Details

sample358.0ms

Algorithm

intervals

Results

6.0ms	34×	body	2560	valid
6.0ms	187×	body	80	valid
4.0ms	29×	body	1280	valid
4.0ms	99×	body	80	nan
2.0ms	16×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify13.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite135.0ms

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:

72.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (48.0ms)

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

prune347.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

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:

46.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
75.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify97.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (67.0ms)

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

prune359.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))))
0.5b	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
0.8b	(fma b_2 b_2 (- (* a c)))
20.6b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite68.0ms

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:

28.0ms	(/ 1 (/ a (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))))
22.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
0.0ms	(fma b_2 b_2 (- (* a c)))
2.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (/ a (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))))
86.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
49.0ms	(fma b_2 b_2 (- (* a c)))
74.0ms	(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

prune349.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
0.5b	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
0.8b	(fma b_2 b_2 (- (* a c)))
20.6b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite70.0ms

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:

41.0ms	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
20.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
0.0ms	(fma b_2 b_2 (- (* a c)))
2.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
79.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
46.0ms	(fma b_2 b_2 (- (* a c)))
75.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

simplify65.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (39.0ms)

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

prune287.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.9b

regimes176.0ms

Accuracy

84.6% (4.3b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 33.6b

bsearch72.0ms

Steps

Iters	Range		Point
7	2.5938763934072053e+128	9.952100372240566e+129	8.230710165919531e+129
7	-3.223583531111825e-78	-6.174882317581048e-80	-7.034196314912654e-79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	17
1	50	17
2	50	17

end0.0ms

sample1.0s

Algorithm

intervals

Results

185.0ms	1040×	body	2560	valid
175.0ms	5788×	body	80	valid
139.0ms	916×	body	1280	valid
88.0ms	2947×	body	80	nan
51.0ms	434×	body	640	valid
28.0ms	125×	body	5120	valid
22.0ms	256×	body	320	valid
9.0ms	148×	body	160	valid