Details

sample71.0ms

Algorithm

intervals

Results

26.0ms	52×	body	1280	valid
17.0ms	59×	body	640	valid
8.0ms	145×	body	80	valid
4.0ms	19×	body	320	valid
3.0ms	84×	body	80	nan
2.0ms	12×	body	160	valid

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 9.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
5.3b	(pow (/ x (+ x y)) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

11.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series413.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(/ (pow (/ x (+ x y)) x) x)
39.0ms	(/ x (+ x y))
237.0ms	(pow (/ x (+ x y)) x)

simplify73.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	554	1456
1	2726	1426
2	5002	1426

prune343.0ms

Filtered

187 candidates to 137 candidates (73.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	3	188

Merged error: 0.8b

Counts

188 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`pow1` `cbrt-undiv` `exp-neg` `expm1-log1p-u` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

4.0ms

(/ (exp (* -1 y)) x)

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(/ (exp (* -1 y)) x)

simplify47.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	118	194
1	313	179
2	1512	177
3	5001	177

prune55.0ms

Filtered

33 candidates to 25 candidates (75.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	33	3	36

Merged error: 0.8b

Counts

36 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x y))
0.0b	(sqrt (+ x y))
0.1b	(/ (sqrt x) (sqrt (+ x y)))
0.1b	(/ (sqrt x) (sqrt (+ x y)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
72×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`associate-/r*`
12×	`associate-/l*`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

4 → 182

Calls

4 calls:

3.0ms	(sqrt (+ x y))
4.0ms	(sqrt (+ x y))
7.0ms	(/ (sqrt x) (sqrt (+ x y)))
8.0ms	(/ (sqrt x) (sqrt (+ x y)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ x y))
34.0ms	(sqrt (+ x y))
67.0ms	(/ (sqrt x) (sqrt (+ x y)))
67.0ms	(/ (sqrt x) (sqrt (+ x y)))

simplify118.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	260	1464
1	826	1378
2	4270	1294
3	5001	1294

prune377.0ms

Filtered

194 candidates to 114 candidates (58.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	194	3	197

Merged error: 0.8b

Counts

197 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
1.5b	(pow (/ x (cbrt (+ x y))) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
27×	`unpow-prod-down`
24×	`cbrt-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
8×	`cbrt-div`
7×	`add-exp-log`
6×	`distribute-lft-out`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-exp` `associate-/r/`
1×	`pow-to-exp` `pow-pow` `div-exp` `div-inv` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
8.0ms	(pow (/ x (cbrt (+ x y))) x)

series494.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (+ x y))
132.0ms	(cbrt (+ x y))
130.0ms	(cbrt (+ x y))
103.0ms	(pow (/ x (cbrt (+ x y))) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	513	774
1	2015	743
2	5001	713

prune299.0ms

Filtered

104 candidates to 82 candidates (78.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	105	2	107

Merged error: 0b

Counts

107 → 2

regimes42.0ms

Accuracy

97.3% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 12.5b

bsearch101.0ms

Steps

Iters	Range		Point
10	5.251099164423855e-21	1.578317661697433e-06	1.5559169625596469e-06
8	-1.1753057616120753e-15	-1.0444048500662454e-19	-1.1520662094029635e-15

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample2.1s

Algorithm

intervals

Results

762.0ms	1544×	body	1280	valid
426.0ms	1410×	body	640	valid
271.0ms	4950×	body	80	valid
168.0ms	852×	body	320	valid
130.0ms	3020×	body	80	nan
53.0ms	423×	body	160	valid