Details

sample192.0ms

Algorithm

intervals

Results

97.0ms	83×	body	1280	valid
46.0ms	67×	body	640	valid
12.0ms	81×	body	80	valid
8.0ms	17×	body	320	valid
3.0ms	8×	body	160	valid

simplify53.0ms

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 (0.0%)

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: 0.2b

Counts

2 → 2

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) (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))
1.8b	(- (cos x) (cos y))

rewrite40.0ms

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)))
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:

920.0ms	(/ (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)))
90.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
60.0ms	(- (cos x) (cos y))

simplify123.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1150	4965
1	4323	3841
2	5001	3834

prune798.0ms

Filtered

217 candidates to 104 candidates (52.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	209	8	217
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	210	9	219

Merged error: 0.1b

Counts

219 → 9

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.8b	(- (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) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 214

Calls

4 calls:

16.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
6.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))
4.0ms	(log (/ (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))))

series2.4s

Counts

4 → 10

Calls

4 calls:

100.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
213.0ms	(- (cos x) (cos y))
2.1s	(log (/ (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))))

simplify137.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1201	5281
1	4371	4115
2	5001	4106

prune882.0ms

Filtered

224 candidates to 109 candidates (51.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	223	10	233

Merged error: 0.0b

Counts

233 → 10

localize44.0ms

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))
1.8b	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

478×	`add-sqr-sqrt`
264×	`prod-diff`
203×	`*-un-lft-identity`
193×	`add-cube-cbrt`
184×	`cbrt-prod`
148×	`unswap-sqr`
141×	`associate-l`
59×	`fma-neg`
55×	`times-frac`
54×	`associate-r`
44×	`swap-sqr`
41×	`distribute-rgt-in` `distribute-lft-in`
23×	`difference-of-squares`
19×	`*-commutative`
14×	`sqrt-prod`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `div-inv`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`diff-log` `associate-*r/`
1×	`pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 422

Calls

4 calls:

2.0ms	(cbrt (cos x))
16.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(- 3.0 (sqrt 5.0))
40.0ms	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))

series259.0ms

Counts

4 → 10

Calls

4 calls:

98.0ms	(cbrt (cos x))
95.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
65.0ms	(- (* (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x))) (cos y))

simplify163.0ms

Algorithm

egg-herbie

Counts

432 → 432

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	1372	8963
1	4513	5773
2	5001	5635

prune1.3s

Filtered

432 candidates to 150 candidates (65.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	432	0	432
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	432	10	442

Merged error: 0.0b

Counts

442 → 10

localize37.0ms

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))
1.8b	(- (cos x) (cos y))

rewrite77.0ms

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:

27.0ms	(* (* (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))
5.0ms	(- (cos x) (cos y))

series299.0ms

Counts

4 → 10

Calls

4 calls:

143.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
101.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
55.0ms	(- (cos x) (cos y))

simplify101.0ms

Algorithm

egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1754	8011
1	5002	6374

prune1.0s

Filtered

322 candidates to 142 candidates (55.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	318	4	322
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	322	10	332

Merged error: 0.0b

Counts

332 → 10

regimes196.0ms

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	62	51
1	64	51
2	64	51

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.9s	2717×	body	1280	valid
1.2s	1849×	body	640	valid
357.0ms	755×	body	320	valid
329.0ms	2329×	body	80	valid
109.0ms	350×	body	160	valid