Details

sample62.0ms

Algorithm

intervals

Results

13.0ms	509×	pre	80	true
12.0ms	119×	body	320	valid
9.0ms	253×	body	80	nan
6.0ms	89×	body	160	valid
3.0ms	19×	body	640	valid
1.0ms	29×	body	80	valid

simplify12.0ms

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: 53.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite59.0ms

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:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune252.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite105.0ms

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:

19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series464.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
187.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify161.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (120.0ms)

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

prune570.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
102×	`*-un-lft-identity`
70×	`add-cube-cbrt`
61×	`prod-diff`
51×	`add-exp-log`
46×	`times-frac`
38×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
27×	`associate-l` `add-cbrt-cube`
21×	`distribute-lft-neg-in`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`neg-mul-1` `associate-r` `associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`diff-log` `div-inv` `associate-/l*`
2×	`sub-neg` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 226

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
148.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify180.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	924	4824
1	4731	3436
2	5001	3436

prune544.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ (* 4.0 (* a c)) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
51×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
34×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`neg-mul-1`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 150

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))

series208.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
46.0ms	(- (* b b) (* (* 4.0 a) c))

simplify99.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	617	3042
1	3211	1947
2	5002	1867

prune336.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	25	9
2	27	9
3	27	9

end0.0ms

sample1.6s

Algorithm

intervals

Results

380.0ms	3659×	body	320	valid
300.0ms	16157×	pre	80	true
274.0ms	8157×	body	80	nan
195.0ms	2849×	body	160	valid
75.0ms	555×	body	640	valid
32.0ms	937×	body	80	valid