Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	37×	body	2560	valid
6.0ms	184×	body	80	valid
5.0ms	36×	body	1280	valid
3.0ms	91×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 38.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite131.0ms

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:

76.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
29.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
54.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063

prune335.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune18.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

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:

47.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
9.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
30.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (64.0ms)

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

prune353.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.5b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 141

Calls

4 calls:

31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))
53.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	369	2603
1	1203	1735
2	5001	1648

prune345.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.5b

regimes193.0ms

Accuracy

86.1% (4.8b remaining)

Error of 10.5b against oracle of 5.7b and baseline of 39.9b

bsearch55.0ms

Steps

Iters	Range		Point
6	2.905752377093217e+53	1.5130510757279288e+54	1.4983382189642058e+54
6	-7.09976396972575e-70	-5.325167427794927e-71	-5.6439472304372656e-71

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

200.0ms	1059×	body	2560	valid
188.0ms	5915×	body	80	valid
127.0ms	880×	body	1280	valid
90.0ms	3014×	body	80	nan
52.0ms	461×	body	640	valid
27.0ms	122×	body	5120	valid
18.0ms	213×	body	320	valid
7.0ms	119×	body	160	valid