Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	190×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	132×	body	80	nan
2.0ms	16×	body	1280	nan
2.0ms	16×	body	640	valid
1.0ms	13×	body	640	nan
1.0ms	13×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	5×	body	160	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
2.8b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.4b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

175×	`add-sqr-sqrt`
169×	`*-un-lft-identity`
102×	`times-frac`
93×	`prod-diff`
81×	`add-cube-cbrt`
46×	`difference-of-squares`
44×	`distribute-lft-out--`
8×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`add-exp-log` `log-prod`
5×	`associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`pow1` `div-inv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`log-div` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `log-pow` `associate--r-`

Counts

3 → 187

Calls

3 calls:

14.0ms	(/ (- x y) (- 1.0 y))
27.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
29.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series178.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (- x y) (- 1.0 y))
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
87.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify87.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	847	3956
1	2766	2899
2	5001	2689

prune342.0ms

Filtered

196 candidates to 98 candidates (50.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

2.8b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.8b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.6b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
4.6b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

278×	`add-sqr-sqrt`
266×	`*-un-lft-identity`
186×	`prod-diff`
154×	`times-frac`
138×	`add-cube-cbrt`
68×	`difference-of-squares`
64×	`distribute-lft-out--`
18×	`log-prod`
12×	`sqrt-prod` `associate-/r/`
10×	`flip3--` `flip--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `fma-neg` `log-pow` `div-inv`
4×	`expm1-log1p-u` `log-div` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 276

Calls

4 calls:

30.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
27.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
22.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
23.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
127.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
131.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify99.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	775	7342
1	2406	5244
2	5002	4770

prune549.0ms

Filtered

288 candidates to 118 candidates (41.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

2.8b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.6b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
4.6b	(log (sqrt (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
4.6b	(log (sqrt (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
145×	`*-un-lft-identity`
93×	`prod-diff`
79×	`times-frac`
77×	`add-cube-cbrt`
38×	`difference-of-squares`
36×	`sqrt-prod`
34×	`distribute-lft-out--`
33×	`log-prod`
13×	`log-pow`
12×	`pow1`
10×	`sqrt-div`
9×	`sqrt-pow1`
7×	`add-exp-log` `flip3--` `flip--`
6×	`log-div` `associate-/r/` `add-log-exp`
5×	`pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `rem-log-exp` `div-inv`
1×	`sub-neg` `diff-log` `div-sub` `associate--r-`

Counts

4 → 196

Calls

4 calls:

27.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
24.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
22.0ms	(log (sqrt (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
22.0ms	(log (sqrt (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
134.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
113.0ms	(log (sqrt (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
119.0ms	(log (sqrt (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))

simplify88.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	888	4451
1	2630	3350
2	5001	3097

prune528.0ms

Filtered

208 candidates to 107 candidates (51.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- x y) (- 1.0 y)) 3)
2.7b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
4.4b	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0))))
12.9b	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0)))

rewrite650.0ms

Algorithm

rewrite-expression-head

Rules

1473×	`add-sqr-sqrt`
1185×	`*-un-lft-identity`
912×	`times-frac`
816×	`prod-diff`
754×	`unpow-prod-down` `cube-prod`
585×	`add-cube-cbrt`
452×	`difference-of-squares`
300×	`distribute-lft-out--`
162×	`sqr-pow`
103×	`log-prod`
82×	`cube-mult` `unpow3`
52×	`associate-/r/`
33×	`associate-/l*`
28×	`flip3--` `flip--` `div-inv`
12×	`add-exp-log` `fma-neg`
9×	`add-cbrt-cube`
8×	`difference-cubes`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `rem-log-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`cube-div` `pow-to-exp` `sub-neg` `log-div` `pow-pow` `frac-2neg` `diff-log` `div-sub` `clear-num` `log-pow`

Counts

4 → 1224

Calls

4 calls:

13.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
110.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
79.0ms	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0))))
315.0ms	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0)))

series881.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
187.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
359.0ms	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0))))
267.0ms	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0)))

simplify362.0ms

Algorithm

egg-herbie

Counts

1236 → 1236

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	2071	40517
1	5001	32680

prune1.3s

Filtered

1236 candidates to 236 candidates (19.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes194.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 18.5b

bsearch117.0ms

Steps

Iters	Range		Point
11	0.8818080259852756	4.2034886563207535e+23	80304997.2964149
5	-195151873765.63306	-77640530132.15767	-79025762686.63672

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	22
1	32	22

end0.0ms

sample983.0ms

Algorithm

intervals

Results

217.0ms	5665×	body	80	valid
158.0ms	851×	body	1280	valid
108.0ms	793×	body	640	valid
97.0ms	3655×	body	80	nan
50.0ms	346×	body	1280	nan
43.0ms	392×	body	640	nan
41.0ms	434×	body	320	valid
19.0ms	257×	body	160	valid
17.0ms	218×	body	320	nan
5.0ms	94×	body	160	nan