Details

sample73.0ms

Algorithm

intervals

Results

22.0ms	136×	body	320	valid
16.0ms	117×	body	160	valid
14.0ms	269×	body	80	nan
0.0ms	3×	body	80	valid

simplify129.0ms

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: 37.0b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.6b	(sqrt (- (* g g) (* h h)))
29.6b	(sqrt (- (* g g) (* h h)))

rewrite208.0ms

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:

57.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
55.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
35.0ms	(sqrt (- (* g g) (* h h)))
39.0ms	(sqrt (- (* g g) (* h h)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
334.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
54.0ms	(sqrt (- (* g g) (* h h)))

simplify92.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2032	5434
1	5001	5392

prune1.5s

Filtered

346 candidates to 241 candidates (69.7%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	322	24	346
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	24	347

Merged error: 30.9b

Counts

347 → 24

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- g) (sqrt (- (* g g) (* h h))))
8.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.6b	(sqrt (- (* g g) (* h h)))
29.6b	(sqrt (- (* g g) (* h h)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

800×	`add-sqr-sqrt`
397×	`sqrt-prod`
360×	`prod-diff`
325×	`*-un-lft-identity`
302×	`difference-of-squares`
173×	`add-cube-cbrt`
144×	`swap-sqr`
130×	`unswap-sqr`
127×	`*-commutative`
113×	`distribute-rgt-neg-in`
111×	`distribute-lft-neg-in`
106×	`associate-l`
62×	`distribute-lft-out--`
56×	`cbrt-div`
53×	`cbrt-prod`
38×	`times-frac`
37×	`neg-mul-1`
36×	`frac-times` `associate-/r*`
23×	`associate-r`
19×	`flip3-+` `flip-+`
18×	`associate-*l/`
10×	`fma-neg`
9×	`associate-/l*`
8×	`add-log-exp`
6×	`pow1`
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` `diff-log` `associate-*r/` `distribute-lft-out`
1×	`associate--l-` `neg-sub0` `sub-neg` `pow1/3` `neg-log` `div-inv`

Counts

4 → 603

Calls

4 calls:

46.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
55.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
34.0ms	(sqrt (- (* g g) (* h h)))
39.0ms	(sqrt (- (* g g) (* h h)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
328.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
53.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify137.0ms

Algorithm

egg-herbie

Counts

615 → 615

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1898	12654
1	5001	10436

prune1.3s

Filtered

615 candidates to 188 candidates (30.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	604	11	615
Fresh	12	11	23
Picked	1	0	1
Done	0	0	0
Total	617	22	639

Merged error: 30.5b

Counts

639 → 22

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
1.4b	(- (- g) (sqrt (- (* g g) (* h h))))
29.6b	(sqrt (- (* g g) (* h h)))
29.6b	(sqrt (- (* g g) (* h h)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

1010×	`add-sqr-sqrt`
585×	`prod-diff`
452×	`*-un-lft-identity`
397×	`sqrt-prod`
327×	`difference-of-squares`
292×	`add-cube-cbrt`
249×	`swap-sqr`
161×	`*-commutative` `unswap-sqr`
145×	`associate-l`
112×	`distribute-rgt-neg-in`
111×	`distribute-lft-neg-in`
93×	`associate-r`
67×	`distribute-lft-out--`
37×	`neg-mul-1`
25×	`fma-neg`
10×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 768

Calls

4 calls:

27.0ms	(- (* g g) (* h h))
45.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
35.0ms	(sqrt (- (* g g) (* h h)))
38.0ms	(sqrt (- (* g g) (* h h)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
60.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
53.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify184.0ms

Algorithm

egg-herbie

Counts

780 → 780

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	1137	13598
1	2907	10157
2	5001	9269

prune762.0ms

Filtered

780 candidates to 112 candidates (14.4%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	779	1	780
Fresh	1	20	21
Picked	0	1	1
Done	0	0	0
Total	780	22	802

Merged error: 30.5b

Counts

802 → 22

localize30.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
1.4b	(- (- g) (sqrt (- (* g g) (* h h))))
29.6b	(sqrt (- (* g g) (* h h)))
29.6b	(sqrt (- (* g g) (* h h)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

1010×	`add-sqr-sqrt`
585×	`prod-diff`
452×	`*-un-lft-identity`
397×	`sqrt-prod`
327×	`difference-of-squares`
292×	`add-cube-cbrt`
249×	`swap-sqr`
161×	`*-commutative` `unswap-sqr`
145×	`associate-l`
112×	`distribute-rgt-neg-in`
111×	`distribute-lft-neg-in`
93×	`associate-r`
67×	`distribute-lft-out--`
37×	`neg-mul-1`
25×	`fma-neg`
10×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 768

Calls

4 calls:

25.0ms	(- (* g g) (* h h))
42.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
38.0ms	(sqrt (- (* g g) (* h h)))
34.0ms	(sqrt (- (* g g) (* h h)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
64.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
52.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify191.0ms

Algorithm

egg-herbie

Counts

780 → 780

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	1137	13598
1	2907	10157
2	5001	9269

prune772.0ms

Filtered

780 candidates to 112 candidates (14.4%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	778	2	780
Fresh	1	19	20
Picked	1	0	1
Done	0	1	1
Total	780	22	802

Merged error: 30.5b

Counts

802 → 22

regimes789.0ms

Accuracy

0% (1.2b remaining)

Error of 32.5b against oracle of 31.3b and baseline of 32.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	23
1	25	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

617.0ms	3732×	body	320	valid
457.0ms	4124×	body	160	valid
433.0ms	8068×	body	80	nan
8.0ms	144×	body	80	valid