Details

sample279.0ms

Algorithm

intervals

Results

8.0ms	196×	body	80	valid
7.0ms	31×	body	2560	valid
5.0ms	32×	body	1280	valid
4.0ms	113×	body	80	nan
1.0ms	11×	body	320	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	640	valid
0.0ms	1×	body	160	valid

simplify12.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
25.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

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:

14.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063

prune369.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
25.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

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:

16.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(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

prune382.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))))
0.6b	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
1.8b	(fma b_2 b_2 (- (* a c)))
25.8b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
60×	`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`
10×	`fma-neg`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`neg-mul-1` `div-exp`
6×	`pow1`
5×	`flip3--` `flip--` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `diff-log` `1-exp`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `fma-udef` `inv-pow`

Counts

4 → 249

Calls

4 calls:

12.0ms	(/ 1 (/ a (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))))
8.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
1.0ms	(fma b_2 b_2 (- (* a c)))
2.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1 (/ a (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))))
82.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
44.0ms	(fma b_2 b_2 (- (* a c)))
73.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

simplify89.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	699	4483
1	2862	3359
2	5002	3174

prune379.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
0.6b	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
1.8b	(fma b_2 b_2 (- (* a c)))
25.8b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `fma-udef` `div-inv`

Counts

4 → 163

Calls

4 calls:

12.0ms	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
12.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
1.0ms	(fma b_2 b_2 (- (* a c)))
2.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
80.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
40.0ms	(fma b_2 b_2 (- (* a c)))
73.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

simplify61.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	478	2988
1	1487	2085
2	5002	1997

prune315.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.0b

regimes207.0ms

Accuracy

81.3% (5.1b remaining)

Error of 10.7b against oracle of 5.6b and baseline of 32.7b

bsearch158.0ms

Steps

Iters	Range		Point
6	389373804.8346531	2491217878.346211	2445759453.473797
10	-2.526452692857176e-177	-2.3364497658215877e-190	-2.4847719492317672e-177
5	-6.06156204214849e-106	-2.323968486468817e-106	-2.369076111042092e-106
7	-4.778085389028276e+17	-4696503048995838.0	-7373025010395948.0

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	24
1	59	24
2	59	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

225.0ms	1087×	body	2560	valid
213.0ms	5897×	body	80	valid
140.0ms	842×	body	1280	valid
99.0ms	2915×	body	80	nan
57.0ms	434×	body	640	valid
31.0ms	122×	body	5120	valid
23.0ms	228×	body	320	valid
8.0ms	116×	body	160	valid