Details

sample17.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	99×	body	80	nan

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))
0.1b	(/ 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:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series209.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ 1.0 (sqrt (+ x 1.0)))
28.0ms	(sqrt (+ x 1.0))
137.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	334	508
1	1222	457
2	5002	445

prune132.0ms

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

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.5b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
234×	`sqrt-prod`
200×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `hypot-def` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 329

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
24.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series815.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
129.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
417.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
143.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify114.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	906	5694
1	3574	5078
2	5001	5052

prune401.0ms

Filtered

341 candidates to 153 candidates (44.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	340	1	341
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	341	4	345

Merged error: 0b

Counts

345 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b	(sqrt (sqrt (+ x 1.0)))
0.4b	(/ x (hypot (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
0.5b	(/ (/ x (hypot (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
131×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
73×	`sqrt-prod`
16×	`distribute-lft-out` `associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `div-inv`
8×	`sqrt-div`
7×	`pow1`
5×	`sqrt-pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `pow1/2` `flip-+`
2×	`frac-2neg` `clear-num` `associate-/r/` `hypot-def`
1×	`associate-/l/`

Counts

4 → 203

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
4.0ms	(sqrt (sqrt (+ x 1.0)))
3.0ms	(/ x (hypot (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
12.0ms	(/ (/ x (hypot (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
85.0ms	(sqrt (sqrt (+ x 1.0)))
593.0ms	(/ x (hypot (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))
1.1s	(/ (/ x (hypot (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1327	4059
1	5001	3853

prune518.0ms

Filtered

215 candidates to 142 candidates (66.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	215	4	219

Merged error: 0b

Counts

219 → 4

localize7.0ms

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)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

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))))
16.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ 1.0 (sqrt (+ x 1.0)))
28.0ms	(sqrt (+ x 1.0))
288.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
133.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	554	1324
1	2324	1174
2	5001	1140

prune239.0ms

Filtered

156 candidates to 103 candidates (66.0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	156	4	160

Merged error: 0b

Counts

160 → 4

regimes37.0ms

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

sample406.0ms

Algorithm

intervals

Results

220.0ms	7999×	body	80	valid
69.0ms	2660×	body	80	nan
0.0ms	1×	body	1280	valid