Details

sample71.0ms

Algorithm

intervals

Results

21.0ms	121×	body	320	valid
17.0ms	246×	body	80	nan
15.0ms	131×	body	160	valid
0.0ms	4×	body	80	valid

simplify135.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	21
1	125	21
2	317	21
3	648	21
4	1073	21
5	1417	21
6	1725	21
7	3333	21
8	5002	21

prune4.0ms

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: 36.2b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.9b	(sqrt (- (* g g) (* h h)))
29.9b	(sqrt (- (* g g) (* h h)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
124×	`associate-l`
112×	`cbrt-div`
110×	`*-un-lft-identity`
108×	`cbrt-prod`
78×	`add-cube-cbrt`
76×	`times-frac`
72×	`frac-times` `associate-/r*`
67×	`sqrt-prod`
52×	`difference-of-squares`
48×	`associate-r`
40×	`unswap-sqr`
36×	`associate-*l/`
34×	`*-commutative`
24×	`swap-sqr`
21×	`flip3--` `flip--`
19×	`flip3-+` `flip-+`
18×	`associate-/l*`
12×	`distribute-lft-out--`
6×	`pow1` `frac-2neg` `clear-num`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `pow1/3` `div-inv` `distribute-lft-out`

Counts

4 → 334

Calls

4 calls:

56.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
56.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.0ms	(sqrt (- (* g g) (* h h)))
34.0ms	(sqrt (- (* g g) (* h h)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
317.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
54.0ms	(sqrt (- (* g g) (* h h)))

simplify96.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2026	5434
1	5001	5392

prune1.4s

Filtered

346 candidates to 241 candidates (69.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	326	20	346
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	327	20	347

Merged error: 31.6b

Counts

347 → 20

localize28.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
9.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.9b	(sqrt (- (* g g) (* h h)))
29.9b	(sqrt (- (* g g) (* h h)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

432×	`add-sqr-sqrt`
237×	`*-un-lft-identity`
225×	`prod-diff`
197×	`add-cube-cbrt`
163×	`associate-l`
129×	`swap-sqr`
116×	`associate-r`
75×	`difference-of-squares`
71×	`unswap-sqr`
68×	`*-commutative`
66×	`sqrt-prod`
56×	`cbrt-div`
53×	`cbrt-prod`
38×	`times-frac`
36×	`frac-times` `associate-/r*`
19×	`flip3-+` `flip-+`
18×	`associate-*l/`
15×	`fma-neg` `distribute-lft-out--`
9×	`associate-/l*`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `frac-2neg` `clear-num` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `distribute-lft-out`
1×	`sub-neg` `distribute-rgt-neg-in` `pow1/3` `diff-log` `div-inv`

Counts

4 → 497

Calls

4 calls:

23.0ms	(- (* g g) (* h h))
57.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
36.0ms	(sqrt (- (* g g) (* h h)))
32.0ms	(sqrt (- (* g g) (* h h)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
336.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
57.0ms	(sqrt (- (* g g) (* h h)))

simplify111.0ms

Algorithm

egg-herbie

Counts

509 → 509

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1907	6340
1	5002	5676

prune1.2s

Filtered

509 candidates to 193 candidates (37.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	501	8	509
Fresh	7	12	19
Picked	1	0	1
Done	0	0	0
Total	509	20	529

Merged error: 31.0b

Counts

529 → 20

localize28.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
3.0b	(- (* g g) (* h h))
29.9b	(sqrt (- (* g g) (* h h)))
29.9b	(sqrt (- (* g g) (* h h)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

642×	`add-sqr-sqrt`
450×	`prod-diff`
364×	`*-un-lft-identity`
316×	`add-cube-cbrt`
234×	`swap-sqr`
202×	`associate-l`
186×	`associate-r`
102×	`*-commutative` `unswap-sqr`
100×	`difference-of-squares`
66×	`sqrt-prod`
30×	`fma-neg`
20×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 662

Calls

4 calls:

24.0ms	(- (* g g) (* h h))
23.0ms	(- (* g g) (* h h))
34.0ms	(sqrt (- (* g g) (* h h)))
32.0ms	(sqrt (- (* g g) (* h h)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
35.0ms	(- (* g g) (* h h))
46.0ms	(sqrt (- (* g g) (* h h)))
56.0ms	(sqrt (- (* g g) (* h h)))

simplify132.0ms

Algorithm

egg-herbie

Counts

674 → 674

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	644	7290
1	1624	4886
2	5002	3368

prune696.0ms

Filtered

674 candidates to 104 candidates (15.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	672	2	674
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	674	20	694

Merged error: 31.0b

Counts

694 → 20

localize24.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
3.0b	(- (* g g) (* h h))
29.9b	(sqrt (- (* g g) (* h h)))
29.9b	(sqrt (- (* g g) (* h h)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

642×	`add-sqr-sqrt`
450×	`prod-diff`
364×	`*-un-lft-identity`
316×	`add-cube-cbrt`
234×	`swap-sqr`
202×	`associate-l`
186×	`associate-r`
102×	`*-commutative` `unswap-sqr`
100×	`difference-of-squares`
66×	`sqrt-prod`
30×	`fma-neg`
20×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 662

Calls

4 calls:

24.0ms	(- (* g g) (* h h))
26.0ms	(- (* g g) (* h h))
32.0ms	(sqrt (- (* g g) (* h h)))
35.0ms	(sqrt (- (* g g) (* h h)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
36.0ms	(- (* g g) (* h h))
56.0ms	(sqrt (- (* g g) (* h h)))
63.0ms	(sqrt (- (* g g) (* h h)))

simplify132.0ms

Algorithm

egg-herbie

Counts

674 → 674

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	644	7292
1	1631	4886
2	5002	3368

prune559.0ms

Filtered

674 candidates to 104 candidates (15.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	672	2	674
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	674	20	694

Merged error: 31.0b

Counts

694 → 20

regimes775.0ms

Accuracy

0% (1.3b remaining)

Error of 32.1b against oracle of 30.8b and baseline of 32.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	35
1	35	35

end0.0ms

sample1.9s

Algorithm

intervals

Results

641.0ms	3687×	body	320	valid
486.0ms	4179×	body	160	valid
435.0ms	7816×	body	80	nan
8.0ms	134×	body	80	valid