Details

sample39.0ms

Algorithm

intervals

Results

10.0ms	36×	body	2560	valid
6.0ms	187×	body	80	valid
4.0ms	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

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize9.0ms

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)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

15.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	549	3056
1	1814	2150
2	5001	2063

prune353.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
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)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 257

Calls

4 calls:

15.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	770	4550
1	3215	3424
2	5002	3236

prune367.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize11.0ms

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)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

15.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series247.0ms

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))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	549	3056
1	1814	2150
2	5001	2063

prune314.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
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)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

309×	`times-frac`
268×	`add-sqr-sqrt`
267×	`*-un-lft-identity`
179×	`add-cube-cbrt`
139×	`sqrt-prod`
61×	`prod-diff`
44×	`distribute-lft-out--` `difference-of-squares`
43×	`distribute-rgt-neg-in`
27×	`associate-/r*`
21×	`distribute-lft-neg-in`
15×	`associate-/r/`
11×	`fma-neg`
10×	`flip3--` `flip--` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv`
7×	`neg-mul-1`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `div-exp`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num`

Counts

4 → 335

Calls

4 calls:

18.0ms	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
33.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

347 → 347

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	885	6487
1	3878	4990
2	5001	4588

prune377.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.0b

regimes202.0ms

Accuracy

84.7% (4.4b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 34.7b

bsearch78.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	17
1	44	17
2	44	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

214.0ms	1069×	body	2560	valid
197.0ms	5770×	body	80	valid
156.0ms	923×	body	1280	valid
92.0ms	2853×	body	80	nan
64.0ms	463×	body	640	valid
36.0ms	127×	body	5120	valid
22.0ms	227×	body	320	valid
8.0ms	131×	body	160	valid