Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
6.0ms	187×	body	80	valid
5.0ms	31×	body	1280	valid
3.0ms	94×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	1×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize9.0ms

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))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

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)
4.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (66.0ms)

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

prune345.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

localize12.0ms

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))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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:

14.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
32.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (61.0ms)

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

prune381.0ms

Filtered

269 candidates to 112 candidates (41.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
5.6b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
23.1b	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

91×	`prod-diff`
75×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
68×	`add-cube-cbrt` `log-prod` `exp-sum`
37×	`sqrt-prod`
31×	`distribute-rgt-neg-in`
30×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`neg-mul-1` `add-log-exp`
7×	`pow1`
6×	`exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log` `log-pow` `difference-of-squares`
2×	`sub-neg` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `neg-log` `rem-exp-log`

Counts

4 → 178

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
67.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	535	4477
1	1473	2268
2	5002	2146

prune287.0ms

Filtered

190 candidates to 83 candidates (43.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.8b	(/ a (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
11.8b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
30×	`associate-/r*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
7×	`flip3--` `flip--`
6×	`fma-neg` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 219

Calls

4 calls:

8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(/ a (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
71.0ms	(/ a (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
180.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify130.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	780	3393
1	3942	3037
2	5001	3020

prune511.0ms

Filtered

231 candidates to 162 candidates (70.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.0b

regimes191.0ms

Accuracy

88% (3.4b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 34.3b

bsearch139.0ms

Steps

Iters	Range		Point
3	5.062782482725967e+112	6.853081242536654e+112	6.7411875700484855e+112
7	-2.1605152142522817e-113	-1.8017938791730603e-115	-2.125553485370055e-113
5	-1.1619433740097673e-94	-3.191731313316827e-95	-3.279454101187687e-95
8	-606286808183387.5	-10825241472.448856	-21584226661136.215

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	27
1	47	27
2	47	27

end0.0ms

sample1.0s

Algorithm

intervals

Results

220.0ms	1073×	body	2560	valid
200.0ms	5855×	body	80	valid
149.0ms	904×	body	1280	valid
91.0ms	2905×	body	80	nan
68.0ms	469×	body	640	valid
23.0ms	243×	body	320	valid
23.0ms	95×	body	5120	valid
7.0ms	116×	body	160	valid