Details

sample313.0ms

Algorithm

intervals

Results

154.0ms	81×	body	1280	valid
72.0ms	53×	body	640	valid
24.0ms	28×	body	320	valid
21.0ms	80×	body	80	valid
9.0ms	14×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

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)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite37.0ms

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

series1.0s

Counts

4 → 10

Calls

4 calls:

891.0ms	(/ (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))
59.0ms	(- (cos x) (cos y))

simplify137.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (97.0ms)

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

prune765.0ms

Filtered

217 candidates to 104 candidates (47.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	210	7	217
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	211	8	219

Merged error: 0.1b

Counts

219 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)) (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite37.0ms

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

series1.6s

Counts

4 → 10

Calls

4 calls:

1.4s	(/ (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)) (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0))
91.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
58.0ms	(- (cos x) (cos y))

simplify133.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1156	4969
1	4380	3845
2	5001	3838

prune780.0ms

Filtered

217 candidates to 104 candidates (47.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	217	8	225

Merged error: 0.1b

Counts

225 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 207

Calls

4 calls:

12.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series1.5s

Counts

4 → 10

Calls

4 calls:

1.3s	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
95.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
63.0ms	(- (cos x) (cos y))

simplify72.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1403	4994
1	5001	3928

prune840.0ms

Filtered

217 candidates to 110 candidates (50.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	210	7	217
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	214	11	225

Merged error: 0b

Counts

225 → 11

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))))) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)) (- 3.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
105×	`prod-diff`
101×	`add-cube-cbrt`
65×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`add-log-exp`
7×	`div-inv`
6×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `fma-neg` `associate-r` `associate-l`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`flip3--` `flip--` `distribute-lft-out--`
2×	`cbrt-undiv` `neg-mul-1` `diff-log` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `distribute-neg-frac` `unswap-sqr`
1×	`neg-sub0` `frac-2neg` `flip3-+` `div-sub` `distribute-frac-neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip-+` `diff-cos`

Counts

4 → 219

Calls

4 calls:

7.0ms	(/ (- (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))))) (* (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))

series1.5s

Counts

4 → 10

Calls

4 calls:

1.4s	(/ (- (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))))) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)) (- 3.0)))
94.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
62.0ms	(- (cos x) (cos y))

simplify70.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1301	5415
1	5002	4213

prune826.0ms

Filtered

229 candidates to 115 candidates (50.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	231	9	240

Merged error: 0b

Counts

240 → 9

regimes312.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	35	28

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.3s	2778×	body	1280	valid
1.4s	1825×	body	640	valid
406.0ms	753×	body	320	valid
381.0ms	2342×	body	80	valid
109.0ms	302×	body	160	valid