Details

sample61.0ms

Algorithm

intervals

Results

13.0ms	122×	body	320	valid
12.0ms	228×	body	80	nan
9.0ms	484×	pre	80	true
6.0ms	88×	body	160	valid
2.0ms	15×	body	640	valid
1.0ms	31×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

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))
26.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite60.0ms

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))
36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms	(- (* b b) (* (* 4.0 a) c))
111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms	(+ (- 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

prune245.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

4 alts after pruning (4 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))
0.3b	(/ (+ 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))

rewrite109.0ms

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:

17.0ms	(- (- 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)))))
47.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series455.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
184.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
146.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify150.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (114.0ms)

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

prune542.0ms

Filtered

243 candidates to 137 candidates (56.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-exp-log`
121×	`prod-diff`
92×	`add-cbrt-cube`
90×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
73×	`prod-exp`
62×	`distribute-rgt-in` `distribute-lft-in`
61×	`sqrt-prod`
46×	`div-exp`
41×	`cbrt-unprod`
37×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
26×	`cbrt-undiv`
12×	`neg-mul-1`
9×	`pow1`
8×	`rec-exp` `1-exp`
7×	`associate-r`
6×	`add-log-exp`
5×	`flip3--` `times-frac` `associate-l` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `div-inv`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `distribute-lft-out--` `difference-of-squares`
1×	`fma-neg` `diff-log` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 269

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
64.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
82.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
146.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
86.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1280	7983
1	5001	5713

prune390.0ms

Filtered

281 candidates to 93 candidates (33.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

304×	`times-frac`
194×	`add-exp-log`
191×	`add-sqr-sqrt` `*-un-lft-identity`
107×	`add-cube-cbrt`
92×	`div-exp` `add-cbrt-cube`
63×	`prod-exp`
42×	`distribute-lft-out--` `difference-of-squares`
40×	`cbrt-undiv`
39×	`div-inv`
27×	`cbrt-unprod`
24×	`associate-/l*`
21×	`distribute-rgt-neg-in` `sqrt-prod`
14×	`rec-exp` `1-exp`
13×	`associate-/r*`
11×	`associate-/r/`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `associate-/l/` `inv-pow`

Counts

4 → 321

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
42.0ms	(/ (/ 1 (/ (* 2.0 a) (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(/ 1 (/ (* 2.0 a) (* 4.0 (* a c))))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
150.0ms	(/ (/ 1 (/ (* 2.0 a) (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(/ 1 (/ (* 2.0 a) (* 4.0 (* a c))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1179	5742
1	5001	5143

prune560.0ms

Filtered

333 candidates to 145 candidates (43.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes91.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	17	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

395.0ms	3684×	body	320	valid
307.0ms	16437×	pre	80	true
297.0ms	8437×	body	80	nan
210.0ms	2906×	body	160	valid
72.0ms	504×	body	640	valid
36.0ms	906×	body	80	valid