Details

sample44.0ms

Algorithm

intervals

Results

7.0ms	191×	body	80	valid
7.0ms	33×	body	2560	valid
6.0ms	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

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize17.0ms

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))))

rewrite108.0ms

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:

65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
39.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735

prune291.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize15.0ms

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))))

rewrite190.0ms

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:

28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
57.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
132.0ms	(/ (/ (+ 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))))))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify134.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	818	5119
1	3560	3863
2	5001	3860

prune521.0ms

Pruning

9 alts after pruning (8 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)))))
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))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `clear-num` `associate-/r*` `flip-+` `div-inv`

Counts

4 → 152

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
54.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
138.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
62.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify126.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	663	3384
1	3444	2233
2	5001	2228

prune346.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

localize13.0ms

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))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
62×	`add-cube-cbrt`
61×	`prod-diff`
34×	`sqrt-prod`
33×	`times-frac`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp` `associate-/l*`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 175

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify94.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	718	3233
1	3185	2119
2	5002	2079

prune552.0ms

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 5.6b and baseline of 29.2b

bsearch186.0ms

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

243.0ms	1090×	body	2560	valid
226.0ms	5831×	body	80	valid
159.0ms	909×	body	1280	valid
103.0ms	2813×	body	80	nan
68.0ms	471×	body	640	valid
32.0ms	109×	body	5120	valid
24.0ms	231×	body	320	valid
9.0ms	128×	body	160	valid