Details

sample58.0ms

Algorithm

intervals

Results

31.0ms	291×	body	80	valid
7.0ms	101×	body	80	nan

simplify226.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	193
6	193
5	189
4	179
3	143
2	79
1	39
0	20

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize147.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 151

Calls

4 calls:

29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
32.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
139.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	1833
1	440
0	179

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize139.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b	(/ c (/ b a))
3.4b	(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* b -2)))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
90×	`add-cube-cbrt`
78×	`times-frac`
60×	`prod-diff`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`associate-/r*`
14×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`div-inv`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`clear-num` `frac-2neg` `flip3--` `sqrt-div` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `associate-/r/` `cbrt-unprod`

Counts

4 → 202

Calls

4 calls:

31.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(/ c (/ b a))
18.0ms	(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* b -2)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms	(/ c (/ b a))
334.0ms	(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* b -2)))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

214 → 214

Iterations

Iter	Nodes
done	5000
2	4152
1	880
0	353

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.7b

localize147.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* b -2)))
12.4b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `flip3--` `flip--`
2×	`cbrt-undiv` `rem-sqrt-square` `neg-mul-1` `sqrt-pow1` `pow1/2` `diff-log` `div-exp`
1×	`associate--l-` `neg-sub0` `clear-num` `sub-neg` `frac-2neg` `neg-log` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* b -2)))
24.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* b -2)))
120.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1865
1	416
0	167

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.7b

localize171.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b	(/ c (/ b a))
3.5b	(* (* 2.0 c) (/ 1 (fma 2.0 (/ c (/ b a)) (* b -2))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
95×	`add-cube-cbrt`
84×	`times-frac`
60×	`prod-diff`
34×	`sqrt-prod`
31×	`add-exp-log`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `add-cbrt-cube`
13×	`associate-/r` `associate-r*`
12×	`prod-exp`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1` `div-exp`
6×	`cbrt-unprod` `div-inv`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `associate-/l*`
2×	`rec-exp` `flip3--` `sqrt-div` `diff-log` `1-exp` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `neg-log` `associate-r/` `associate-/r/` `un-div-inv` `-commutative`

Counts

4 → 219

Calls

4 calls:

34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(/ c (/ b a))
27.0ms	(* (* 2.0 c) (/ 1 (fma 2.0 (/ c (/ b a)) (* b -2))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms	(/ c (/ b a))
226.0ms	(* (* 2.0 c) (/ 1 (fma 2.0 (/ c (/ b a)) (* b -2))))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify845.0ms

Counts

231 → 231

Iterations

Iter	Nodes
done	5000
1	1001
0	384

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.7b

regimes586.0ms

Accuracy

86.9% (2.0b remaining)

Error of 7.6b against oracle of 5.6b and baseline of 21.2b

bsearch192.0ms

Steps

Iters	Range		Point
3	5.437233749566996e+22	6.419404774371196e+22	6.358019085320933e+22
8	-6.412561728939963e+28	-6.810701174428621e+25	-6.336287344206649e+28

simplify17.0ms

Iterations

Iter	Nodes
done	48
1	48
0	41

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.3s	8777×	body	80	valid
346.0ms	2964×	body	80	nan