
9×	`pow1`
7×	`cbrt-unprod`
6×	`associate-l`
5×	`associate-*r/`
4×	`div-exp` `pow-prod-down`
3×	`cosh-def` `un-div-inv` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `*-commutative` `add-log-exp`
1×	`associate-*l/` `div-inv`

Counts

2 → 63

Calls

2 calls:

8.0ms	(* (cosh x) (* (sin y) (/ 1 y)))
8.0ms	(* (sin y) (/ 1 y))

series102.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(* (cosh x) (* (sin y) (/ 1 y)))
26.0ms	(* (sin y) (/ 1 y))

simplify45.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	333	408
1	1434	326
2	5002	297

prune107.0ms

Filtered

69 candidates to 43 candidates (62.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Merged error: 0b

Counts

76 → 7

regimes118.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	8
1	10	8

end0.0ms

sample2.4s

Algorithm

intervals

Results

939.0ms	2981×	body	1280	valid
492.0ms	2507×	body	640	valid
391.0ms	8336×	body	80	valid
185.0ms	1269×	body	320	valid
60.0ms	639×	body	160	valid