Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	37×	body	1280	valid
7.0ms	191×	body	80	valid
7.0ms	33×	body	2560	valid
3.0ms	96×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

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:

63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

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

prune225.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
27.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite175.0ms

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:

22.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
57.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
136.0ms	(/ (/ (+ 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))))))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify100.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (78.0ms)

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

prune406.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.7b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
27.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite86.0ms

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×	`flip3--` `sqrt-prod` `flip--`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `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 → 72

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
39.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
144.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify64.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	469	942
1	2644	746
2	5001	738

prune216.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c) 4.0))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

195×	`times-frac`
92×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
87×	`add-cube-cbrt`
48×	`add-exp-log`
31×	`div-exp`
25×	`associate-/r*`
18×	`add-cbrt-cube`
17×	`div-inv`
10×	`add-log-exp`
9×	`cbrt-undiv`
8×	`1-exp`
6×	`pow1` `prod-exp`
5×	`rec-exp`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `cbrt-unprod` `inv-pow`

Counts

4 → 180

Calls

4 calls:

52.0ms	(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c) 4.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c) 4.0))
46.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify115.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	962	2811
1	4463	2486
2	5001	2326

prune373.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

regimes198.0ms

Accuracy

94.5% (1.3b remaining)

Error of 7.0b against oracle of 5.6b and baseline of 29.4b

bsearch176.0ms

Steps

Iters	Range	Point
6	4.231934083523606e+52	2.717919616353272e+53	2.043334298601045e+53
10	-1.5811508713279925e-284	-6.201918159587988e-296	-7.499564665356541e-290
9	-4.3398659734944224e+136	-6.188138656270848e+129	-4.2975228517561493e+130

Iters

Range

Point

4.231934083523606e+52

2.717919616353272e+53

2.043334298601045e+53

-1.5811508713279925e-284

-6.201918159587988e-296

-7.499564665356541e-290

-4.3398659734944224e+136

-6.188138656270848e+129

-4.2975228517561493e+130

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	33
1	55	33
2	55	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

228.0ms	1090×	body	2560	valid
212.0ms	5831×	body	80	valid
160.0ms	909×	body	1280	valid
96.0ms	2813×	body	80	nan
62.0ms	471×	body	640	valid
28.0ms	109×	body	5120	valid
23.0ms	231×	body	320	valid
9.0ms	128×	body	160	valid