Details

sample172.0ms

Algorithm

intervals

Results

88.0ms	79×	body	1280	valid
36.0ms	54×	body	640	valid
12.0ms	25×	body	320	valid
11.0ms	82×	body	80	valid
5.0ms	16×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune18.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.3b

Counts

2 → 2

localize36.0ms

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

rewrite38.0ms

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:

3.0ms	(/ (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)))
14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))

series987.0ms

Counts

4 → 10

Calls

4 calls:

848.0ms	(/ (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)))
83.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
56.0ms	(- (cos x) (cos y))

simplify132.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (93.0ms)

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

prune758.0ms

Filtered

217 candidates to 104 candidates (47.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	206	11	217
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	207	12	219

Merged error: 0.1b

Counts

219 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
96×	`prod-diff`
93×	`*-un-lft-identity`
89×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-prod` `sub-neg` `fma-neg`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`pow1/3` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 172

Calls

4 calls:

1.0ms	(cbrt (cos x))
14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
1.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

series320.0ms

Counts

4 → 10

Calls

4 calls:

92.0ms	(cbrt (cos x))
82.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
147.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

simplify85.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	783	3562
1	2885	2609
2	5001	2340

prune610.0ms

Filtered

182 candidates to 75 candidates (41.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	183	11	194

Merged error: 0.1b

Counts

194 → 11

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
96×	`prod-diff`
93×	`*-un-lft-identity`
89×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-prod` `sub-neg` `fma-neg`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`pow1/3` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 172

Calls

4 calls:

2.0ms	(cbrt (cos x))
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
1.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

series340.0ms

Counts

4 → 10

Calls

4 calls:

93.0ms	(cbrt (cos x))
87.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
159.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

simplify97.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	783	3571
1	2885	2618
2	5001	2349

prune672.0ms

Filtered

182 candidates to 75 candidates (41.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	182	11	193

Merged error: 0.1b

Counts

193 → 11

localize34.0ms

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))
2.0b	(- (cos x) (cos y))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

184×	`add-sqr-sqrt`
183×	`prod-diff`
172×	`*-un-lft-identity`
164×	`add-cube-cbrt`
110×	`times-frac`
82×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
12×	`associate-r` `div-inv`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg` `fma-neg`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
2×	`diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 291

Calls

4 calls:

22.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
17.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series273.0ms

Counts

4 → 10

Calls

4 calls:

129.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
85.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
58.0ms	(- (cos x) (cos y))

simplify98.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1730	7731
1	5001	6094

prune892.0ms

Filtered

301 candidates to 127 candidates (42.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	297	4	301
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	300	12	312

Merged error: 0.1b

Counts

312 → 12

regimes197.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	36
1	36	36

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.9s	2746×	body	1280	valid
1.2s	1803×	body	640	valid
366.0ms	781×	body	320	valid
326.0ms	2337×	body	80	valid
103.0ms	333×	body	160	valid