Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	181×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	24×	body	640	valid
4.0ms	24×	body	1280	nan
3.0ms	24×	body	640	nan
3.0ms	88×	body	80	nan
2.0ms	13×	body	320	valid
1.0ms	15×	body	160	valid
1.0ms	14×	body	160	nan
1.0ms	8×	body	320	nan

simplify20.0ms

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

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: 18.4b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
3.3b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.6b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`fma-neg` `add-cbrt-cube` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 227

Calls

4 calls:

16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
21.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms	(/ (- x y) (- 1.0 y))
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
82.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify104.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	986	4621
1	3240	3344
2	5001	3134

prune383.0ms

Filtered

239 candidates to 126 candidates (52.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	237	3	240

Merged error: 0.1b

Counts

240 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.1b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
3.3b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
202×	`*-un-lft-identity`
144×	`times-frac`
102×	`add-cube-cbrt`
93×	`prod-diff`
58×	`difference-of-squares`
50×	`distribute-lft-out--`
24×	`log-prod`
12×	`associate-/r/`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`flip3--` `add-cbrt-cube` `flip--` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `div-exp`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 248

Calls

4 calls:

18.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
15.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms	(/ (- x y) (- 1.0 y))
121.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
48.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify118.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1074	4812
1	3721	3718
2	5001	3710

prune453.0ms

Filtered

260 candidates to 157 candidates (60.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	259	4	263

Merged error: 0b

Counts

263 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0))))
0.2b	(fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-log-exp` `log-pow` `fma-udef`

Counts

2 → 24

Calls

2 calls:

1.0ms	(log (fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0))))
1.0ms	(fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0)))

series236.0ms

Counts

2 → 6

Calls

2 calls:

157.0ms	(log (fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0))))
78.0ms	(fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	135	299
1	355	245
2	1721	235
3	5002	224

prune68.0ms

Filtered

30 candidates to 26 candidates (86.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	30	4	34

Merged error: 0b

Counts

34 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- x y) (- 1.0 y)) 3)
3.3b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
5.6b	(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))))
10.6b	(/ (- (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)))

rewrite342.0ms

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:

10.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
60.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
48.0ms	(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))))
99.0ms	(/ (- (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)))

series801.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
171.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
328.0ms	(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))))
243.0ms	(/ (- (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)))

simplify372.0ms

Algorithm

egg-herbie

Counts

1236 → 1236

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2071	40517
1	5001	32680

prune1.1s

Filtered

1236 candidates to 236 candidates (19.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1236	0	1236
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	1236	4	1240

Merged error: 0b

Counts

1240 → 4

regimes116.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.7b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	18
1	25	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

276.0ms	5641×	body	80	valid
203.0ms	819×	body	1280	valid
145.0ms	804×	body	640	valid
126.0ms	672×	body	1280	nan
110.0ms	751×	body	640	nan
97.0ms	2661×	body	80	nan
65.0ms	481×	body	320	valid
48.0ms	454×	body	320	nan
22.0ms	255×	body	160	valid
18.0ms	261×	body	160	nan