Details

sample68.0ms

Algorithm

intervals

Results

25.0ms	52×	body	1280	valid
17.0ms	59×	body	640	valid
7.0ms	145×	body	80	valid
4.0ms	19×	body	320	valid
3.0ms	84×	body	80	nan
1.0ms	12×	body	160	valid

simplify108.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (7.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune4.0ms

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

localize6.0ms

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)

rewrite34.0ms

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×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

10.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series400.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ (pow (/ x (+ x y)) x) x)
40.0ms	(/ x (+ x y))
231.0ms	(pow (/ x (+ x y)) x)

simplify72.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	537	1436
1	2640	1406
2	5001	1406

prune332.0ms

Filtered

181 candidates to 131 candidates (72.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Merged error: 0.8b

Counts

182 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

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` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

4.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify46.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	114	186
1	303	172
2	1465	170
3	5003	170

prune50.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	31	3	34

Merged error: 0.8b

Counts

34 → 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)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
68×	`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×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 172

Calls

4 calls:

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

series208.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ x y))
36.0ms	(sqrt (+ x y))
66.0ms	(/ (sqrt x) (sqrt (+ x y)))
67.0ms	(/ (sqrt x) (sqrt (+ x y)))

simplify114.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	247	1432
1	784	1348
2	4067	1266
3	5002	1266

prune335.0ms

Filtered

184 candidates to 104 candidates (56.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0.8b

Counts

187 → 3

localize13.0ms

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)

rewrite21.0ms

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×	`flip3-+` `add-cbrt-cube` `flip-+` `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 → 84

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
10.0ms	(pow (/ x (cbrt (+ x y))) x)

series465.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (+ x y))
124.0ms	(cbrt (+ x y))
122.0ms	(cbrt (+ x y))
98.0ms	(pow (/ x (cbrt (+ x y))) x)

simplify49.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	497	752
1	1928	723
2	5002	694

prune255.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	97	2	99

Merged error: 0b

Counts

99 → 2

regimes40.0ms

Accuracy

97.3% (0.3b remaining)

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

bsearch95.0ms

Steps

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

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample2.0s

Algorithm

intervals

Results

751.0ms	1544×	body	1280	valid
417.0ms	1410×	body	640	valid
265.0ms	4950×	body	80	valid
169.0ms	852×	body	320	valid
121.0ms	3020×	body	80	nan
52.0ms	423×	body	160	valid