Details

sample155.0ms

Algorithm

intervals

Results

17.0ms	32×	body	2560	valid
14.0ms	185×	body	80	valid
14.0ms	31×	body	1280	valid
8.0ms	108×	body	80	nan
3.0ms	6×	body	5120	valid
3.0ms	11×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify126.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

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))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite219.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

105.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
46.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
122.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

183 → 183

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	242	5993
1	578	4337
2	2130	3551
done	5000	3006

prune515.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize31.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
2.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
7.9b	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
23.3b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`flip3--` `fma-neg` `flip--` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 217

Calls

4 calls:

23.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
76.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
54.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
4.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
243.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
288.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
125.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.2s

Counts

229 → 229

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	313	6352
1	752	5415
2	3626	5099
done	5000	5039

prune849.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
2.7b	(/ (/ (+ 0 (* a c)) (pow (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) 1)) a)
7.9b	(/ (+ 0 (* a c)) (pow (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) 1))
23.3b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

252×	`times-frac`
210×	`add-sqr-sqrt`
175×	`*-un-lft-identity`
141×	`add-cube-cbrt`
96×	`unpow-prod-down`
37×	`associate-/l*`
34×	`difference-of-squares`
32×	`sqrt-prod`
19×	`add-exp-log`
18×	`prod-diff`
17×	`distribute-lft-out--`
16×	`sqr-pow`
13×	`associate-/r*`
11×	`add-cbrt-cube`
10×	`div-exp`
6×	`fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l/`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

4 → 275

Calls

4 calls:

24.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
138.0ms	(/ (/ (+ 0 (* a c)) (pow (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) 1)) a)
64.0ms	(/ (+ 0 (* a c)) (pow (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) 1))
2.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series747.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
219.0ms	(/ (/ (+ 0 (* a c)) (pow (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) 1)) a)
290.0ms	(/ (+ 0 (* a c)) (pow (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) 1))
112.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify667.0ms

Counts

287 → 287

Iterations

Useful iterations: done (644.0ms)

Iter	Nodes	Cost
0	405	9065
1	1039	7203
done	5000	6674

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize50.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
1.4b	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
23.3b	(sqrt (fma (- c) a (* b_2 b_2)))
23.3b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 112

Calls

4 calls:

16.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
23.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
3.0ms	(sqrt (fma (- c) a (* b_2 b_2)))
3.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
132.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
115.0ms	(sqrt (fma (- c) a (* b_2 b_2)))
115.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.1s

Counts

124 → 124

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	82	2306
1	165	1828
2	413	1510
3	1922	1352
done	5000	1260

prune474.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

regimes333.0ms

Accuracy

93.8% (1.5b remaining)

Error of 6.7b against oracle of 5.2b and baseline of 29.6b

bsearch259.0ms

Steps

Iters	Range	Point
6	1.9101351599902807e+102	2.525038855038462e+103	1.302994705082702e+103
10	-7.077564636162835e-218	-5.427763013235534e-237	-1.3430967517097796e-234
10	-2.8734245235493903e+48	-2.602501271628617e+37	-2.7947637937473138e+48

Iters

Range

Point

1.9101351599902807e+102

2.525038855038462e+103

1.302994705082702e+103

-7.077564636162835e-218

-5.427763013235534e-237

-1.3430967517097796e-234

-2.8734245235493903e+48

-2.602501271628617e+37

-2.7947637937473138e+48

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	68
1	46	68
done	46	68

end0.0ms

sample2.8s

Algorithm

intervals

Results

724.0ms	2894×	body	80	nan
482.0ms	1053×	body	2560	valid
410.0ms	5806×	body	80	valid
345.0ms	935×	body	1280	valid
217.0ms	466×	body	640	valid
48.0ms	111×	body	5120	valid
38.0ms	233×	body	320	valid
12.0ms	106×	body	160	valid