Details

sample243.0ms

Algorithm

intervals

Results

117.0ms	80×	body	1280	valid
63.0ms	61×	body	640	valid
24.0ms	88×	body	80	valid
14.0ms	19×	body	320	valid
4.0ms	8×	body	160	valid

simplify59.0ms

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

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))
2.9b	(- (cos x) (cos y))

rewrite64.0ms

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:

2.0ms	(/ (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)))
41.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series1.0s

Counts

4 → 10

Calls

4 calls:

881.0ms	(/ (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))
51.0ms	(- (cos x) (cos y))

simplify129.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (95.0ms)

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

prune821.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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))
2.9b	(- (cos x) (cos y))
3.3b	(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))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
105×	`prod-diff`
102×	`add-cube-cbrt`
64×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
13×	`log-prod`
9×	`add-exp-log`
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`
3×	`flip3--` `flip--` `distribute-lft-out--`
2×	`diff-log` `associate-*r/` `rem-log-exp` `unswap-sqr`
1×	`log-div` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `diff-cos`

Counts

4 → 204

Calls

4 calls:

40.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))
2.0ms	(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))))

series2.1s

Counts

4 → 10

Calls

4 calls:

94.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
58.0ms	(- (cos x) (cos y))
2.0s	(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))))

simplify136.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1190	4916
1	4386	3812
2	5001	3805

prune916.0ms

Pruning

9 alts after pruning (8 fresh and 1 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))
2.9b	(- (cos x) (cos y))

rewrite138.0ms

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:

70.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
39.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series293.0ms

Counts

4 → 10

Calls

4 calls:

142.0ms	(* (* (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))
59.0ms	(- (cos x) (cos y))

simplify86.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1730	7731
1	5001	6094

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
1.0b	(- 3.0 (sqrt 5.0))
2.9b	(- (cos x) (cos y))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`sqrt-prod`
8×	`add-log-exp`
6×	`cbrt-prod` `fma-neg`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`
1×	`diff-cos`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt (sin x))
1.0ms	(cbrt (sin x))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series264.0ms

Counts

4 → 10

Calls

4 calls:

100.0ms	(cbrt (sin x))
102.0ms	(cbrt (sin x))
0.0ms	(- 3.0 (sqrt 5.0))
61.0ms	(- (cos x) (cos y))

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	453	880
1	1376	631
2	5001	612

prune726.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes225.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	66
1	68	66
2	69	66
3	69	66

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.9s	2716×	body	1280	valid
1.8s	1820×	body	640	valid
668.0ms	2349×	body	80	valid
546.0ms	751×	body	320	valid
190.0ms	364×	body	160	valid