Details

sample59.0ms

Algorithm

intervals

Results

12.0ms	162×	body	160	valid
10.0ms	531×	pre	80	true
10.0ms	275×	body	80	nan
8.0ms	40×	body	320	valid
2.0ms	54×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

localize11.0ms

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)))) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
40.3b	(+ (- 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)))
37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune264.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

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)))))

rewrite102.0ms

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:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
45.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify160.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (118.0ms)

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

prune575.0ms

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

rewrite113.0ms

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:

52.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
159.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1010	8634
1	5001	5618

prune469.0ms

Pruning

8 alts after pruning (8 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	(/ (/ (/ (* 4.0 (* a c)) 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))

rewrite90.0ms

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:

8.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
39.0ms	(/ (/ (/ (* 4.0 (* a c)) 2.0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))

series296.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (/ (* 4.0 (* a c)) 2.0) a)
154.0ms	(/ (/ (/ (* 4.0 (* a c)) 2.0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms	(- (* b b) (* (* 4.0 a) c))

simplify91.0ms

Algorithm

egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1395	8363
1	5001	7159

prune886.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes109.0ms

Accuracy

0% (0.1b 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	17	9
1	17	9

end0.0ms

sample1.5s

Algorithm

intervals

Results

351.0ms	4789×	body	160	valid
306.0ms	16372×	pre	80	true
296.0ms	8372×	body	80	nan
147.0ms	1339×	body	320	valid
70.0ms	1872×	body	80	valid