Details

sample62.0ms

Algorithm

intervals

Results

18.0ms	40×	body	1280	valid
17.0ms	46×	body	640	valid
10.0ms	142×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	4
1	15	4
2	15	4

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (sin y)) (* z (cos y)))
0.1b	(* x (sin y))
0.1b	(* z (cos y))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

3 → 54

Calls

3 calls:

3.0ms	(+ (* x (sin y)) (* z (cos y)))
3.0ms	(* x (sin y))
3.0ms	(* z (cos y))

series152.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(+ (* x (sin y)) (* z (cos y)))
42.0ms	(* x (sin y))
37.0ms	(* z (cos y))

simplify74.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	197	270
1	757	245
2	2524	245
3	5001	244

prune158.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (cos y))
0.2b	(* (sqrt (* x (sin y))) (sqrt (* x (sin y))))
6.8b	(sqrt (* x (sin y)))
6.8b	(sqrt (* x (sin y)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1`
32×	`sqrt-pow1`
23×	`pow-prod-down`
14×	`add-sqr-sqrt`
12×	`pow1/2`
10×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-up`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-r` `associate-l`
6×	`sqrt-prod` `pow-sqr`
4×	`expm1-log1p-u` `swap-sqr` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 97

Calls

4 calls:

3.0ms	(* z (cos y))
14.0ms	(* (sqrt (* x (sin y))) (sqrt (* x (sin y))))
2.0ms	(sqrt (* x (sin y)))
2.0ms	(sqrt (* x (sin y)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* z (cos y))
42.0ms	(* (sqrt (* x (sin y))) (sqrt (* x (sin y))))
50.0ms	(sqrt (* x (sin y)))
55.0ms	(sqrt (* x (sin y)))

simplify45.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	278	495
1	1233	416
2	5001	398

prune241.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (sin y))
0.1b	(* z (cos y))
0.1b	(* z (cos y))
0.3b	(* (sqrt (* z (cos y))) (sqrt (* z (cos y))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

59×	`pow1`
28×	`sqrt-pow1`
23×	`pow-prod-down`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r` `associate-l`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1/2` `pow-prod-up`
6×	`pow-sqr`
4×	`expm1-log1p-u` `swap-sqr` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 111

Calls

4 calls:

3.0ms	(* x (sin y))
3.0ms	(* z (cos y))
3.0ms	(* z (cos y))
15.0ms	(* (sqrt (* z (cos y))) (sqrt (* z (cos y))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* x (sin y))
35.0ms	(* z (cos y))
38.0ms	(* z (cos y))
37.0ms	(* (sqrt (* z (cos y))) (sqrt (* z (cos y))))

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	246	413
1	1151	365
2	5001	356

prune265.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow z 2) (pow (cos y) 2))
0.1b	(* x (sin y))
0.3b	(pow (cos y) 2)
27.3b	(pow (* (pow z 2) (pow (cos y) 2)) (/ 1 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
32×	`add-exp-log`
23×	`pow-exp`
19×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
18×	`unpow-prod-down`
17×	`unswap-sqr`
16×	`pow-unpow`
14×	`pow-to-exp`
12×	`sqr-pow`
11×	`associate-r` `associate-l` `unpow2`
9×	`times-frac`
8×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-prod-down`
2×	`*-commutative` `cbrt-unprod`
1×	`div-inv`

Counts

4 → 130

Calls

4 calls:

12.0ms	(* (pow z 2) (pow (cos y) 2))
3.0ms	(* x (sin y))
1.0ms	(pow (cos y) 2)
5.0ms	(pow (* (pow z 2) (pow (cos y) 2)) (/ 1 2))

series236.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (pow z 2) (pow (cos y) 2))
39.0ms	(* x (sin y))
17.0ms	(pow (cos y) 2)
127.0ms	(pow (* (pow z 2) (pow (cos y) 2)) (/ 1 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	451	748
1	2008	630
2	5001	603

prune353.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

57% (12.9b remaining)

Error of 13.0b against oracle of 0.1b and baseline of 30.1b

bsearch244.0ms

Steps

Iters	Range		Point
8	-4.990614210601742e-290	-3.957916901742115e-293	-4.008635328086667e-293
9	-1.3699581405989777e-211	-3.590391089736032e-219	-8.811798188204722e-213
10	-1.0472707424533275e-157	-7.369787736381232e-169	-4.926365677979376e-161
7	-3.986342568864759e+59	-2.3992734897128167e+58	-2.419249552228977e+58

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	45
1	51	45

end0.0ms

sample1.8s

Algorithm

intervals

Results

701.0ms	1559×	body	1280	valid
350.0ms	1186×	body	640	valid
315.0ms	4288×	body	80	valid
132.0ms	646×	body	320	valid
46.0ms	321×	body	160	valid