Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	185×	body	80	valid
7.0ms	29×	body	640	valid
4.0ms	17×	body	1280	valid
3.0ms	23×	body	640	nan
3.0ms	92×	body	80	nan
3.0ms	15×	body	1280	nan
2.0ms	16×	body	320	nan
1.0ms	12×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	7×	body	160	nan

simplify19.0ms

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: 17.9b

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))
4.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite75.0ms

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:

20.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
18.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
48.0ms	(/ (- x y) (- 1.0 y))
49.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
87.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify102.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (68.0ms)

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

prune392.0ms

Filtered

239 candidates to 126 candidates (52.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	232	7	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	233	7	240

Merged error: 0.1b

Counts

240 → 7

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)))
5.9b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
6.7b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite30.0ms

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)))))
3.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
40.0ms	(* (- x y) (/ 1 (- 1.0 y)))
85.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
55.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify68.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (54.0ms)

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

prune239.0ms

Filtered

137 candidates to 97 candidates (70.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	139	5	144

Merged error: 0.1b

Counts

144 → 5

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))))
4.0b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite75.0ms

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:

16.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
9.0ms	(/ (- x y) (- 1.0 y))
17.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
124.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify112.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (72.0ms)

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

prune526.0ms

Filtered

260 candidates to 157 candidates (60.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	260	5	265

Merged error: 0.1b

Counts

265 → 5

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)))

series280.0ms

Counts

2 → 6

Calls

2 calls:

161.0ms	(log (fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0))))
119.0ms	(fma (* 1.0 (exp 1.0)) (- x y) (* 1.0 (exp 1.0)))

simplify49.0ms

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

prune64.0ms

Filtered

30 candidates to 26 candidates (86.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	30	5	35

Merged error: 0.1b

Counts

35 → 5

regimes186.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.3b

bsearch112.0ms

Steps

Iters	Range		Point
9	2622764.913020247	58586406052719.45	12727887057.006495
7	-591489333.2348301	-16040781.538086794	-152389660.09060627

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample1.3s

Algorithm

intervals

Results

271.0ms	5692×	body	80	valid
182.0ms	779×	body	1280	valid
136.0ms	808×	body	640	valid
125.0ms	715×	body	1280	nan
102.0ms	727×	body	640	nan
91.0ms	2567×	body	80	nan
59.0ms	466×	body	320	valid
45.0ms	441×	body	320	nan
21.0ms	255×	body	160	valid
15.0ms	225×	body	160	nan