Details

sample98.0ms

Algorithm: halfpoints

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	7
1	47	7
2	84	7
3	121	7
4	206	7
5	410	7
6	1017	7
7	2074	7
8	5001	7

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.9b	(- (exp x) (exp (- x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
27×	`add-cube-cbrt`
25×	`associate-*l/`
14×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`pow1` `add-log-exp`
6×	`associate-r` `associate-/r*`
5×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `clear-num` `*-commutative` `flip--` `flip-+` `div-inv`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log`

Counts

4 → 122

Calls

4 calls:

13.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
8.0ms	(+ (exp x) (exp (- x)))
13.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms	(- (exp x) (exp (- x)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
27.0ms	(+ (exp x) (exp (- x)))
84.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
37.0ms	(- (exp x) (exp (- x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	560	1117
1	2557	1003
2	5001	1001

prune361.0ms

Filtered

134 candidates to 97 candidates (72.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	4	135

Merged error: 0.0b

Counts

135 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (cos y) (/ 2.0 (+ (exp x) (exp (- x)))))
0.0b	(/ 2.0 (+ (exp x) (exp (- x))))
0.0b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.9b	(- (exp x) (exp (- x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

130×	`times-frac`
122×	`*-un-lft-identity`
93×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
29×	`associate-/r*`
20×	`associate-/r/`
19×	`associate-l`
17×	`distribute-lft-out`
16×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*`
13×	`associate-*l/`
7×	`div-inv`
6×	`pow1` `add-log-exp`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `distribute-lft-out--` `difference-of-squares`
4×	`frac-2neg` `clear-num`
3×	`associate-r`
2×	`flip3--` `prod-exp` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 196

Calls

4 calls:

13.0ms	(/ (cos y) (/ 2.0 (+ (exp x) (exp (- x)))))
7.0ms	(/ 2.0 (+ (exp x) (exp (- x))))
14.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
5.0ms	(- (exp x) (exp (- x)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (cos y) (/ 2.0 (+ (exp x) (exp (- x)))))
39.0ms	(/ 2.0 (+ (exp x) (exp (- x))))
82.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
41.0ms	(- (exp x) (exp (- x)))

simplify94.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	751	2245
1	3518	2100
2	5002	2097

prune711.0ms

Filtered

208 candidates to 153 candidates (73.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	209	3	212

Merged error: 0b

Counts

212 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)
0.0b	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
0.0b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.9b	(- (exp x) (exp (- x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
40×	`times-frac`
36×	`unpow-prod-down`
34×	`add-cube-cbrt`
23×	`cbrt-prod`
19×	`associate-l`
13×	`associate-*l/`
12×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`distribute-lft-out` `add-log-exp`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`pow-unpow` `associate-/r/`
3×	`associate-r` `associate-/r*` `div-inv`
2×	`cbrt-undiv` `flip3--` `flip3-+` `unpow3` `div-exp` `pow-exp` `prod-exp` `flip--` `rem-cbrt-cube` `cbrt-unprod` `flip-+` `associate-/l/` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 133

Calls

4 calls:

10.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)
11.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
13.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
5.0ms	(- (exp x) (exp (- x)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)
38.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
82.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
41.0ms	(- (exp x) (exp (- x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	643	1338
1	2646	1243
2	5001	1229

prune470.0ms

Filtered

145 candidates to 99 candidates (68.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	145	3	148

Merged error: 0b

Counts

148 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
0.0b	(* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (/ (cos y) (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))))
0.0b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.9b	(- (exp x) (exp (- x)))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

1523×	`sqrt-prod`
1372×	`*-un-lft-identity`
1259×	`associate-/r*`
1237×	`times-frac`
1103×	`add-sqr-sqrt`
972×	`frac-times`
959×	`add-cube-cbrt`
460×	`associate-/l*`
201×	`distribute-lft-out`
167×	`associate-r`
156×	`sqrt-div`
112×	`associate-/l/`
78×	`flip3-+` `clear-num` `flip-+`
77×	`frac-2neg`
65×	`associate-l`
62×	`associate-/r/`
54×	`associate-*r/`
32×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
31×	`associate-*l/`
26×	`div-inv`
11×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
2×	`flip3--` `pow-prod-down` `un-div-inv` `*-commutative` `flip--`
1×	`sub-neg` `sqrt-undiv` `diff-log`

Counts

4 → 1441

Calls

4 calls:

9.0ms	(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
169.0ms	(* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (/ (cos y) (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))))
13.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
5.0ms	(- (exp x) (exp (- x)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))
149.0ms	(* (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0)) (/ (cos y) (/ (sqrt 2.0) (sqrt (+ (exp x) (exp (- x)))))))
81.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
37.0ms	(- (exp x) (exp (- x)))

simplify374.0ms

Algorithm

egg-herbie

Counts

1453 → 1453

Iterations

Useful iterations: 1 (99.0ms)

Iter	Nodes	Cost
0	4664	37031
1	5001	35662

prune2.6s

Filtered

1453 candidates to 521 candidates (35.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1452	1	1453
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	1453	3	1456

Merged error: 0b

Counts

1456 → 3

regimes48.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	18
1	27	18
2	27	18

end0.0ms

sample1.9s

Algorithm: halfpoints