Details

sample37.0ms

Algorithm

intervals

Results

6.0ms	30×	body	2560	valid
6.0ms	172×	body	80	valid
5.0ms	35×	body	1280	valid
3.0ms	103×	body	80	nan
2.0ms	18×	body	640	valid
1.0ms	6×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	7×	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: 34.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite72.0ms

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:

40.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (46.0ms)

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

prune340.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite63.0ms

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:

28.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
35.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (65.0ms)

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

prune372.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
569×	`add-sqr-sqrt`
568×	`*-un-lft-identity`
396×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
76×	`sqrt-prod`
64×	`distribute-rgt-neg-in`
61×	`prod-diff`
44×	`add-exp-log`
43×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/r*`
21×	`distribute-lft-neg-in`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 548

Calls

4 calls:

36.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (/ 1 a) (/ 1 (- (- 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))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

560 → 560

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1887	10995
1	5001	9278

prune733.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

0.0ms	(cbrt a)
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt a)
32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	430	2499
1	1359	1621
2	5001	1533

prune279.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

regimes232.0ms

Accuracy

84.3% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 34.3b

bsearch62.0ms

Steps

Iters	Range		Point
6	2.6216430800597077e+98	1.6496650416179864e+99	1.3176462918432122e+99
6	-4.147465441909223e-81	-6.416385900146894e-82	-4.011579732710567e-81

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample991.0ms

Algorithm

intervals

Results

202.0ms	1041×	body	2560	valid
195.0ms	5848×	body	80	valid
142.0ms	879×	body	1280	valid
85.0ms	2867×	body	80	nan
62.0ms	487×	body	640	valid
29.0ms	118×	body	5120	valid
23.0ms	228×	body	320	valid
7.0ms	110×	body	160	valid