Details

sample52.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
9.0ms	39×	body	1280	valid
9.0ms	166×	body	80	valid
4.0ms	22×	body	640	valid
4.0ms	77×	body	80	nan
2.0ms	12×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

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: 35.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b	(- (* b b) (* (* 4.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune254.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	7	103

Merged error: 4.4b

Counts

103 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
172.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify146.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	829	5119
1	3763	3863
2	5001	3860

prune476.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	243	8	251

Merged error: 4.4b

Counts

251 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

5.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
8.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
14.3b	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
146×	`*-un-lft-identity`
102×	`add-cube-cbrt` `times-frac`
90×	`prod-diff`
82×	`log-prod` `exp-sum`
44×	`sqrt-prod`
41×	`distribute-rgt-neg-in`
33×	`associate-/l*` `difference-of-squares`
30×	`distribute-lft-neg-in`
22×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
10×	`neg-mul-1` `fma-neg`
9×	`associate-/r*`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 273

Calls

4 calls:

20.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
14.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
176.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
72.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify160.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	978	7738
1	3964	4917
2	5001	4916

prune587.0ms

Filtered

285 candidates to 145 candidates (50.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	285	8	293

Merged error: 4.4b

Counts

293 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.4b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
142.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	668	3371
1	3482	2161
2	5001	2072

prune264.0ms

Filtered

164 candidates to 82 candidates (50.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	165	7	172

Merged error: 4.4b

Counts

172 → 7

regimes148.0ms

Accuracy

93% (1.7b remaining)

Error of 7.2b against oracle of 5.5b and baseline of 29.8b

bsearch143.0ms

Steps

Iters	Range	Point
7	3.0106008231332273e+28	3.853441604264477e+30	3.7841174599135035e+30
8	-2.927933099620566e-203	-2.4110032972616562e-207	-2.8254292841125695e-206
2	-4.193597519284562e+95	-3.5355996581575456e+95	-4.111347786643685e+95

Iters

Range

Point

3.0106008231332273e+28

3.853441604264477e+30

3.7841174599135035e+30

-2.927933099620566e-203

-2.4110032972616562e-207

-2.8254292841125695e-206

-4.193597519284562e+95

-3.5355996581575456e+95

-4.111347786643685e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	28
1	50	28
2	50	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

356.0ms	1132×	body	2560	valid
323.0ms	5781×	body	80	valid
229.0ms	895×	body	1280	valid
158.0ms	2866×	body	80	nan
95.0ms	466×	body	640	valid
40.0ms	107×	body	5120	valid
37.0ms	247×	body	320	valid
11.0ms	109×	body	160	valid