Details

sample178.0ms

Algorithm

intervals

Results

98.0ms	91×	body	1280	valid
32.0ms	49×	body	640	valid
15.0ms	33×	body	320	valid
10.0ms	70×	body	80	valid
4.0ms	13×	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

prune16.0ms

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

localize35.0ms

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 250

Calls

4 calls:

6.0ms	(/ (/ (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)
14.0ms	(* (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:

962.0ms	(/ (/ (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)
101.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
56.0ms	(- (cos x) (cos y))

simplify81.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1406	7067
1	5002	5887

prune1.1s

Filtered

260 candidates to 139 candidates (53.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	247	13	260
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	249	13	262

Merged error: 0.0b

Counts

262 → 13

localize32.0ms

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))) (/ 1 3.0))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.0b	(- (cos x) (cos y))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 237

Calls

4 calls:

13.0ms	(* (/ (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))) (/ 1 3.0))
14.0ms	(* (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:

937.0ms	(* (/ (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))) (/ 1 3.0))
87.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
51.0ms	(- (cos x) (cos y))

simplify74.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1414	5897
1	5001	4588

prune956.0ms

Filtered

247 candidates to 118 candidates (47.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	242	5	247
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	248	12	260

Merged error: 0.0b

Counts

260 → 12

localize33.0ms

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) 3.0) (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))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 250

Calls

4 calls:

6.0ms	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))

series1.2s

Counts

4 → 10

Calls

4 calls:

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

simplify91.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1405	7108
1	5001	5926

prune1.1s

Filtered

260 candidates to 139 candidates (53.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	256	4	260
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	261	11	272

Merged error: 0.0b

Counts

272 → 11

localize36.0ms

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) 3.0) (fma (/ (/ (- (* 3.0 3.0) (* (sqrt 5.0) (sqrt 5.0))) (+ 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	(* (sqrt 5.0) (sqrt 5.0))
2.0b	(- (cos x) (cos y))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
136×	`*-un-lft-identity`
132×	`add-cube-cbrt`
130×	`times-frac`
87×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
22×	`sqrt-prod`
21×	`pow1`
13×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
12×	`associate-r` `associate-l`
11×	`div-inv`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`cbrt-undiv` `sub-neg` `fma-neg` `div-exp` `associate-/r*` `pow-sqr` `difference-of-squares`
2×	`flip3--` `associate-r/` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `clear-num` `rem-square-sqrt` `diff-cos` `associate-/l/`

Counts

4 → 263

Calls

4 calls:

6.0ms	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (/ (/ (- (* 3.0 3.0) (* (sqrt 5.0) (sqrt 5.0))) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms	(* (sqrt 5.0) (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series2.6s

Counts

4 → 10

Calls

4 calls:

2.5s	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (/ (/ (- (* 3.0 3.0) (* (sqrt 5.0) (sqrt 5.0))) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
94.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(* (sqrt 5.0) (sqrt 5.0))
54.0ms	(- (cos x) (cos y))

simplify97.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1428	7620
1	5001	6521

prune1.3s

Filtered

273 candidates to 143 candidates (52.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	267	6	273
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	274	10	284

Merged error: 0b

Counts

284 → 10

regimes199.0ms

Accuracy

0% (0.4b 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	35	30
1	35	30

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.9s	2706×	body	1280	valid
1.2s	1829×	body	640	valid
386.0ms	817×	body	320	valid
341.0ms	2316×	body	80	valid
100.0ms	332×	body	160	valid