Details

sample54.0ms

Algorithm

intervals

Results

11.0ms	156×	body	160	valid
10.0ms	502×	pre	80	true
8.0ms	246×	body	80	nan
4.0ms	40×	body	320	valid
2.0ms	60×	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: 42.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite35.0ms

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)))
4.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(- (* b b) (* (* 4.0 a) c))
111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
85.0ms	(+ (- 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

prune268.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

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

rewrite57.0ms

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:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
194.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify151.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	832	5100
1	3967	3830
2	5001	3828

prune564.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
132×	`add-sqr-sqrt` `*-un-lft-identity`
124×	`add-cube-cbrt`
92×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
9×	`pow1`
7×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `times-frac` `diff-log` `div-exp` `pow-prod-down` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `flip3-+` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv`

Counts

4 → 285

Calls

4 calls:

17.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
151.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify88.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1010	8635
1	5001	5618

prune469.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize14.0ms

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

448×	`times-frac`
307×	`add-sqr-sqrt` `*-un-lft-identity`
199×	`add-cube-cbrt`
61×	`prod-diff`
57×	`sqrt-prod`
54×	`distribute-lft-out--` `difference-of-squares`
48×	`distribute-rgt-neg-in`
38×	`add-exp-log` `add-cbrt-cube` `div-inv`
32×	`associate-/l*`
21×	`distribute-lft-neg-in`
19×	`cbrt-undiv` `div-exp`
11×	`fma-neg`
10×	`associate-/r*` `add-log-exp`
7×	`neg-mul-1`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `frac-2neg` `clear-num` `associate-/r/` `associate-/l/`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 390

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
22.0ms	(/ (/ (/ (* 4.0 (* a c)) 2.0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
153.0ms	(/ (/ (/ (* 4.0 (* a c)) 2.0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1395	8363
1	5001	7159

prune895.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes123.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	26	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

345.0ms	4842×	body	160	valid
308.0ms	16172×	pre	80	true
274.0ms	8172×	body	80	nan
140.0ms	1320×	body	320	valid
66.0ms	1838×	body	80	valid