Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	84×	body	1280	valid
4.0ms	137×	body	80	valid
3.0ms	21×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	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: 15.0b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 54

Calls

3 calls:

8.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series163.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(/ 1.0 (hypot 1.0 x))
85.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	200	410
1	601	393
2	1999	391
3	5001	391

prune138.0ms

Filtered

63 candidates to 45 candidates (71.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	3	64

Merged error: 14.5b

Counts

64 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.1b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-*r/`
6×	`add-log-exp`
4×	`pow1` `flip3--` `associate--l+` `frac-sub` `flip--` `associate-/l/` `distribute-lft-out`
3×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
1×	`flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 110

Calls

4 calls:

12.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
6.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(/ 1.0 (hypot 1.0 x))
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	407	1275
1	1594	1181
2	5001	1177

prune332.0ms

Filtered

122 candidates to 88 candidates (72.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	121	4	125

Merged error: 14.5b

Counts

125 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
1.1b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
19.2b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`cube-div` `associate-*r/` `associate--l+`
3×	`sub-neg` `pow-unpow` `cbrt-div` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `flip3--` `distribute-lft-in` `unpow3` `div-exp` `pow-exp` `frac-sub` `flip--` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `rem-cbrt-cube`

Counts

4 → 133

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series78.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
33.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify73.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	463	917
1	2143	815
2	5001	807

prune330.0ms

Filtered

145 candidates to 76 candidates (52.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	145	4	149

Merged error: 14.5b

Counts

149 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (hypot 1.0 x) 3)
0.5b	(/ (pow 1.0 3) (pow (hypot 1.0 x) 3))
1.1b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (/ (pow 1.0 3) (pow (hypot 1.0 x) 3)))))
19.2b	(cbrt (/ (pow 1.0 3) (pow (hypot 1.0 x) 3)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
158×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
153×	`unpow-prod-down` `cube-prod`
148×	`cbrt-prod`
51×	`cube-mult` `unpow3` `sqr-pow`
17×	`add-exp-log`
12×	`associate-/r` `associate-/l`
9×	`div-exp`
7×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`associate-*r/` `associate--l+`
3×	`sub-neg` `pow-unpow` `cbrt-div`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `div-inv`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `rem-cube-cbrt`

Counts

4 → 386

Calls

4 calls:

2.0ms	(pow (hypot 1.0 x) 3)
11.0ms	(/ (pow 1.0 3) (pow (hypot 1.0 x) 3))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (/ (pow 1.0 3) (pow (hypot 1.0 x) 3)))))
14.0ms	(cbrt (/ (pow 1.0 3) (pow (hypot 1.0 x) 3)))

series136.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (hypot 1.0 x) 3)
68.0ms	(/ (pow 1.0 3) (pow (hypot 1.0 x) 3))
34.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (/ (pow 1.0 3) (pow (hypot 1.0 x) 3)))))
7.0ms	(cbrt (/ (pow 1.0 3) (pow (hypot 1.0 x) 3)))

simplify138.0ms

Algorithm

egg-herbie

Counts

398 → 398

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	634	3164
1	3078	3022
2	5002	2908

prune575.0ms

Filtered

398 candidates to 123 candidates (30.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	395	3	398
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	398	4	402

Merged error: 14.5b

Counts

402 → 4

regimes79.0ms

Accuracy

0% (0.0b remaining)

Error of 14.6b against oracle of 14.6b and baseline of 14.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	36
1	29	36

end0.0ms

sample809.0ms

Algorithm

intervals

Results

469.0ms	2862×	body	1280	valid
119.0ms	4063×	body	80	valid
79.0ms	625×	body	640	valid
25.0ms	287×	body	320	valid
9.0ms	163×	body	160	valid