Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	36×	body	2560	valid
6.0ms	187×	body	80	valid
3.0ms	22×	body	1280	valid
3.0ms	76×	body	80	nan
1.0ms	5×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune254.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.2b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
150.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
188.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune518.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.3b	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
5.2b	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

3063×	`times-frac`
1689×	`add-sqr-sqrt`
1446×	`*-un-lft-identity`
1204×	`add-cube-cbrt`
242×	`difference-of-squares`
237×	`associate-/l*`
124×	`sqrt-prod`
121×	`distribute-lft-out--`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1025

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
57.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
97.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify237.0ms

Algorithm

egg-herbie

Counts

1037 → 1037

Iterations

Useful iterations: 1 (64.0ms)

Iter	Nodes	Cost
0	4259	21067
1	5001	20479

prune2.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.9b

localize17.0ms

Local error

Found 4 expressions with local error:

5.5b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
6.4b	(/ (/ 1 (/ (/ (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2) a) c)) a)
15.2b	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

3330×	`times-frac`
1934×	`add-sqr-sqrt`
1497×	`*-un-lft-identity`
1279×	`add-cube-cbrt`
327×	`difference-of-squares`
242×	`associate-/l*`
224×	`log-prod` `exp-sum`
115×	`sqrt-prod`
109×	`distribute-lft-out--`
53×	`div-inv`
36×	`add-exp-log`
25×	`div-exp`
18×	`add-cbrt-cube`
10×	`cbrt-undiv`
7×	`pow1`
6×	`exp-prod` `add-log-exp`
4×	`sqrt-div` `associate-/r/`
3×	`rec-exp` `flip3--` `1-exp` `associate-/r*` `log-pow` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `diff-log` `clear-num` `rem-exp-log` `associate-/l/`

Counts

4 → 1049

Calls

4 calls:

6.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms	(/ (/ 1 (/ (/ (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2) a) c)) a)
10.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
98.0ms	(/ (/ 1 (/ (/ (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2) a) c)) a)
74.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify284.0ms

Algorithm

egg-herbie

Counts

1061 → 1061

Iterations

Useful iterations: 1 (75.0ms)

Iter	Nodes	Cost
0	4904	25555
1	5002	25501

prune3.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.9b

regimes246.0ms

Accuracy

82.7% (4.6b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 32.3b

bsearch74.0ms

Steps

Iters	Range		Point
6	1.7071993853452014e+98	1.0593861995340862e+99	1.0479007947857462e+99
8	-2.0898868129100636e-78	-1.06178241226232e-82	-4.653701756906352e-82

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

211.0ms	1069×	body	2560	valid
191.0ms	5770×	body	80	valid
149.0ms	923×	body	1280	valid
92.0ms	2853×	body	80	nan
57.0ms	463×	body	640	valid
30.0ms	127×	body	5120	valid
21.0ms	227×	body	320	valid
11.0ms	131×	body	160	valid