Details

sample79.0ms

Algorithm

intervals

Results

19.0ms	28×	body	1280	valid
16.0ms	37×	body	2560	valid
14.0ms	186×	body	80	valid
7.0ms	91×	body	80	nan
6.0ms	20×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

65.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
47.0ms	(- (* b_2 b_2) (* a c))
122.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

187 → 187

Iterations

Iter	Nodes
3	4034
2	1423
1	576
0	248

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

62.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
27.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
55.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

187 → 187

Iterations

Iter	Nodes
3	4034
2	1423
1	576
0	248

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize51.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.3b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.3b	(- (* b_2 b_2) (* b_2 b_2))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite327.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
33×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-+l-`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 204

Calls

4 calls:

153.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
145.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms	(- (* b_2 b_2) (* b_2 b_2))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
210.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
2.0ms	(- (* b_2 b_2) (* b_2 b_2))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify852.0ms

Counts

216 → 216

Iterations

Iter	Nodes
2	2029
1	786
0	327

prune2.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.4b	(/ a (* a c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`times-frac` `flip3--` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--`

Counts

4 → 101

Calls

4 calls:

14.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(/ a (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(/ a (* a c))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

113 → 113

Iterations

Iter	Nodes
3	3328
2	1033
1	365
0	170

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

regimes448.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.5b

bsearch130.0ms

Steps

Iters	Range	Point
8	6.45623811977989e+97	1.5556153764929518e+101	2.0930248844306297e+100
10	-1.305087172727865e-183	-3.833210530916389e-194	-1.6508238928289048e-192
0	-3.554202870153192e+151	-3.44863726843118e+151	-3.5014200692921863e+151

Iters

Range

Point

6.45623811977989e+97

1.5556153764929518e+101

2.0930248844306297e+100

-1.305087172727865e-183

-3.833210530916389e-194

-1.6508238928289048e-192

-3.554202870153192e+151

-3.44863726843118e+151

-3.5014200692921863e+151

simplify8.0ms

Iterations

Iter	Nodes
2	36
1	36
0	33

end0.0ms

sample3.6s

Algorithm

intervals

Results

803.0ms	1100×	body	2560	valid
723.0ms	5836×	body	80	valid
713.0ms	497×	body	640	valid
620.0ms	918×	body	1280	valid
275.0ms	2972×	body	80	nan
81.0ms	107×	body	5120	valid
59.0ms	194×	body	320	valid
24.0ms	118×	body	160	valid