Details

sample152.0ms

Algorithm

intervals

Results

44.0ms	186×	body	80	valid
32.0ms	37×	body	2560	valid
22.0ms	28×	body	1280	valid
15.0ms	91×	body	80	nan
11.0ms	19×	body	640	valid
5.0ms	11×	body	320	valid
1.0ms	3×	body	160	valid

simplify164.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize38.0ms

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)))

rewrite73.0ms

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:

1.0ms	(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))))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma (* -4 a) c (* b b))
113.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
107.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
103.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.6s

Counts

179 → 179

Iterations

Iter	Nodes
3	3048
2	1154
1	495
0	222

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize43.0ms

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))))

rewrite137.0ms

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:

68.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
17.0ms	(- (* b b) (* 4 (* a c)))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
71.0ms	(- (* b b) (* 4 (* a c)))
105.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
98.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify5.4s

Counts

173 → 173

Iterations

Iter	Nodes
3	6002
2	1722
1	597
0	239

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize29.0ms

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))))

rewrite151.0ms

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:

96.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
19.0ms	(- (* b b) (* 4 (* a c)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
67.0ms	(- (* b b) (* 4 (* a c)))
148.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
109.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify4.1s

Counts

181 → 181

Iterations

Iter	Nodes
3	5940
2	1809
1	644
0	262

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize37.0ms

Local error

Found 4 expressions with local error:

8.9b	(- (- b) (* (sqrt (* (cbrt (- (* b b) (* 4 (* a c)))) (cbrt (- (* b b) (* 4 (* a c)))))) (sqrt (cbrt (- (* b b) (* 4 (* a c)))))))
23.6b	(cbrt (- (* b b) (* 4 (* a c))))
23.6b	(cbrt (- (* b b) (* 4 (* a c))))
23.6b	(cbrt (- (* b b) (* 4 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`cbrt-prod`
8×	`add-log-exp`
6×	`distribute-lft-neg-in` `cbrt-div` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`pow1/3`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 85

Calls

4 calls:

17.0ms	(- (- b) (* (sqrt (* (cbrt (- (* b b) (* 4 (* a c)))) (cbrt (- (* b b) (* 4 (* a c)))))) (sqrt (cbrt (- (* b b) (* 4 (* a c)))))))
5.0ms	(cbrt (- (* b b) (* 4 (* a c))))
5.0ms	(cbrt (- (* b b) (* 4 (* a c))))
5.0ms	(cbrt (- (* b b) (* 4 (* a c))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b) (* (sqrt (* (cbrt (- (* b b) (* 4 (* a c)))) (cbrt (- (* b b) (* 4 (* a c)))))) (sqrt (cbrt (- (* b b) (* 4 (* a c)))))))
104.0ms	(cbrt (- (* b b) (* 4 (* a c))))
146.0ms	(cbrt (- (* b b) (* 4 (* a c))))
128.0ms	(cbrt (- (* b b) (* 4 (* a c))))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
3	3118
2	958
1	330
0	133

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes801.0ms

Accuracy

79.9% (5.6b remaining)

Error of 11.2b against oracle of 5.5b and baseline of 33.6b

bsearch198.0ms

Steps

Iters	Range		Point
6	1.0281935457265552e+141	5.100996805178893e+141	2.88466596167667e+141
10	-1.305087172727865e-183	-3.833210530916389e-194	-1.2890050783826923e-183

simplify9.0ms

Iterations

Iter	Nodes
2	37
1	37
0	29

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.1s	1101×	body	2560	valid
1.0s	5836×	body	80	valid
830.0ms	2978×	body	80	nan
711.0ms	915×	body	1280	valid
307.0ms	500×	body	640	valid
140.0ms	106×	body	5120	valid
113.0ms	194×	body	320	valid
32.0ms	117×	body	160	valid