Details

sample187.0ms

Algorithm

intervals

Results

85.0ms	80×	body	1280	valid
50.0ms	73×	body	640	valid
14.0ms	64×	body	80	valid
12.0ms	24×	body	320	valid
5.0ms	15×	body	160	valid

simplify58.0ms

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)

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

Merged error: 0.3b

Counts

2 → 2

localize38.0ms

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))) 3.0)
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 258

Calls

4 calls:

7.0ms	(/ (/ (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))) 3.0)
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series1.1s

Counts

4 → 10

Calls

4 calls:

998.0ms	(/ (/ (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))) 3.0)
89.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
58.0ms	(- (cos x) (cos y))

simplify87.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1424	7224
1	5001	6044

prune1.2s

Filtered

268 candidates to 145 candidates (54.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	257	11	268
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	258	12	270

Merged error: 0b

Counts

270 → 12

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))
3.3b	(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

rewrite619.0ms

Algorithm

rewrite-expression-head

Rules

2966×	`add-sqr-sqrt`
1756×	`*-un-lft-identity`
1644×	`times-frac`
1544×	`add-cube-cbrt`
1467×	`prod-diff`
996×	`associate-r`
804×	`swap-sqr`
738×	`associate-l`
722×	`distribute-rgt-in` `distribute-lft-in`
402×	`unswap-sqr`
273×	`difference-of-squares`
224×	`associate-*r/`
216×	`*-commutative`
202×	`frac-sub` `sin-mult`
188×	`associate-/l*`
162×	`frac-times`
124×	`associate-/r*`
121×	`div-inv`
103×	`associate-/l/`
67×	`distribute-lft-out`
43×	`clear-num`
41×	`frac-2neg`
34×	`sqrt-prod`
32×	`distribute-lft-out--`
18×	`associate-*l/`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-neg`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `un-div-inv` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`flip3-+` `pow-prod-down` `flip-+` `diff-cos`

Counts

4 → 2143

Calls

4 calls:

145.0ms	(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))
197.0ms	(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

series349.0ms

Counts

4 → 10

Calls

4 calls:

115.0ms	(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
0.0ms	(- 3.0 (sqrt 5.0))
51.0ms	(- (cos x) (cos y))
183.0ms	(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

simplify654.0ms

Algorithm

egg-herbie

Counts

2153 → 2153

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5002	84248

prune8.1s

Filtered

2153 candidates to 805 candidates (37.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	2152	1	2153
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	2154	11	2165

Merged error: 0b

Counts

2165 → 11

localize38.0ms

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))
1.3b	(- (cos x) (cos y))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-sqr-sqrt`
183×	`prod-diff`
178×	`*-un-lft-identity`
168×	`add-cube-cbrt`
111×	`times-frac`
82×	`distribute-rgt-in` `distribute-lft-in`
31×	`associate-l`
19×	`sqrt-prod`
18×	`associate-r`
12×	`div-inv`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--` `difference-of-squares` `unswap-sqr`
8×	`add-log-exp`
6×	`sub-neg` `fma-neg`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`*-commutative`
2×	`diff-log` `associate-*l/`
1×	`diff-cos`

Counts

4 → 312

Calls

4 calls:

26.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))

series284.0ms

Counts

4 → 10

Calls

4 calls:

139.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
92.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
52.0ms	(- (cos x) (cos y))

simplify96.0ms

Algorithm

egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1766	8011
1	5001	6374

prune1.2s

Filtered

322 candidates to 142 candidates (44.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	320	2	322
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	322	11	333

Merged error: 0b

Counts

333 → 11

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (/ (/ (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))) 3.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 236

Calls

4 calls:

10.0ms	(log (exp (/ (/ (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))) 3.0)))
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))

series1.2s

Counts

4 → 10

Calls

4 calls:

1.0s	(log (exp (/ (/ (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))) 3.0)))
92.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
59.0ms	(- (cos x) (cos y))

simplify156.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1344	5597
1	4922	4473
2	5001	4473

prune1.0s

Filtered

246 candidates to 128 candidates (52.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	246	11	257

Merged error: 0b

Counts

257 → 11

regimes324.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	30
1	41	30

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.9s	2682×	body	1280	valid
1.3s	1834×	body	640	valid
389.0ms	776×	body	320	valid
358.0ms	2368×	body	80	valid
110.0ms	340×	body	160	valid