Details

sample50.0ms

Algorithm

intervals

Results

8.0ms	169×	body	80	valid
6.0ms	27×	body	1280	valid
6.0ms	32×	body	640	valid
4.0ms	32×	body	640	nan
4.0ms	22×	body	1280	nan
4.0ms	99×	body	80	nan
3.0ms	23×	body	320	valid
2.0ms	15×	body	320	nan
1.0ms	8×	body	160	nan
0.0ms	5×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 21.5b

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))
1.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite78.0ms

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:

17.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
9.0ms	(/ (- x y) (- 1.0 y))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
22.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify105.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (70.0ms)

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

prune387.0ms

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: 0.0b

Counts

240 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
3.8b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
5.1b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`associate-r`
17×	`times-frac`
15×	`prod-diff`
14×	`add-exp-log`
11×	`pow1`
9×	`add-cbrt-cube`
7×	`flip3--` `flip--` `add-log-exp`
6×	`log-prod` `fma-neg` `distribute-lft-out--`
5×	`associate-l` `log-pow` `difference-of-squares`
4×	`expm1-log1p-u` `log-div` `prod-exp` `log1p-expm1-u`
3×	`associate--r+` `unswap-sqr`
2×	`frac-times` `sub-neg` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `associate--r-`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 125

Calls

4 calls:

6.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
14.0ms	(* (- x y) (/ 1 (- 1.0 y)))
3.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
4.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
40.0ms	(* (- x y) (/ 1 (- 1.0 y)))
83.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
49.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify67.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	602	1451
1	2439	1102
2	5002	1066

prune234.0ms

Filtered

137 candidates to 99 candidates (72.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	137	3	140

Merged error: 0.0b

Counts

140 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x (pow y 2)) (/ 1 y))
2.4b	(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
2.8b	(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
8.3b	(/ x (pow y 2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

636×	`times-frac`
469×	`add-sqr-sqrt`
440×	`*-un-lft-identity`
428×	`add-cube-cbrt`
364×	`prod-diff`
141×	`unpow-prod-down`
49×	`unpow2` `sqr-pow`
44×	`div-inv`
28×	`fma-neg`
15×	`difference-of-squares`
10×	`add-exp-log`
8×	`associate-/r*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `div-exp` `associate-/l*` `distribute-lft-out--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `fma-udef`

Counts

4 → 500

Calls

4 calls:

32.0ms	(- (/ x (pow y 2)) (/ 1 y))
1.0ms	(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
1.0ms	(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
5.0ms	(/ x (pow y 2))

series150.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ x (pow y 2)) (/ 1 y))
59.0ms	(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
35.0ms	(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
22.0ms	(/ x (pow y 2))

simplify143.0ms

Algorithm

egg-herbie

Counts

512 → 512

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	1276	10765
1	3395	6095
2	5003	6012

prune451.0ms

Filtered

512 candidates to 134 candidates (26.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	511	1	512
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	511	4	515

Merged error: 0.0b

Counts

515 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

8.3b	(/ x (pow y 2))
8.3b	(/ x (pow y 2))
15.9b	(cbrt (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
15.9b	(cbrt (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/r*`
14×	`add-exp-log`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`cbrt-prod` `div-exp` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow1/3` `pow-exp` `clear-num` `div-inv`

Counts

4 → 128

Calls

4 calls:

5.0ms	(/ x (pow y 2))
5.0ms	(/ x (pow y 2))
1.0ms	(cbrt (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
2.0ms	(cbrt (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ x (pow y 2))
22.0ms	(/ x (pow y 2))
137.0ms	(cbrt (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
124.0ms	(cbrt (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))

simplify186.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	284	942
1	945	854
2	4901	828
3	5001	828

prune437.0ms

Filtered

140 candidates to 96 candidates (68.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	140	4	144

Merged error: 0.0b

Counts

144 → 4

regimes263.0ms

Accuracy

96.7% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 18.2b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

294.0ms	5644×	body	80	valid
219.0ms	840×	body	1280	valid
164.0ms	845×	body	640	valid
158.0ms	754×	body	1280	nan
117.0ms	727×	body	640	nan
96.0ms	2586×	body	80	nan
61.0ms	451×	body	320	valid
47.0ms	415×	body	320	nan
20.0ms	220×	body	160	valid
19.0ms	225×	body	160	nan