Details

sample43.0ms

Algorithm

intervals

Results

10.0ms	35×	body	2560	valid
7.0ms	180×	body	80	valid
5.0ms	29×	body	1280	valid
3.0ms	88×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	7×	body	160	valid
0.0ms	3×	body	320	valid

simplify14.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

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:

49.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify78.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128

prune347.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

61.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify91.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	656	3422
1	2594	2238
2	5001	2193

prune328.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
6.0b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
141×	`prod-diff`
101×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
51×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
33×	`distribute-lft-neg-in`
28×	`div-inv`
15×	`fma-neg`
11×	`neg-mul-1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 240

Calls

4 calls:

9.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
39.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
111.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify121.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	847	8137
1	2676	5939
2	5001	5143

prune398.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.0b	(- (* b b) (* 4.0 (* a c)))
10.3b	(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

1238×	`times-frac`
575×	`prod-diff`
514×	`add-sqr-sqrt`
510×	`*-un-lft-identity`
506×	`add-cube-cbrt`
141×	`sqrt-prod`
126×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
107×	`associate-/r/`
104×	`div-inv`
94×	`sqrt-div`
49×	`flip3--` `flip--`
42×	`neg-mul-1`
25×	`add-exp-log`
15×	`fma-neg`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
8×	`add-log-exp`
6×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*` `difference-of-squares`
2×	`sub-neg` `diff-log` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `clear-num` `frac-sub` `cbrt-unprod` `inv-pow`

Counts

4 → 720

Calls

4 calls:

15.0ms	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
111.0ms	(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify316.0ms

Algorithm

egg-herbie

Counts

732 → 732

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2117	39375
1	5002	28113

prune749.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes161.0ms

Accuracy

85.8% (4.1b remaining)

Error of 9.5b against oracle of 5.5b and baseline of 34.2b

bsearch51.0ms

Steps

Iters	Range		Point
5	5.10808278574109e+145	1.867402505400959e+146	1.4350402825055232e+146
3	-2.6939693106550122e-64	-1.9710978016715664e-64	-2.648789841343547e-64

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	19
1	35	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

254.0ms	1094×	body	2560	valid
220.0ms	5855×	body	80	valid
169.0ms	919×	body	1280	valid
109.0ms	2917×	body	80	nan
59.0ms	415×	body	640	valid
28.0ms	102×	body	5120	valid
26.0ms	222×	body	320	valid
8.0ms	112×	body	160	valid