Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	255×	body	80	valid
1.0ms	84×	body	80	nan
0.0ms	1×	body	1280	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

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: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series227.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ 1.0 (sqrt (+ x 1.0)))
31.0ms	(sqrt (+ x 1.0))
150.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	331	509
1	1196	457
2	5002	445

prune123.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Merged error: 0b

Counts

81 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

242×	`*-un-lft-identity`
210×	`associate-/r*`
200×	`add-sqr-sqrt`
184×	`sqrt-prod`
169×	`frac-times`
149×	`add-cube-cbrt`
106×	`times-frac`
91×	`associate-/l*`
43×	`distribute-lft-out`
32×	`add-exp-log`
31×	`clear-num`
30×	`frac-2neg`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
13×	`associate-r/` `associate-l/`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`sqrt-pow1` `pow1/2` `un-div-inv` `hypot-def`
1×	`rem-sqrt-square` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 409

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
11.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
35.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
9.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series937.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
434.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
147.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
215.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

421 → 421

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1322	5216
1	5002	4502

prune425.0ms

Filtered

421 candidates to 175 candidates (41.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	420	1	421
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	422	3	425

Merged error: 0b

Counts

425 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.6b	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-prod`
106×	`*-un-lft-identity`
92×	`times-frac`
84×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
34×	`sqrt-div`
28×	`associate-/r*`
16×	`distribute-lft-out`
14×	`pow1` `sqrt-pow1`
12×	`add-exp-log` `pow-flip` `associate-/l*`
10×	`rem-sqrt-square`
8×	`associate-/r/` `add-cbrt-cube`
6×	`pow1/2`
4×	`expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `inv-pow` `add-log-exp`
2×	`cbrt-undiv` `rec-exp` `1-exp`

Counts

4 → 226

Calls

4 calls:

10.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
10.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
8.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
9.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

369.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
378.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
219.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
223.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	460	2442
1	1748	2188
2	5001	1992

prune353.0ms

Filtered

238 candidates to 108 candidates (45.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	238	3	241

Merged error: 0b

Counts

241 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.0b	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
52×	`times-frac`
43×	`add-cube-cbrt`
42×	`sqrt-prod`
30×	`associate-r`
16×	`distribute-lft-out`
13×	`associate-r/` `associate-/l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`pow1`
6×	`associate-l` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def` `clear-num`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `prod-exp` `un-div-inv` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log` `*-commutative` `hypot-def`

Counts

4 → 158

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
19.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ 1.0 (sqrt (+ x 1.0)))
37.0ms	(sqrt (+ x 1.0))
315.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
145.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	567	1366
1	2375	1212
2	5002	1173

prune250.0ms

Filtered

170 candidates to 110 candidates (64.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	170	3	173

Merged error: 0b

Counts

173 → 3

regimes34.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample307.0ms

Algorithm

intervals

Results

150.0ms	7997×	body	80	valid
48.0ms	2601×	body	80	nan
0.0ms	3×	body	1280	valid