Details

sample70.0ms

Algorithm

intervals

Results

16.0ms	122×	body	320	valid
13.0ms	498×	pre	80	true
11.0ms	242×	body	80	nan
8.0ms	95×	body	160	valid
2.0ms	12×	body	640	valid
2.0ms	27×	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

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: 52.8b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))
27.3b	(+ (- 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))
12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune230.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	2	103

Merged error: 0.1b

Counts

103 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* 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)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 158

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
17.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
152.0ms	(/ (/ (+ 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)))))

simplify126.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	674	2663
1	3471	2411
2	5001	2406

prune435.0ms

Filtered

170 candidates to 117 candidates (68.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	6	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0b

Counts

172 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* 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))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

121×	`prod-diff`
90×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
83×	`add-cube-cbrt`
64×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
37×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
12×	`neg-mul-1`
10×	`prod-exp` `cbrt-unprod`
7×	`pow1` `associate-r`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u`
3×	`sub-neg` `associate-l`
2×	`sqrt-div` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `fma-neg` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 212

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms	(- (* b b) (* (* 4.0 a) c))
108.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
155.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify148.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	773	5902
1	4284	3766
2	5001	3741

prune315.0ms

Filtered

224 candidates to 85 candidates (37.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	225	6	231

Merged error: 0b

Counts

231 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (* b b) (* (* 4.0 a) c))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
73×	`times-frac`
70×	`add-cube-cbrt`
61×	`prod-diff`
42×	`sqrt-prod`
30×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
9×	`div-exp` `div-inv`
7×	`neg-mul-1` `associate-/r` `associate-/l`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `1-exp` `prod-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `associate-/l/`

Counts

4 → 209

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series379.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
177.0ms	(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
49.0ms	(- (* b b) (* (* 4.0 a) c))

simplify103.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	757	4277
1	3241	3087
2	5001	3006

prune357.0ms

Filtered

221 candidates to 109 candidates (49.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	221	6	227

Merged error: 0b

Counts

227 → 6

regimes99.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample2.1s

Algorithm

intervals

Results

488.0ms	3591×	body	320	valid
436.0ms	16149×	pre	80	true
368.0ms	8149×	body	80	nan
273.0ms	2944×	body	160	valid
94.0ms	523×	body	640	valid
45.0ms	942×	body	80	valid