Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	40×	body	2560	valid
7.0ms	171×	body	80	valid
7.0ms	35×	body	1280	valid
4.0ms	89×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	1×	body	5120	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
37.0ms	(- (* b b) (* 4.0 (* a c)))
61.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5001	2128

prune572.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
30×	`add-exp-log`
29×	`add-cube-cbrt`
20×	`associate-/r*`
18×	`add-cbrt-cube`
14×	`div-exp`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
9×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `flip--`
6×	`pow1` `distribute-rgt-neg-in` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `sqrt-div` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `inv-pow`

Counts

4 → 148

Calls

4 calls:

44.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
50.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
99.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
38.0ms	(- (* b b) (* 4.0 (* a c)))
64.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	590	2075
1	2867	1822
2	5002	1745

prune579.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
0.2b	(/ 1 (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

391×	`times-frac`
201×	`add-sqr-sqrt`
200×	`*-un-lft-identity`
136×	`add-cube-cbrt`
101×	`add-exp-log`
68×	`div-exp`
49×	`associate-/r*`
32×	`distribute-lft-out--` `difference-of-squares`
27×	`add-cbrt-cube`
22×	`rec-exp` `1-exp` `div-inv`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
14×	`cbrt-undiv`
12×	`prod-exp`
8×	`pow1`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`pow-flip`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`inv-pow`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `remove-double-div`

Counts

4 → 314

Calls

4 calls:

49.0ms	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
64.0ms	(/ 1 (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
85.0ms	(/ 1 (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))))
38.0ms	(- (* b b) (* 4.0 (* a c)))
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1035	5076
1	5001	4326

prune943.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.3b	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

462×	`times-frac`
274×	`add-sqr-sqrt`
273×	`*-un-lft-identity`
161×	`add-cube-cbrt`
91×	`add-exp-log`
60×	`div-exp`
56×	`distribute-lft-out--` `difference-of-squares`
38×	`div-inv`
34×	`associate-/r*`
31×	`sqrt-prod`
28×	`distribute-rgt-neg-in`
27×	`add-cbrt-cube`
19×	`associate-/r/`
16×	`rec-exp` `1-exp`
14×	`cbrt-undiv`
12×	`prod-exp`
11×	`flip3--` `flip--`
10×	`associate-/l*`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/` `inv-pow`

Counts

4 → 355

Calls

4 calls:

39.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
60.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
100.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
38.0ms	(- (* b b) (* 4.0 (* a c)))
64.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify82.0ms

Algorithm

egg-herbie

Counts

367 → 367

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1285	6523
1	5001	5806

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.9b

regimes439.0ms

Accuracy

85.3% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 33.9b

bsearch90.0ms

Steps

Iters	Range		Point
8	2.068553019413577e+125	1.5793235108451263e+128	8.824801410527501e+125
4	-9.285856612195885e-64	-5.291128096587059e-64	-5.365827530591872e-64

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	16
1	36	16

end0.0ms

sample1.3s

Algorithm

intervals

Results

290.0ms	1087×	body	2560	valid
259.0ms	5861×	body	80	valid
198.0ms	890×	body	1280	valid
125.0ms	3052×	body	80	nan
82.0ms	476×	body	640	valid
34.0ms	107×	body	5120	valid
24.0ms	195×	body	320	valid
10.0ms	114×	body	160	valid