Details

sample57.0ms

Algorithm

intervals

Results

10.0ms	148×	body	160	valid
10.0ms	561×	pre	80	true
10.0ms	305×	body	80	nan
4.0ms	40×	body	320	valid
2.0ms	68×	body	80	valid

simplify12.0ms

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

prune3.0ms

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: 43.8b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.0b	(+ (- b) (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:

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

series314.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5002	735

prune245.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Merged error: 0.2b

Counts

103 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`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`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(/ (/ (+ 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)))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
156.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
190.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify161.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	832	5099
1	3967	3830
2	5001	3828

prune548.0ms

Filtered

243 candidates to 137 candidates (56.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	234	9	243
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	238	11	249

Merged error: 0.0b

Counts

249 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
0.1b	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

rewrite46.0ms

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`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `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 → 230

Calls

4 calls:

1.0ms	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
9.0ms	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
15.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
10.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
89.0ms	(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
158.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
193.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify130.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	767	5084
1	3166	3826
2	5001	3733

prune481.0ms

Filtered

242 candidates to 132 candidates (54.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	242	11	253

Merged error: 0.0b

Counts

253 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
133×	`add-sqr-sqrt`
131×	`*-un-lft-identity`
123×	`add-cube-cbrt`
92×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
19×	`neg-mul-1`
11×	`fma-neg`
10×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `associate-l`
2×	`associate-/r/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `times-frac` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 285

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
156.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify163.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	797	8337
1	4394	5185
2	5001	5161

prune386.0ms

Filtered

297 candidates to 105 candidates (35.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	2	7	9
Picked	0	1	1
Done	1	0	1
Total	299	9	308

Merged error: 0.0b

Counts

308 → 9

regimes141.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample1.5s

Algorithm

intervals

Results

347.0ms	4861×	body	160	valid
290.0ms	16254×	pre	80	true
283.0ms	8254×	body	80	nan
140.0ms	1309×	body	320	valid
64.0ms	1830×	body	80	valid