Details

sample61.0ms

Algorithm

intervals

Results

14.0ms	154×	body	160	valid
9.0ms	520×	pre	80	true
9.0ms	264×	body	80	nan
4.0ms	42×	body	320	valid
2.0ms	60×	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: 44.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite111.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
62.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	438	855
1	1702	750
2	5002	735

prune252.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (- b) (sqrt (- (* 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)))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`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`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
60.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
169.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify146.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	829	5121
1	3772	3863
2	5001	3860

prune574.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

180×	`prod-diff`
134×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
125×	`add-cube-cbrt`
95×	`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`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `sub-neg` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv`

Counts

4 → 286

Calls

4 calls:

89.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
31.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
137.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1007	8654
1	5001	5569

prune635.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 175

Calls

4 calls:

19.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
11.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
40.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify101.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	728	3239
1	3326	2118
2	5003	2079

prune372.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	12
1	21	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

342.0ms	4849×	body	160	valid
289.0ms	8347×	body	80	nan
282.0ms	16347×	pre	80	true
142.0ms	1336×	body	320	valid
64.0ms	1815×	body	80	valid