Details

sample194.0ms

Algorithm

intervals

Results

104.0ms	99×	body	1280	valid
51.0ms	65×	body	640	valid
9.0ms	66×	body	80	valid
7.0ms	15×	body	320	valid
3.0ms	11×	body	160	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	74	30
1	193	27
2	704	27
3	2994	27
4	5001	27

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
109×	`*-un-lft-identity`
105×	`prod-diff`
103×	`add-cube-cbrt`
64×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`div-inv`
6×	`pow1` `fma-neg` `associate-r` `associate-l`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`flip3--` `associate-/r` `flip--` `associate-/l` `distribute-lft-out--`
2×	`diff-log` `associate-*r/` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `diff-cos`

Counts

4 → 207

Calls

4 calls:

2.0ms	(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
39.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series1.0s

Counts

4 → 10

Calls

4 calls:

880.0ms	(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
86.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
50.0ms	(- (cos x) (cos y))

simplify128.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1160	4965
1	4402	3841
2	5001	3834

prune751.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
2.4b	(- (cos x) (cos y))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`cbrt-prod` `prod-diff`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

0.0ms	(cbrt 16.0)
1.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
4.0ms	(- (cos x) (cos y))

series53.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
53.0ms	(- (cos x) (cos y))

simplify114.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	255	549
1	748	444
2	3867	426
3	5001	416

prune528.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

138×	`add-sqr-sqrt`
118×	`*-un-lft-identity`
106×	`add-cube-cbrt`
105×	`prod-diff`
74×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
28×	`associate-l`
17×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`associate-r`
8×	`pow1` `add-log-exp`
7×	`div-inv`
6×	`fma-neg` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
2×	`diff-log` `associate-r/` `pow-prod-down` `-commutative`
1×	`cbrt-undiv` `div-exp` `associate-*l/` `diff-cos`

Counts

4 → 221

Calls

4 calls:

24.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
35.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series219.0ms

Counts

4 → 10

Calls

4 calls:

83.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
86.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
50.0ms	(- (cos x) (cos y))

simplify117.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1116	3998
1	4264	2949
2	5001	2942

prune835.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

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))))
0.4b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

197×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
183×	`prod-diff`
174×	`add-cube-cbrt`
164×	`distribute-rgt-in` `distribute-lft-in`
127×	`times-frac`
31×	`associate-l`
22×	`sqrt-prod`
14×	`add-exp-log` `add-cbrt-cube`
13×	`div-inv`
11×	`pow1`
9×	`difference-of-squares`
8×	`add-log-exp`
6×	`sub-neg` `fma-neg`
5×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-r/` `associate-r*` `pow-prod-down` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`diff-log` `*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `associate-*l/` `diff-cos`

Counts

4 → 302

Calls

4 calls:

62.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
22.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
7.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series240.0ms

Counts

4 → 10

Calls

4 calls:

91.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
89.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.0ms	(- 3.0 (sqrt 5.0))
59.0ms	(- (cos x) (cos y))

simplify141.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1422	6730
1	4122	5346
2	5001	5309

prune839.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	50
1	58	50
2	58	50

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.2s	2742×	body	1280	valid
1.3s	1901×	body	640	valid
366.0ms	773×	body	320	valid
324.0ms	2241×	body	80	valid
106.0ms	343×	body	160	valid