Details

sample60.0ms

Algorithm

intervals

Results

12.0ms	523×	pre	80	true
10.0ms	153×	body	160	valid
8.0ms	267×	body	80	nan
6.0ms	56×	body	320	valid
2.0ms	47×	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: 45.9b

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))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite110.0ms

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:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
40.0ms	(- (* b b) (* (* 4.0 a) c))
98.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
70.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

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

prune250.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series412.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
136.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
168.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify156.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (119.0ms)

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

prune567.0ms

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

rewrite195.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
87.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
54.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
140.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1010	8634
1	5001	5618

prune485.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b	(/ 2.0 (* a c))
0.3b	(/ 4.0 (/ 2.0 (* a c)))
0.3b	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

389×	`times-frac`
281×	`add-sqr-sqrt`
255×	`*-un-lft-identity`
169×	`add-cube-cbrt`
117×	`add-exp-log`
85×	`associate-r`
77×	`add-cbrt-cube`
62×	`div-exp`
42×	`distribute-lft-out--` `difference-of-squares`
37×	`cbrt-undiv`
33×	`associate-/l*`
27×	`prod-exp`
26×	`associate-l`
21×	`distribute-rgt-neg-in` `sqrt-prod`
19×	`div-inv`
17×	`cbrt-unprod`
16×	`associate-/r/`
11×	`associate-/r*`
8×	`unswap-sqr`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 368

Calls

4 calls:

65.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
7.0ms	(/ 2.0 (* a c))
12.0ms	(/ 4.0 (/ 2.0 (* a c)))
155.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series289.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
19.0ms	(/ 2.0 (* a c))
17.0ms	(/ 4.0 (/ 2.0 (* a c)))
142.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify81.0ms

Algorithm

egg-herbie

Counts

380 → 380

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1494	5557
1	5001	4952

prune878.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes129.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	25	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

327.0ms	4898×	body	160	valid
288.0ms	16357×	pre	80	true
272.0ms	8357×	body	80	nan
133.0ms	1294×	body	320	valid
61.0ms	1808×	body	80	valid