Details

sample361.0ms

Algorithm

intervals

Results

7.0ms	191×	body	80	valid
6.0ms	34×	body	2560	valid
5.0ms	36×	body	1280	valid
3.0ms	96×	body	80	nan
1.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

65.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
30.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune226.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.9b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.6b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
27.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
51.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
125.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
152.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269

prune477.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.9b	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
27.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp` `sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`cbrt-undiv`
8×	`add-log-exp`
6×	`prod-exp` `div-inv`
5×	`pow1`
4×	`associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `neg-log` `associate-/r/` `associate-/l/`

Counts

4 → 180

Calls

4 calls:

22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
34.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
163.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
139.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
53.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	814	2582
1	3787	2402
2	5001	2379

prune411.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
32×	`add-exp-log`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
17×	`div-exp`
13×	`add-cbrt-cube`
10×	`add-log-exp`
7×	`1-exp` `associate-/r*`
6×	`pow1` `prod-exp`
5×	`cbrt-undiv` `div-inv`
4×	`rec-exp` `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 → 104

Calls

4 calls:

44.0ms	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
10.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
29.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	521	1129
1	2179	976
2	5001	931

prune185.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.5b

regimes193.0ms

Accuracy

82.2% (4.2b remaining)

Error of 9.8b against oracle of 5.6b and baseline of 29.2b

bsearch94.0ms

Steps

Iters	Range		Point
10	1.0940858654514709e+88	1.774287867247786e+103	9.826999448380506e+96
9	-1.1345718484749e-82	-1.1127264026331332e-88	-1.3696943711263392e-83

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

196.0ms	1092×	body	2560	valid
189.0ms	5828×	body	80	valid
139.0ms	910×	body	1280	valid
86.0ms	2813×	body	80	nan
58.0ms	470×	body	640	valid
24.0ms	109×	body	5120	valid
20.0ms	235×	body	320	valid
7.0ms	126×	body	160	valid