Details

sample58.0ms

Algorithm

intervals

Results

14.0ms	290×	body	80	nan
11.0ms	546×	pre	80	true
10.0ms	138×	body	160	valid
4.0ms	118×	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: 26.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
26.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite31.0ms

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)))
12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (43.0ms)

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

prune269.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- 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	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite60.0ms

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

series460.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- 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))
49.0ms	(- (* b b) (* (* 4.0 a) c))
187.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify163.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (120.0ms)

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

prune577.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))
0.3b	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-exp-log`
69×	`times-frac`
63×	`add-cbrt-cube`
50×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`div-exp`
31×	`prod-exp`
27×	`cbrt-undiv`
26×	`add-cube-cbrt`
17×	`cbrt-unprod`
13×	`associate-/r*`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/l*`
8×	`1-exp`
7×	`div-inv`
6×	`distribute-rgt-neg-in` `sqrt-prod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `div-sub` `associate-*r/` `prod-diff` `associate-/r/`

Counts

4 → 160

Calls

4 calls:

13.0ms	(/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))
19.0ms	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))

series436.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))
122.0ms	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
48.0ms	(- (* b b) (* (* 4.0 a) c))
100.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))

simplify49.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	946	2601
1	5001	2153

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

949×	`times-frac`
582×	`add-sqr-sqrt` `*-un-lft-identity`
390×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
95×	`add-exp-log`
83×	`associate-/r*`
63×	`add-cbrt-cube`
51×	`div-exp`
48×	`distribute-rgt-neg-in` `sqrt-prod`
31×	`cbrt-undiv`
29×	`associate-/l*`
25×	`prod-exp`
23×	`div-inv`
13×	`cbrt-unprod`
8×	`1-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`div-sub` `associate-/l/`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `associate-/r/` `flip--`

Counts

4 → 519

Calls

4 calls:

25.0ms	(/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c))
18.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c)
34.0ms	(/ (* 1 (/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series440.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c))
102.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c)
129.0ms	(/ (* 1 (/ 4.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a) c))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))

simplify122.0ms

Algorithm

egg-herbie

Counts

531 → 531

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1937	10186
1	5001	9722

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes146.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	33	15
2	33	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

319.0ms	4446×	body	160	valid
314.0ms	16681×	pre	80	true
291.0ms	8681×	body	80	nan
128.0ms	3554×	body	80	valid