Details

sample40.0ms

Algorithm

intervals

Results

7.0ms	183×	body	80	valid
6.0ms	28×	body	2560	valid
5.0ms	29×	body	1280	valid
3.0ms	89×	body	80	nan
3.0ms	22×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	7×	body	160	valid
0.0ms	1×	body	320	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

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:

62.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

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

prune290.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite184.0ms

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))))
79.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- 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))
184.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify144.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	829	5119
1	3763	3863
2	5001	3860

prune525.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.5b	(/ (* 2.0 a) (* 4.0 (* a c)))
25.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
51×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
34×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`neg-mul-1`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 150

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	610	3042
1	3078	1945
2	5002	1857

prune289.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
25×	`add-exp-log`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
9×	`div-exp`
8×	`pow1`
7×	`neg-mul-1`
6×	`prod-exp`
5×	`flip3--` `associate-/r/` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `times-frac` `diff-log` `1-exp` `associate-/l*`
2×	`frac-times` `sub-neg` `pow-flip` `sqrt-div` `associate-*r/` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `associate-/r` `div-inv` `inv-pow`

Counts

4 → 162

Calls

4 calls:

78.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(- (* b b) (* (* 4.0 a) c))
42.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	613	3343
1	2374	2171
2	5002	2121

prune282.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.5b

regimes187.0ms

Accuracy

95% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 30.1b

bsearch212.0ms

Steps

Iters	Range	Point
8	3.1248942757642245e+89	1.1714167766929137e+92	6.09240124692818e+90
12	-2.833440705943036e-251	-4.668939852252329e-295	-2.1023086245622604e-293
10	-7.651517840437919e+135	-3.890563902308465e+123	-4.739386840053889e+131

Iters

Range

Point

3.1248942757642245e+89

1.1714167766929137e+92

6.09240124692818e+90

-2.833440705943036e-251

-4.668939852252329e-295

-2.1023086245622604e-293

-7.651517840437919e+135

-3.890563902308465e+123

-4.739386840053889e+131

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample1.2s

Algorithm

intervals

Results

238.0ms	1058×	body	2560	valid
223.0ms	5792×	body	80	valid
164.0ms	935×	body	1280	valid
104.0ms	2915×	body	80	nan
63.0ms	453×	body	640	valid
29.0ms	101×	body	5120	valid
27.0ms	225×	body	320	valid
8.0ms	113×	body	160	valid