Details

sample45.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
6.0ms	34×	body	1280	valid
5.0ms	25×	body	2560	valid
4.0ms	115×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
1.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

19.0ms	(* (* 4.0 a) c)
8.0ms	(- (* b b) (* (* 4.0 a) c))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (* 4.0 a) c)
43.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune188.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

22.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
136.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
167.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune439.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.7b	(/ (* 2.0 a) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
62.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	429	637
1	2471	542
2	5003	534

prune230.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-exp-log`
166×	`div-exp`
119×	`prod-exp`
64×	`1-exp`
60×	`add-cbrt-cube`
34×	`rec-exp`
31×	`times-frac`
26×	`cbrt-undiv`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`cbrt-unprod`
14×	`associate-/r/`
13×	`associate-/l*`
11×	`frac-times`
10×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`associate-*l/`
5×	`pow1` `associate-*r/`
4×	`sqrt-prod`
3×	`diff-log` `un-div-inv` `div-inv`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

66.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1172	2503
1	5001	2016

prune289.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

regimes174.0ms

Accuracy

92.5% (1.7b remaining)

Error of 9.0b against oracle of 7.3b and baseline of 29.3b

bsearch361.0ms

Steps

Iters	Range	Point
9	2.5943009456277367e+151	2.863179527023367e+158	1.3257937988037266e+154
6	-3.405927582379186e-150	-4.860750269204613e-151	-4.9276367402926466e-151
7	-3.260864156300871e+111	-2.161458270686658e+109	-2.9224158984269497e+111

Iters

Range

Point

2.5943009456277367e+151

2.863179527023367e+158

1.3257937988037266e+154

-3.405927582379186e-150

-4.860750269204613e-151

-4.9276367402926466e-151

-3.260864156300871e+111

-2.161458270686658e+109

-2.9224158984269497e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	56
1	57	56

end0.0ms

sample1.2s

Algorithm

intervals

Results

234.0ms	1059×	body	2560	valid
226.0ms	5787×	body	80	valid
163.0ms	896×	body	1280	valid
108.0ms	2934×	body	80	nan
70.0ms	490×	body	640	valid
30.0ms	114×	body	5120	valid
28.0ms	228×	body	320	valid
8.0ms	120×	body	160	valid