Details

sample54.0ms

Algorithm

intervals

Results

11.0ms	34×	body	2560	valid
11.0ms	209×	body	80	valid
5.0ms	22×	body	1280	valid
4.0ms	18×	body	640	valid
4.0ms	79×	body	80	nan
0.0ms	4×	body	160	valid
0.0ms	3×	body	320	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: 34.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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:

37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune293.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
4.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
55.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
30.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
176.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify127.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	674	2663
1	3462	2412
2	5001	2406

prune475.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
14.1b	(/ (* 2.0 a) (* 4.0 (* a c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

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:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (75.0ms)

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

prune322.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite58.0ms

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:

28.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (54.0ms)

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

prune298.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes256.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.3b

bsearch188.0ms

Steps

Iters	Range	Point
8	1.9559514031553493e+101	2.0413668072230428e+104	9.373511171447418e+103
9	1.0311906074547519e-259	1.091011630730822e-254	1.0417939395900796e-259
9	-2.3467190644739184e+107	-3.2019781887028674e+101	-1.7431685240570133e+102

Iters

Range

Point

1.9559514031553493e+101

2.0413668072230428e+104

9.373511171447418e+103

1.0311906074547519e-259

1.091011630730822e-254

1.0417939395900796e-259

-2.3467190644739184e+107

-3.2019781887028674e+101

-1.7431685240570133e+102

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	25
1	45	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

246.0ms	1070×	body	2560	valid
232.0ms	5839×	body	80	valid
166.0ms	884×	body	1280	valid
108.0ms	2849×	body	80	nan
76.0ms	496×	body	640	valid
28.0ms	102×	body	5120	valid
24.0ms	220×	body	320	valid
7.0ms	103×	body	160	valid