Details

sample59.0ms

Algorithm

intervals

Results

14.0ms	138×	body	320	valid
11.0ms	232×	body	80	nan
9.0ms	488×	pre	80	true
6.0ms	88×	body	160	valid
1.0ms	10×	body	640	valid
1.0ms	20×	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: 54.0b

localize11.0ms

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))
26.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite58.0ms

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

series303.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune256.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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))

rewrite101.0ms

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))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series459.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
182.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify154.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (114.0ms)

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

prune556.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `flip3-+` `fma-neg` `diff-log` `prod-diff` `flip--` `flip-+` `fma-udef`

Counts

4 → 105

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
0.0ms	(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))

series731.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* (* 4.0 a) c))
175.0ms	(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
274.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
233.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))

simplify108.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	598	2143
1	3014	1804
2	5001	1754

prune419.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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))
0.4b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
133×	`add-sqr-sqrt`
131×	`*-un-lft-identity`
123×	`add-cube-cbrt`
92×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
19×	`neg-mul-1`
11×	`fma-neg`
10×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `associate-l`
2×	`associate-/r/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `times-frac` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 285

Calls

4 calls:

59.0ms	(* 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))
18.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
157.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify158.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	797	8337
1	4394	5185
2	5001	5161

prune430.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes87.0ms

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	24	12
1	24	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

389.0ms	3618×	body	320	valid
299.0ms	16096×	pre	80	true
278.0ms	8096×	body	80	nan
209.0ms	2913×	body	160	valid
75.0ms	528×	body	640	valid
35.0ms	941×	body	80	valid