Details

sample44.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
6.0ms	34×	body	1280	valid
5.0ms	25×	body	2560	valid
4.0ms	115×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite111.0ms

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:

67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
41.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune235.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.5b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite190.0ms

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:

23.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
87.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
58.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
140.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
173.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
64.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify112.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	640	2692
1	2944	2439
2	5001	2426

prune436.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.7b	(/ (* 2.0 a) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite67.0ms

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:

9.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	413	627
1	2231	543
2	5001	535

prune224.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
40×	`div-exp`
31×	`times-frac`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv`
10×	`add-log-exp`
6×	`rec-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod` `cbrt-unprod`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `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` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

41.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
41.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	660	1395
1	3283	1186
2	5001	1152

prune257.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.7b

regimes147.0ms

Accuracy

94% (1.4b remaining)

Error of 6.8b against oracle of 5.4b and baseline of 29.4b

bsearch158.0ms

Steps

Iters	Range	Point
9	1.7695728335377845e+74	3.738006738925262e+80	2.0572050780400815e+80
6	-3.405927582379186e-150	-4.860750269204613e-151	-4.9276367402926466e-151
7	-3.260864156300871e+111	-2.161458270686658e+109	-2.3929031452945402e+111

Iters

Range

Point

1.7695728335377845e+74

3.738006738925262e+80

2.0572050780400815e+80

-3.405927582379186e-150

-4.860750269204613e-151

-4.9276367402926466e-151

-3.260864156300871e+111

-2.161458270686658e+109

-2.3929031452945402e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	36
1	49	36

end0.0ms

sample1.2s

Algorithm

intervals

Results

233.0ms	1059×	body	2560	valid
212.0ms	5787×	body	80	valid
162.0ms	896×	body	1280	valid
113.0ms	2934×	body	80	nan
67.0ms	490×	body	640	valid
30.0ms	114×	body	5120	valid
24.0ms	228×	body	320	valid
8.0ms	120×	body	160	valid