Details

sample52.0ms

Algorithm

intervals

Results

12.0ms	516×	pre	80	true
10.0ms	146×	body	160	valid
9.0ms	260×	body	80	nan
4.0ms	110×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(- (* b b) (* (* 4.0 a) c))
37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5002	735

prune258.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

18.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
48.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
183.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify155.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	832	5099
1	3967	3830
2	5001	3828

prune553.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.6b	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b	(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
138×	`times-frac`
96×	`*-un-lft-identity`
60×	`difference-of-squares`
56×	`add-cube-cbrt`
52×	`cbrt-prod`
50×	`sqrt-prod`
42×	`associate-/l*`
20×	`distribute-lft-out--`
19×	`add-exp-log` `add-cbrt-cube`
16×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*` `sqr-pow`
10×	`distribute-rgt-neg-in`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-mult` `cbrt-div` `frac-2neg` `unpow3` `prod-exp` `clear-num` `cbrt-unprod`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `pow-exp` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 217

Calls

4 calls:

89.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
9.0ms	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
5.0ms	(pow (- (* b b) (* (* 4.0 a) c)) 3)

series466.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
181.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
44.0ms	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
93.0ms	(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify151.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	880	4267
1	4566	3879
2	5001	3878

prune698.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 (* a c)) a)
0.2b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(- (* b b) (* (* 4.0 a) c))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
91×	`*-un-lft-identity`
57×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
17×	`distribute-lft-out`
15×	`associate-/r*` `div-inv`
10×	`cbrt-undiv` `div-exp`
8×	`neg-mul-1` `associate-/l*` `add-log-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `sum-log` `flip--` `associate-/l/`

Counts

4 → 184

Calls

4 calls:

8.0ms	(/ (* 4.0 (* a c)) a)
8.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(- (* b b) (* (* 4.0 a) c))

series284.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* 4.0 (* a c)) a)
79.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
150.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms	(- (* b b) (* (* 4.0 a) c))

simplify114.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	839	2756
1	4554	2476
2	5002	2473

prune508.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes128.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	13
1	43	13
2	43	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

310.0ms	4403×	body	160	valid
297.0ms	16455×	pre	80	true
275.0ms	8455×	body	80	nan
125.0ms	3597×	body	80	valid