Details

sample96.0ms

Algorithm

intervals

Results

22.0ms	33×	body	2560	valid
20.0ms	185×	body	80	valid
16.0ms	32×	body	1280	valid
9.0ms	97×	body	80	nan
5.0ms	12×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify174.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.6b	(fma (* a c) -4 (* b b))
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
22.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

25.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
13.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
83.0ms	(fma (* a c) -4 (* b b))
115.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
94.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	2002
3	2002
2	773
1	335
0	156

prune687.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
0.6b	(fma (* a c) -4 (* b b))
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
22.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
18×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
7×	`div-exp`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 192

Calls

4 calls:

39.0ms	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
0.0ms	(fma (* a c) -4 (* b b))
16.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
73.0ms	(fma (* a c) -4 (* b b))
129.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
135.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.4s

Counts

204 → 204

Iterations

Iter	Nodes
done	2000
3	2000
2	1575
1	616
0	271

prune905.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (sqrt (fma (* a c) -4 (* b b))) b)))
0.6b	(fma (* a c) -4 (* b b))
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
22.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
507×	`add-sqr-sqrt`
420×	`*-un-lft-identity`
334×	`add-cube-cbrt`
86×	`difference-of-squares`
58×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/r*`
18×	`prod-diff`
16×	`add-cbrt-cube`
15×	`flip3--` `flip--`
13×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`fma-neg` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `fma-udef` `associate-/l/`

Counts

4 → 453

Calls

4 calls:

40.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (fma (* a c) -4 (* b b))) b)))
0.0ms	(fma (* a c) -4 (* b b))
15.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms	(sqrt (fma (* a c) -4 (* b b)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (fma (* a c) -4 (* b b))) b)))
87.0ms	(fma (* a c) -4 (* b b))
104.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
105.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.4s

Counts

465 → 465

Iterations

Iter	Nodes
done	2002
2	2002
1	1751
0	600

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.8b

localize95.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
22.2b	(sqrt (fma (* a c) -4 (* b b)))
22.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite20.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

7.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
8.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
95.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
93.0ms	(sqrt (fma (* a c) -4 (* b b)))
115.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	2003
4	2003
3	925
2	319
1	173
0	86

prune812.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 22.8b

regimes373.0ms

Accuracy

92.8% (0.8b remaining)

Error of 22.0b against oracle of 21.2b and baseline of 33.0b

bsearch114.0ms

Steps

Iters	Range		Point
8	8.942303404061595e-155	1.797707377495175e-151	1.0362819647114397e-153

simplify8.0ms

Iterations

Iter	Nodes
done	25
1	25
0	23

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.2s	1106×	body	2560	valid
908.0ms	2940×	body	80	nan
869.0ms	5933×	body	80	valid
725.0ms	842×	body	1280	valid
479.0ms	210×	body	320	valid
268.0ms	437×	body	640	valid
141.0ms	120×	body	5120	valid
29.0ms	113×	body	160	valid