Details

sample48.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
7.0ms	191×	body	80	valid
7.0ms	37×	body	1280	valid
3.0ms	96×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

70.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune242.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
27.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
62.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
131.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
167.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune433.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.7b	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`flip3--` `sqrt-prod` `flip--`
3×	`cbrt-undiv` `times-frac` `diff-log` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `clear-num` `associate-/r*` `flip-+` `div-inv`

Counts

4 → 72

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
58.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
134.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
64.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	486	961
1	2986	812
2	5001	807

prune386.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.8b	(/ (/ (* 4.0 (* a c)) 2.0) a)
27.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1` `div-inv`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 95

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
64.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	547	833
1	2713	755
2	5002	755

prune272.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.5b

regimes173.0ms

Accuracy

96% (0.9b remaining)

Error of 6.6b against oracle of 5.7b and baseline of 29.2b

bsearch199.0ms

Steps

Iters	Range	Point
10	1.0940858654514709e+88	1.774287867247786e+103	1.7521504885677008e+103
9	-7.604767348394258e-257	-1.5878992896022604e-264	-1.9415295134599817e-260
9	-4.3398659734944224e+136	-6.188138656270848e+129	-4.2975228517561493e+130

Iters

Range

Point

1.0940858654514709e+88

1.774287867247786e+103

1.7521504885677008e+103

-7.604767348394258e-257

-1.5878992896022604e-264

-1.9415295134599817e-260

-4.3398659734944224e+136

-6.188138656270848e+129

-4.2975228517561493e+130

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	25
1	45	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

244.0ms	1090×	body	2560	valid
226.0ms	5831×	body	80	valid
164.0ms	909×	body	1280	valid
99.0ms	2813×	body	80	nan
65.0ms	471×	body	640	valid
29.0ms	109×	body	5120	valid
24.0ms	231×	body	320	valid
9.0ms	128×	body	160	valid