Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	189×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	87×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 34.0b

localize14.0ms

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)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

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:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune296.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.5b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

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:

16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
147.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
181.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify131.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (94.0ms)

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

prune514.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

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:

3.0ms	(- (* b b) (* 4.0 (* a c)))
19.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify88.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	597	3032
1	2832	1946
2	5002	1857

prune307.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite61.0ms

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)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
50.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify78.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	614	3343
1	2331	2171
2	5002	2121

prune299.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

regimes214.0ms

Accuracy

93.4% (1.6b remaining)

Error of 6.9b against oracle of 5.3b and baseline of 30.0b

bsearch153.0ms

Steps

Iters	Range	Point
6	4.706455236749836e+29	5.491842449186372e+30	5.349311795482947e+30
8	-2.235079772666708e-277	-1.6616892678067201e-280	-6.223133960169616e-279
7	-2.963931757502914e+119	-3.3757792073266624e+117	-5.955152059551362e+118

Iters

Range

Point

4.706455236749836e+29

5.491842449186372e+30

5.349311795482947e+30

-2.235079772666708e-277

-1.6616892678067201e-280

-6.223133960169616e-279

-2.963931757502914e+119

-3.3757792073266624e+117

-5.955152059551362e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	46	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

242.0ms	1073×	body	2560	valid
230.0ms	5759×	body	80	valid
172.0ms	914×	body	1280	valid
107.0ms	2900×	body	80	nan
67.0ms	451×	body	640	valid
28.0ms	100×	body	5120	valid
24.0ms	229×	body	320	valid
10.0ms	132×	body	160	valid