Details

sample182.0ms

Algorithm

intervals

Results

104.0ms	103×	body	1280	valid
31.0ms	48×	body	640	valid
15.0ms	72×	body	80	valid
10.0ms	23×	body	320	valid
3.0ms	10×	body	160	valid

simplify55.0ms

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)

Merged error: 0.3b

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)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.1b	(- (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))

series987.0ms

Counts

4 → 10

Calls

4 calls:

844.0ms	(/ (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)))
85.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
57.0ms	(- (cos x) (cos y))

simplify124.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (88.0ms)

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

prune817.0ms

Filtered

217 candidates to 104 candidates (47.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

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))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.1b	(- (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 (/ (- 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))

series1.3s

Counts

4 → 10

Calls

4 calls:

1.2s	(/ (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))
87.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
50.0ms	(- (cos x) (cos y))

simplify126.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (93.0ms)

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

prune859.0ms

Filtered

217 candidates to 104 candidates (47.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

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))
1.1b	(- (cos x) (cos y))

rewrite64.0ms

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:

21.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))

series289.0ms

Counts

4 → 10

Calls

4 calls:

139.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
90.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
60.0ms	(- (cos x) (cos y))

simplify83.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1730	7731
1	5001	6094

prune1.1s

Filtered

301 candidates to 127 candidates (42.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

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))
1.1b	(- (cos x) (cos y))
1.3b	(log (exp (- (cos x) (cos y))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 210

Calls

4 calls:

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

series211.0ms

Counts

4 → 10

Calls

4 calls:

96.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
60.0ms	(- (cos x) (cos y))
55.0ms	(log (exp (- (cos x) (cos y))))

simplify104.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	969	3961
1	3434	2838
2	5001	2581

prune749.0ms

Filtered

220 candidates to 92 candidates (41.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes273.0ms

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	43	32
1	43	32

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.9s	2743×	body	1280	valid
1.2s	1852×	body	640	valid
347.0ms	744×	body	320	valid
338.0ms	2313×	body	80	valid
104.0ms	348×	body	160	valid