Details

sample59.0ms

Algorithm

intervals

Results

15.0ms	134×	body	320	valid
9.0ms	514×	pre	80	true
9.0ms	258×	body	80	nan
6.0ms	78×	body	160	valid
3.0ms	19×	body	640	valid
1.0ms	25×	body	80	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: 52.7b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
22.6b	(+ (- 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)))
11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune242.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	4	103

Merged error: 0.1b

Counts

103 → 4

localize16.0ms

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))))
0.2b	(/ (/ (+ 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)))))

rewrite59.0ms

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))
11.0ms	(- (- 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))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
186.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify160.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (117.0ms)

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

prune505.0ms

Filtered

243 candidates to 137 candidates (56.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	237	6	243
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	240	7	247

Merged error: 0b

Counts

247 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

180×	`prod-diff`
152×	`add-exp-log`
135×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
125×	`add-cube-cbrt`
92×	`sqrt-prod` `add-cbrt-cube`
73×	`prod-exp`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
46×	`div-exp`
41×	`cbrt-unprod`
26×	`cbrt-undiv`
19×	`neg-mul-1`
10×	`fma-neg`
9×	`pow1`
8×	`rec-exp` `1-exp` `add-log-exp`
7×	`associate-r`
5×	`flip3--` `times-frac` `associate-l` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `log1p-expm1-u` `associate-/l` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `div-inv`
2×	`pow-flip` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `associate-/r`
1×	`associate--l-` `neg-sub0` `neg-log` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 343

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
23.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
90.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1248	10439
1	5002	7042

prune403.0ms

Filtered

355 candidates to 108 candidates (30.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	354	1	355
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	355	7	362

Merged error: 0b

Counts

362 → 7

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))))
0.2b	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 311

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
178.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
116.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify143.0ms

Algorithm

egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1036	8821
1	4170	5621
2	5001	5595

prune378.0ms

Filtered

323 candidates to 116 candidates (35.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	324	6	330

Merged error: 0b

Counts

330 → 6

regimes89.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	10
1	22	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

394.0ms	3645×	body	320	valid
302.0ms	16187×	pre	80	true
288.0ms	8187×	body	80	nan
218.0ms	2994×	body	160	valid
80.0ms	521×	body	640	valid
30.0ms	840×	body	80	valid