Details

sample144.0ms

Algorithm

intervals

Results

30.0ms	87×	body	80	nan
28.0ms	198×	body	80	valid
26.0ms	31×	body	2560	valid
22.0ms	28×	body	1280	valid
11.0ms	17×	body	640	valid
4.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	155
6	155
5	151
4	144
3	117
2	65
1	29
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma c (* -4 a) (* b b))
0.1b	(/ (/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 2) a)
1.0b	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
24.3b	(sqrt (fma c (* -4 a) (* b b)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
168×	`*-un-lft-identity`
159×	`times-frac`
116×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/l*`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`diff-log` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 240

Calls

4 calls:

0.0ms	(fma c (* -4 a) (* b b))
33.0ms	(/ (/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 2) a)
15.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma c (* -4 a) (* b b))
119.0ms	(/ (/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 2) a)
98.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
116.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.8s

Counts

252 → 252

Iterations

Iter	Nodes
done	5000
2	2255
1	772
0	341

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma c (* -4 a) (* b b))
0.1b	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
7.5b	(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a))
24.3b	(sqrt (fma c (* -4 a) (* b b)))

rewrite913.0ms

Algorithm

rewrite-expression-head

Rules

26601×	`times-frac`
13477×	`add-sqr-sqrt`
13469×	`*-un-lft-identity`
13425×	`add-cube-cbrt`
7420×	`prod-diff`
2904×	`sqrt-prod`
1926×	`distribute-rgt-neg-in`
1917×	`distribute-lft-neg-in`
721×	`div-inv`
639×	`neg-mul-1`
106×	`fma-neg`
22×	`associate-/l*` `distribute-lft-out--`
12×	`difference-of-squares`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-out--` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `fma-udef` `flip--` `sub-div` `associate-/l/`

Counts

4 → 7718

Calls

4 calls:

0.0ms	(fma c (* -4 a) (* b b))
15.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
80.0ms	(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a))
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma c (* -4 a) (* b b))
167.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
119.0ms	(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a))
119.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify12.0s

Counts

7730 → 7730

Iterations

Iter	Nodes
done	6661
0	6661

prune1.0m

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma c (* -4 a) (* b b))
0.3b	(* (/ (sqrt (fma c (* -4 a) (* b b))) 2) (/ 1 a))
12.6b	(- (/ (/ (- b) 2) a) (* (/ (sqrt (fma c (* -4 a) (* b b))) 2) (/ 1 a)))
24.3b	(sqrt (fma c (* -4 a) (* b b)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

423×	`times-frac`
243×	`add-sqr-sqrt`
218×	`*-un-lft-identity`
215×	`add-cube-cbrt`
106×	`fma-neg` `prod-diff`
54×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
26×	`add-exp-log`
22×	`associate-l`
18×	`neg-mul-1`
16×	`add-cbrt-cube`
15×	`sqrt-prod`
13×	`associate-r`
11×	`div-inv`
9×	`unswap-sqr`
8×	`div-exp` `prod-exp`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `frac-sub` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`associate-*r/` `un-div-inv`
2×	`frac-times` `rec-exp` `1-exp` `div-sub` `associate-*l/` `sub-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `distribute-rgt-out--` `pow1/2` `diff-log` `pow-prod-down` `*-commutative` `fma-udef` `flip--`

Counts

4 → 334

Calls

4 calls:

0.0ms	(fma c (* -4 a) (* b b))
15.0ms	(* (/ (sqrt (fma c (* -4 a) (* b b))) 2) (/ 1 a))
29.0ms	(- (/ (/ (- b) 2) a) (* (/ (sqrt (fma c (* -4 a) (* b b))) 2) (/ 1 a)))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma c (* -4 a) (* b b))
172.0ms	(* (/ (sqrt (fma c (* -4 a) (* b b))) 2) (/ 1 a))
123.0ms	(- (/ (/ (- b) 2) a) (* (/ (sqrt (fma c (* -4 a) (* b b))) 2) (/ 1 a)))
87.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify2.0s

Counts

346 → 346

Iterations

Iter	Nodes
done	5000
2	4658
1	1382
0	546

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2))
0.2b	(/ 1 (/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2)))
11.5b	(- (/ (/ (- b) 2) a) (/ 1 (/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2))))
24.3b	(sqrt (fma c (* -4 a) (* b b)))

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

103700×	`times-frac`
48677×	`add-sqr-sqrt`
48572×	`*-un-lft-identity`
48553×	`add-cube-cbrt`
23108×	`prod-diff`
8739×	`sqrt-prod`
5913×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2277×	`div-inv`
1971×	`neg-mul-1`
430×	`associate-/r/`
106×	`fma-neg`
93×	`associate-/r*`
30×	`add-exp-log`
27×	`difference-of-squares`
18×	`add-cbrt-cube` `div-exp`
9×	`cbrt-undiv`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `distribute-lft-out--`
2×	`clear-num` `frac-2neg` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

4 → 23701

Calls

4 calls:

7.0ms	(/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2))
13.0ms	(/ 1 (/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2)))
117.0ms	(- (/ (/ (- b) 2) a) (/ 1 (/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2))))
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2))
112.0ms	(/ 1 (/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2)))
103.0ms	(- (/ (/ (- b) 2) a) (/ 1 (/ a (/ (sqrt (fma c (* -4 a) (* b b))) 2))))
92.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify29.0s

Counts

23713 → 23713

Iterations

Iter	Nodes
done	20031
0	20031

prune2.4m

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.6b

regimes299.0ms

Accuracy

83% (4.8b remaining)

Error of 10.7b against oracle of 5.8b and baseline of 34.3b

bsearch305.0ms

Steps

Iters	Range		Point
9	6.2301214455520334e+75	1.9082112581546424e+85	1.6691257204922504e+85
4	-2.3602019652593256e-123	-1.5355849018748885e-123	-2.3344326820285623e-123
9	-2.9300981025422624e-27	-1.2024011261401705e-33	-6.936587154412951e-28
8	-1.0943378505721803e-12	-1.4409381956716427e-15	-7.363255598823911e-15

simplify9.0ms

Iterations

Iter	Nodes
done	46
2	46
1	44
0	36

end0.0ms

sample3.1s

Algorithm

intervals

Results

933.0ms	1057×	body	2560	valid
760.0ms	891×	body	1280	valid
619.0ms	5842×	body	80	valid
261.0ms	2845×	body	80	nan
170.0ms	456×	body	640	valid
91.0ms	228×	body	320	valid
74.0ms	114×	body	5120	valid
20.0ms	117×	body	160	valid