Details

sample290.0ms

Algorithm

intervals

Results

9.0ms	166×	body	80	valid
8.0ms	33×	body	2560	valid
8.0ms	39×	body	1280	valid
4.0ms	22×	body	640	valid
3.0ms	77×	body	80	nan
1.0ms	12×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7

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: 35.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

25.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune264.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	7	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	7	113

Merged error: 4.4b

Counts

113 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.0b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
21×	`distribute-lft-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg` `associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 284

Calls

4 calls:

15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
166.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify145.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	919	5579
1	3918	4508
2	5001	4505

prune525.0ms

Filtered

296 candidates to 172 candidates (58.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	293	3	296
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	294	9	303

Merged error: 4.4b

Counts

303 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.8b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
630×	`add-sqr-sqrt`
629×	`*-un-lft-identity`
433×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
82×	`sqrt-prod`
70×	`distribute-rgt-neg-in`
60×	`prod-diff`
28×	`associate-/r*`
22×	`div-inv`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 569

Calls

4 calls:

11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
27.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
181.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
155.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify132.0ms

Algorithm

egg-herbie

Counts

581 → 581

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1755	10832
1	5002	9428

prune1.0s

Filtered

581 candidates to 328 candidates (56.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	577	4	581
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	581	9	590

Merged error: 4.4b

Counts

590 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.6b	(- (* b_2 b_2) (* a c))
0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
168×	`*-un-lft-identity`
159×	`times-frac`
116×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`neg-mul-1` `div-exp`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 249

Calls

4 calls:

13.0ms	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
37.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	802	4369
1	3203	3287
2	5002	3111

prune282.0ms

Filtered

261 candidates to 107 candidates (41.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	259	2	261
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	261	9	270

Merged error: 4.4b

Counts

270 → 9

regimes168.0ms

Accuracy

92.8% (1.7b remaining)

Error of 7.2b against oracle of 5.4b and baseline of 29.8b

bsearch99.0ms

Steps

Iters	Range	Point
7	3.0106008231332273e+28	3.853441604264477e+30	3.7841174599135035e+30
7	-2.7658122324780073e-177	-4.963613050543331e-179	-1.3880501838027266e-178
2	-4.193597519284562e+95	-3.5355996581575456e+95	-4.111347786643685e+95

Iters

Range

Point

3.0106008231332273e+28

3.853441604264477e+30

3.7841174599135035e+30

-2.7658122324780073e-177

-4.963613050543331e-179

-1.3880501838027266e-178

-4.193597519284562e+95

-3.5355996581575456e+95

-4.111347786643685e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	41	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

292.0ms	1137×	body	2560	valid
257.0ms	5779×	body	80	valid
186.0ms	893×	body	1280	valid
118.0ms	2863×	body	80	nan
76.0ms	464×	body	640	valid
33.0ms	107×	body	5120	valid
30.0ms	249×	body	320	valid
9.0ms	110×	body	160	valid