Details

sample38.0ms

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

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

prune2.0ms

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)))

rewrite52.0ms

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:

33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
2.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune224.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

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)))

rewrite95.0ms

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:

14.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
138.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
174.0ms	(/ (+ 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

prune411.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize16.0ms

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)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
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` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

2.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- 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)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	429	637
1	2471	542
2	5003	534

prune205.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (* (/ 2.0 4.0) (/ 1 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)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-exp-log`
51×	`prod-exp`
44×	`div-exp`
29×	`add-cbrt-cube`
16×	`rec-exp` `1-exp`
14×	`associate-/r/`
12×	`add-sqr-sqrt`
11×	`pow1` `frac-times` `*-un-lft-identity`
10×	`cbrt-undiv` `add-log-exp`
9×	`cbrt-unprod`
8×	`flip3--` `flip--`
7×	`add-cube-cbrt` `associate-*l/`
5×	`associate-*r/`
4×	`sqrt-prod`
3×	`pow-flip` `times-frac` `diff-log` `pow-prod-down` `un-div-inv` `associate-/l*`
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-/r*` `div-inv` `inv-pow`

Counts

4 → 116

Calls

4 calls:

60.0ms	(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
2.0ms	(- (* 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)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	739	1499
1	3418	1216
2	5001	1210

prune238.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

regimes172.0ms

Accuracy

92.4% (1.9b remaining)

Error of 7.2b against oracle of 5.3b and baseline of 29.8b

bsearch131.0ms

Steps

Iters	Range	Point
5	5.10808278574109e+145	1.867402505400959e+146	1.6656334680497556e+146
7	-2.782279184329671e-219	-5.296311981150072e-221	-1.0621980184587312e-219
7	-2.963931757502914e+119	-3.3757792073266624e+117	-3.439785982885987e+117

Iters

Range

Point

5.10808278574109e+145

1.867402505400959e+146

1.6656334680497556e+146

-2.782279184329671e-219

-5.296311981150072e-221

-1.0621980184587312e-219

-2.963931757502914e+119

-3.3757792073266624e+117

-3.439785982885987e+117

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	28
1	47	28

end0.0ms

sample1.1s

Algorithm

intervals

Results

255.0ms	1073×	body	2560	valid
229.0ms	5759×	body	80	valid
166.0ms	914×	body	1280	valid
107.0ms	2900×	body	80	nan
65.0ms	451×	body	640	valid
27.0ms	100×	body	5120	valid
25.0ms	229×	body	320	valid
10.0ms	132×	body	160	valid