Details

sample110.0ms

Algorithm

intervals

Results

31.0ms	37×	body	2560	valid
23.0ms	186×	body	80	valid
15.0ms	28×	body	1280	valid
10.0ms	91×	body	80	nan
8.0ms	19×	body	640	valid
4.0ms	11×	body	320	valid
1.0ms	3×	body	160	valid

simplify129.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* -4 a) c (* b b))
0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma (* -4 a) c (* b b))
44.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
21.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma (* -4 a) c (* b b))
155.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
104.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
119.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.3s

Counts

179 → 179

Iterations

Iter	Nodes
done	2000
3	2000
2	1190
1	497
0	222

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.6b	(- (* b b) (* 4 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

86.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
18.0ms	(- (* b b) (* 4 (* a c)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
64.0ms	(- (* b b) (* 4 (* a c)))
126.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
127.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.4s

Counts

173 → 173

Iterations

Iter	Nodes
done	2005
3	2005
2	1867
1	599
0	239

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
0.6b	(- (* b b) (* 4 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.9b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
11×	`fma-neg`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

111.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
12.0ms	(- (* b b) (* 4 (* a c)))
35.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
62.0ms	(- (* b b) (* 4 (* a c)))
105.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
128.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts

181 → 181

Iterations

Iter	Nodes
done	2000
3	2000
2	1945
1	648
0	262

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a))
0.8b	(fma b b (* -4 (* a c)))
1.1b	(- (- b) (sqrt (fma b b (* -4 (* a c)))))
22.9b	(sqrt (fma b b (* -4 (* a c))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
25×	`add-exp-log`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
10×	`fma-neg`
9×	`div-exp`
8×	`pow1` `add-log-exp`
7×	`neg-mul-1`
6×	`prod-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `times-frac` `1-exp` `associate-/l*`
2×	`diff-log` `cbrt-unprod` `pow-flip` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `associate-/r/` `fma-udef` `div-inv` `flip--` `inv-pow`

Counts

4 → 154

Calls

4 calls:

48.0ms	(/ 1 (* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a))
0.0ms	(fma b b (* -4 (* a c)))
22.0ms	(- (- b) (sqrt (fma b b (* -4 (* a c)))))
2.0ms	(sqrt (fma b b (* -4 (* a c))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 1 (* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a))
78.0ms	(fma b b (* -4 (* a c)))
98.0ms	(- (- b) (sqrt (fma b b (* -4 (* a c)))))
90.0ms	(sqrt (fma b b (* -4 (* a c))))

simplify1.2s

Counts

166 → 166

Iterations

Iter	Nodes
done	2002
3	2002
2	1356
1	534
0	233

prune2.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

regimes339.0ms

Accuracy

79.5% (5.8b remaining)

Error of 11.3b against oracle of 5.5b and baseline of 33.7b

bsearch222.0ms

Steps

Iters	Range		Point
8	6.45623811977989e+97	1.5556153764929518e+101	1.786204067849289e+100
10	-1.305087172727865e-183	-3.833210530916389e-194	-1.2890050783826923e-183

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.3s	5836×	body	80	valid
1.2s	1101×	body	2560	valid
873.0ms	2978×	body	80	nan
833.0ms	915×	body	1280	valid
272.0ms	500×	body	640	valid
108.0ms	194×	body	320	valid
108.0ms	106×	body	5120	valid
33.0ms	117×	body	160	valid