Details

sample88.0ms

Algorithm

intervals

Results

23.0ms	149×	body	160	valid
17.0ms	262×	body	80	nan
16.0ms	518×	pre	80	true
9.0ms	47×	body	320	valid
5.0ms	60×	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: 44.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite62.0ms

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:

5.0ms	(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))
16.0ms	(+ (- 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)))
50.0ms	(- (* b b) (* (* 4.0 a) c))
108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (44.0ms)

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

prune265.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* 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)))))

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))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
31.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
146.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify155.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (119.0ms)

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

prune553.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b	(/ 4.0 (/ 2.0 (* a c)))
0.3b	(/ 2.0 (* a c))
0.4b	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite185.0ms

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:

39.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
7.0ms	(/ 4.0 (/ 2.0 (* a c)))
3.0ms	(/ 2.0 (* a c))
113.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series313.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
24.0ms	(/ 4.0 (/ 2.0 (* a c)))
21.0ms	(/ 2.0 (* a c))
150.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify80.0ms

Algorithm

egg-herbie

Counts

380 → 380

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1494	5557
1	5001	4952

prune887.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-exp-log`
77×	`add-cbrt-cube`
73×	`times-frac`
62×	`div-exp`
52×	`prod-exp`
45×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-undiv`
26×	`associate-l`
22×	`cbrt-unprod`
12×	`div-inv`
10×	`rec-exp` `1-exp`
9×	`pow1` `associate-r` `associate-/r` `associate-/l`
6×	`associate-/r/`
5×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `pow-flip` `pow-prod-down` `flip--` `unswap-sqr`
1×	`frac-times` `associate-l/` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 197

Calls

4 calls:

5.0ms	(/ 4.0 (/ 2.0 (* a c)))
3.0ms	(/ 2.0 (* a c))
27.0ms	(/ 1 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
94.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ 1 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 4.0 (/ 2.0 (* a c)))
26.0ms	(/ 2.0 (* a c))
160.0ms	(/ 1 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
150.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ 1 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify115.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	908	2351
1	4887	1865
2	5001	1864

prune476.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes122.0ms

Accuracy

0% (0.4b 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	20	12
1	20	12

end0.0ms

sample2.4s

Algorithm

intervals

Results

632.0ms	4903×	body	160	valid
539.0ms	8306×	body	80	nan
481.0ms	16306×	pre	80	true
239.0ms	1304×	body	320	valid
125.0ms	1793×	body	80	valid