Details

sample199.0ms

Algorithm

intervals

Results

111.0ms	100×	body	1280	valid
38.0ms	55×	body	640	valid
13.0ms	20×	body	320	valid
9.0ms	66×	body	80	valid
9.0ms	15×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	30
1	182	30
2	657	30
3	2727	30
4	5001	30

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.8b	(- (cos x) (cos y))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-cube-cbrt` `add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg`
5×	`sqrt-prod`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 94

Calls

4 calls:

53.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
31.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))

series277.0ms

Counts

4 → 10

Calls

4 calls:

139.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
86.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
51.0ms	(- (cos x) (cos y))

simplify68.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	622	1094
1	2643	1002
2	5003	1002

prune555.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
0.3b	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.8b	(- (cos x) (cos y))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`pow1` `add-exp-log` `associate-*r/` `add-cbrt-cube`
14×	`*-un-lft-identity`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `sqrt-prod`
9×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
8×	`add-cube-cbrt` `sub-neg` `add-log-exp`
7×	`associate-r`
5×	`difference-of-squares`
4×	`frac-times`
3×	`distribute-lft-out--`
2×	`diff-log` `associate-l/` `-commutative`
1×	`times-frac` `diff-cos`

Counts

4 → 100

Calls

4 calls:

36.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
140.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
3.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))

series282.0ms

Counts

4 → 10

Calls

4 calls:

91.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
140.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
51.0ms	(- (cos x) (cos y))

simplify71.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	622	1310
1	2603	1087
2	5003	1087

prune577.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
0.3b	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
1.8b	(- (cos x) (cos y))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`associate-l`
29×	`*-un-lft-identity`
23×	`add-exp-log` `add-cbrt-cube`
20×	`pow1` `times-frac`
19×	`add-cube-cbrt`
18×	`associate-*r/`
12×	`sqrt-prod`
11×	`prod-exp` `cbrt-unprod`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `pow-prod-down`
9×	`difference-of-squares`
8×	`flip3--` `flip--`
7×	`sub-neg`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`frac-times`
3×	`associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`cbrt-undiv` `diff-log` `div-exp` `div-inv` `diff-cos`

Counts

4 → 126

Calls

4 calls:

22.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
37.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
142.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
3.0ms	(- (cos x) (cos y))

series383.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
92.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
138.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
57.0ms	(- (cos x) (cos y))

simplify83.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	793	1560
1	3284	1315
2	5003	1315

prune863.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
0.3b	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
0.5b	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
1.8b	(- (cos x) (cos y))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`associate-l`
34×	`sqrt-prod`
29×	`*-un-lft-identity`
23×	`pow1` `add-exp-log` `add-cbrt-cube`
19×	`add-cube-cbrt` `times-frac` `associate-*r/`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`difference-of-squares`
8×	`flip3--` `associate-r` `flip--`
7×	`sub-neg`
6×	`add-log-exp`
5×	`frac-times` `associate-*l/` `distribute-lft-out--`
4×	`sqrt-div`
3×	`*-commutative`
1×	`diff-log` `div-inv` `diff-cos`

Counts

4 → 128

Calls

4 calls:

36.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
142.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
51.0ms	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
3.0ms	(- (cos x) (cos y))

series453.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
142.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
156.0ms	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
58.0ms	(- (cos x) (cos y))

simplify86.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	831	1778
1	3358	1487
2	5001	1487

prune836.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

regimes276.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	46
1	55	46

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.1s	2747×	body	1280	valid
1.3s	1823×	body	640	valid
378.0ms	743×	body	320	valid
343.0ms	2317×	body	80	valid
122.0ms	370×	body	160	valid