Details

sample197.0ms

Algorithm

intervals

Results

108.0ms	100×	body	1280	valid
38.0ms	47×	body	640	valid
10.0ms	21×	body	320	valid
10.0ms	71×	body	80	valid
5.0ms	17×	body	160	valid

simplify54.0ms

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

prune17.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (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)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.6b	(- (cos x) (cos y))

rewrite59.0ms

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)))
38.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series1.0s

Counts

4 → 10

Calls

4 calls:

869.0ms	(/ (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)))
92.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
58.0ms	(- (cos x) (cos y))

simplify130.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (92.0ms)

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

prune823.0ms

Filtered

217 candidates to 104 candidates (47.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

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) (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.6b	(- (cos x) (cos y))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 216

Calls

4 calls:

8.0ms	(* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))
40.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series1.0s

Counts

4 → 10

Calls

4 calls:

894.0ms	(* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ 1 (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))
55.0ms	(- (cos x) (cos y))

simplify166.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1248	5063
1	4890	3859
2	5001	3859

prune877.0ms

Filtered

226 candidates to 103 candidates (45.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.6b	(- (cos x) (cos y))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
105×	`prod-diff`
101×	`*-un-lft-identity`
95×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `add-exp-log` `fma-neg` `associate-r` `associate-l` `add-cbrt-cube` `div-inv`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`flip3--` `flip--` `distribute-lft-out--`
2×	`diff-log` `associate-*r/` `unswap-sqr`
1×	`exp-prod` `exp-to-pow` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `diff-cos` `rem-exp-log`

Counts

4 → 190

Calls

4 calls:

2.0ms	(exp (* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))))
67.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))

series1.2s

Counts

4 → 10

Calls

4 calls:

1.1s	(exp (* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))))
88.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
52.0ms	(- (cos x) (cos y))

simplify123.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1115	4181
1	4269	3105
2	5001	3098

prune844.0ms

Filtered

200 candidates to 90 candidates (45.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.6b	(- (cos x) (cos y))
2.1b	(- (log (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0)) (log (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt` `*-un-lft-identity`
43×	`prod-diff`
36×	`add-cube-cbrt`
18×	`pow1`
14×	`log-pow`
10×	`fma-neg` `sqrt-prod`
9×	`log-prod`
8×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--` `associate--r+`
1×	`rem-log-exp` `diff-cos`

Counts

4 → 126

Calls

4 calls:

1.0ms	(log (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))
10.0ms	(- (log (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0)) (log (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))

series2.3s

Counts

4 → 10

Calls

4 calls:

355.0ms	(log (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.0ms	(- 3.0 (sqrt 5.0))
53.0ms	(- (cos x) (cos y))
1.9s	(- (log (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0)) (log (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))

simplify97.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	738	3517
1	2485	2616
2	5001	2600

prune680.0ms

Filtered

136 candidates to 79 candidates (58.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes154.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	27
1	32	27

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.0s	2812×	body	1280	valid
1.2s	1770×	body	640	valid
352.0ms	740×	body	320	valid
332.0ms	2350×	body	80	valid
102.0ms	328×	body	160	valid