Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	30×	body	1280	valid
6.0ms	185×	body	80	valid
6.0ms	33×	body	2560	valid
3.0ms	97×	body	80	nan
2.0ms	18×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	2×	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: 31.9b

localize9.0ms

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))))
1.2b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

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:

70.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
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)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
61.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(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	3055
1	1826	2150
2	5001	2063

prune328.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize10.0ms

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))))
1.2b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

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:

45.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
61.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(- (* b_2 b_2) (* a c))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (63.0ms)

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

prune353.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

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))))
1.2b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
146×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
130×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
13×	`add-exp-log` `associate-l`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sqrt-div` `associate-*r/` `div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 292

Calls

4 calls:

99.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
30.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	906	7441
1	3295	4548
2	5001	4309

prune320.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.2b	(- (* b_2 b_2) (* a c))
6.2b	(+ (- (/ b_2 a)) (- (/ (sqrt (- (* b_2 b_2) (* a c))) a)))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
30×	`fma-def`
25×	`distribute-rgt-neg-in`
23×	`distribute-lft-neg-in`
15×	`sqrt-prod`
14×	`add-log-exp`
12×	`distribute-lft-out`
7×	`div-inv`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `neg-log` `sum-log` `log1p-expm1-u`
3×	`neg-mul-1` `flip3--` `associate-/r*` `flip--`
2×	`neg-sub0` `distribute-rgt-out` `associate-/l/` `distribute-neg-frac`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `associate-+r-` `sub-neg` `rem-sqrt-square` `distribute-neg-out` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-exp` `unsub-neg` `prod-diff` `frac-add` `clear-num` `flip-+`

Counts

4 → 142

Calls

4 calls:

16.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
8.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(+ (- (/ b_2 a)) (- (/ (sqrt (- (* b_2 b_2) (* a c))) a)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
29.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(+ (- (/ b_2 a)) (- (/ (sqrt (- (* b_2 b_2) (* a c))) a)))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	466	1014
1	1638	944
2	5002	931

prune377.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.1b

regimes150.0ms

Accuracy

84.7% (4.3b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 33.7b

bsearch79.0ms

Steps

Iters	Range		Point
10	8.043557394408689e+68	7.456819745307919e+79	7.351468977489713e+79
7	-1.316548984668948e-60	-1.056498470782689e-62	-2.8813430075089506e-61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	39	16
2	39	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

193.0ms	1070×	body	2560	valid
191.0ms	5935×	body	80	valid
132.0ms	860×	body	1280	valid
89.0ms	2988×	body	80	nan
49.0ms	429×	body	640	valid
29.0ms	121×	body	5120	valid
19.0ms	219×	body	320	valid
6.0ms	109×	body	160	valid