Details

sample41.0ms

Algorithm

intervals

Results

7.0ms	33×	body	2560	valid
7.0ms	186×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	6×	body	160	valid

simplify12.0ms

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: 34.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

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:

62.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	405	780
1	1563	685
2	5001	674

prune227.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.4b	(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))))
79.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
54.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
190.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune428.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0b	(/ (* 2.0 a) (* 4.0 (* a c)))
22.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (59.0ms)

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

prune223.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-exp-log`
166×	`div-exp`
119×	`prod-exp`
64×	`1-exp`
60×	`add-cbrt-cube`
34×	`rec-exp`
31×	`times-frac`
26×	`cbrt-undiv`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`cbrt-unprod`
14×	`associate-/r/`
13×	`associate-/l*`
11×	`frac-times`
10×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`associate-*l/`
5×	`pow1` `associate-*r/`
4×	`sqrt-prod`
3×	`diff-log` `un-div-inv` `div-inv`
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*` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

66.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1172	2503
1	5001	2016

prune284.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

regimes196.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.5b

bsearch150.0ms

Steps

Iters	Range	Point
7	1.2310742480127578e+144	1.3446930168628618e+146	1.458057835821772e+144
8	-4.3329860630795565e-185	-1.209307133318773e-187	-3.3193805664383666e-186
7	-2.3419197238566892e+109	-5.519096697972622e+107	-2.2237630570465103e+109

Iters

Range

Point

1.2310742480127578e+144

1.3446930168628618e+146

1.458057835821772e+144

-4.3329860630795565e-185

-1.209307133318773e-187

-3.3193805664383666e-186

-2.3419197238566892e+109

-5.519096697972622e+107

-2.2237630570465103e+109

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	36
1	47	36

end0.0ms

sample1.2s

Algorithm

intervals

Results

235.0ms	1052×	body	2560	valid
220.0ms	5865×	body	80	valid
167.0ms	932×	body	1280	valid
98.0ms	2817×	body	80	nan
64.0ms	453×	body	640	valid
30.0ms	113×	body	5120	valid
24.0ms	235×	body	320	valid
8.0ms	120×	body	160	valid