Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	187×	body	80	valid
8.0ms	36×	body	2560	valid
5.0ms	26×	body	1280	valid
3.0ms	19×	body	640	valid
3.0ms	73×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify12.0ms

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
done	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite117.0ms

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:

68.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
25.0ms	(+ (- 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))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

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

prune297.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
7.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite204.0ms

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:

31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
88.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
157.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
80.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Counts

244 → 244

Iterations

Useful iterations: 2 (98.0ms)

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

prune543.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.2b	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
7.8b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
48×	`add-exp-log`
37×	`sqrt-prod`
30×	`add-cbrt-cube`
27×	`associate-r`
25×	`distribute-rgt-neg-in`
24×	`times-frac`
21×	`distribute-lft-neg-in`
17×	`prod-exp`
16×	`div-exp`
10×	`fma-neg`
9×	`cbrt-undiv` `cbrt-unprod`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `neg-mul-1`
6×	`associate-/l/`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-*l/` `flip-+` `log1p-expm1-u`
3×	`rec-exp` `flip3--` `1-exp` `associate-l` `flip--` `unswap-sqr`
2×	`sqrt-div` `diff-log` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 200

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
41.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
100.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
163.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
198.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify209.0ms

Counts

212 → 212

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	894	4210
1	4980	2901
2	5001	2901
done	5001	2901

prune471.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.3b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
7.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
71×	`add-cube-cbrt`
60×	`prod-diff`
51×	`add-exp-log`
46×	`times-frac`
41×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
27×	`associate-l` `add-cbrt-cube`
21×	`distribute-lft-neg-in`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
10×	`fma-neg`
8×	`cbrt-undiv` `cbrt-unprod` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-/r*`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 227

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
123.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
61.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
161.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
196.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify153.0ms

Counts

239 → 239

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	910	4844
1	4351	3468
2	5001	3468
done	5001	3468

prune492.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

regimes256.0ms

Accuracy

88% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 31.7b

bsearch160.0ms

Steps

Iters	Range	Point
6	1.4800420954007604e+99	6.083502279918113e+99	3.314242005915538e+99
7	-1.0239697416173795e-228	-3.8766937197960597e-230	-3.9143071953980664e-230
10	-4.9909276054097234e+78	-4.785667473127655e+65	-4.287313385232319e+78

Iters

Range

Point

1.4800420954007604e+99

6.083502279918113e+99

3.314242005915538e+99

-1.0239697416173795e-228

-3.8766937197960597e-230

-3.9143071953980664e-230

-4.9909276054097234e+78

-4.785667473127655e+65

-4.287313385232319e+78

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	35
1	41	35
done	41	35

end0.0ms

sample1.2s

Algorithm

intervals

Results

258.0ms	1107×	body	2560	valid
223.0ms	5758×	body	80	valid
167.0ms	913×	body	1280	valid
108.0ms	2871×	body	80	nan
74.0ms	488×	body	640	valid
29.0ms	105×	body	5120	valid
25.0ms	222×	body	320	valid
10.0ms	110×	body	160	valid