Details

sample78.0ms

Algorithm

intervals

Results

18.0ms	185×	body	80	valid
17.0ms	30×	body	2560	valid
10.0ms	25×	body	1280	valid
9.0ms	99×	body	80	nan
6.0ms	20×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify11.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
2.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune230.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

2.0ms	(- (* b b) (* (* 4.0 a) c))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

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))
176.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	640	2579
1	3155	2333
2	5001	2320

prune428.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b	(- (* b b) (* (* 4.0 a) c))
14.6b	(/ (* 2.0 a) (* 4.0 (* a c)))
25.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

283×	`add-exp-log`
136×	`div-exp`
121×	`prod-exp`
109×	`add-cbrt-cube`
42×	`cbrt-undiv`
41×	`cbrt-unprod`
40×	`1-exp`
32×	`times-frac`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`rec-exp`
14×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
4×	`flip3--` `flip--` `div-inv`
3×	`sqrt-prod`
2×	`frac-times` `frac-2neg` `sqrt-div` `associate-r/` `clear-num` `associate-/r`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*l/` `associate-/l/`

Counts

4 → 167

Calls

4 calls:

40.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1087	2499
1	5002	1931

prune284.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
0.8b	(- (* b b) (* (* 4.0 a) c))
25.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

1901×	`times-frac`
815×	`add-sqr-sqrt`
814×	`*-un-lft-identity`
810×	`add-cube-cbrt`
102×	`div-inv`
87×	`add-exp-log`
70×	`div-exp`
44×	`associate-/l*`
25×	`add-cbrt-cube`
15×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r/`
13×	`associate-/r*`
10×	`add-log-exp`
5×	`pow1`
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` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 720

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
31.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
43.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify153.0ms

Algorithm

egg-herbie

Counts

732 → 732

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3961	9260
1	5001	8103

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.6b

regimes175.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.5b

bsearch213.0ms

Steps

Iters	Range	Point
7	6.714891876596302e+121	1.686395921989292e+123	2.1125387673008883e+122
10	-5.399505147647774e-194	-1.4984247517127078e-204	-3.27314384198807e-203
4	-1.078360482931843e+145	-7.501243017467935e+144	-7.603816824088264e+144

Iters

Range

Point

6.714891876596302e+121

1.686395921989292e+123

2.1125387673008883e+122

-5.399505147647774e-194

-1.4984247517127078e-204

-3.27314384198807e-203

-1.078360482931843e+145

-7.501243017467935e+144

-7.603816824088264e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	35
1	47	35

end0.0ms

sample2.3s

Algorithm

intervals

Results

577.0ms	5894×	body	80	valid
533.0ms	1083×	body	2560	valid
368.0ms	896×	body	1280	valid
266.0ms	2938×	body	80	nan
142.0ms	438×	body	640	valid
69.0ms	117×	body	5120	valid
57.0ms	229×	body	320	valid
17.0ms	100×	body	160	valid