Details

sample39.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
8.0ms	194×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	76×	body	80	nan
1.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	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: 34.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b	(- (* b b) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

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:

33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735

prune291.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b	(- (* b b) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
48×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
8×	`distribute-rgt-neg-in`
6×	`pow1`
5×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 134

Calls

4 calls:

25.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
12.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
74.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	556	1665
1	2664	1442
2	5002	1371

prune307.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
0.4b	(- (* b b) (* 4.0 (* a c)))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* 4.0 (* a c)))
41.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify85.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	170	540
1	622	506
2	2864	498
3	5001	488

prune273.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- 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))
10.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`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`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 232

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
148.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
181.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	818	5119
1	3560	3863
2	5001	3860

prune501.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.7b

regimes202.0ms

Accuracy

89.8% (2.9b remaining)

Error of 8.7b against oracle of 5.8b and baseline of 34.3b

bsearch189.0ms

Steps

Iters	Range	Point
8	1.5276508475467709e+44	4.1560730947117816e+46	3.5595090602930848e+44
7	1.2547523394300577e-213	9.43081911393732e-212	1.7911864756464395e-213
11	-1.829086240692416e+154	-2.187052964502477e+134	-8.555281377770497e+140

Iters

Range

Point

1.5276508475467709e+44

4.1560730947117816e+46

3.5595090602930848e+44

1.2547523394300577e-213

9.43081911393732e-212

1.7911864756464395e-213

-1.829086240692416e+154

-2.187052964502477e+134

-8.555281377770497e+140

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	29
1	47	29
2	47	29

end0.0ms

sample1.1s

Algorithm

intervals

Results

251.0ms	1104×	body	2560	valid
234.0ms	5868×	body	80	valid
172.0ms	910×	body	1280	valid
107.0ms	2861×	body	80	nan
62.0ms	422×	body	640	valid
29.0ms	96×	body	5120	valid
28.0ms	212×	body	320	valid
9.0ms	120×	body	160	valid