Details

sample134.0ms

Algorithm

intervals

Results

41.0ms	185×	body	80	valid
25.0ms	33×	body	2560	valid
22.0ms	32×	body	1280	valid
13.0ms	97×	body	80	nan
6.0ms	12×	body	640	valid
6.0ms	5×	body	5120	valid
3.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a -4) c)
0.8b	(fma b b (* (* a -4) c))
1.1b	(- (sqrt (fma b b (* (* a -4) c))) b)
22.2b	(sqrt (fma b b (* (* a -4) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

14.0ms	(* (* a -4) c)
0.0ms	(fma b b (* (* a -4) c))
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
9.0ms	(sqrt (fma b b (* (* a -4) c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* a -4) c)
68.0ms	(fma b b (* (* a -4) c))
151.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
93.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2002
3	2002
2	915
1	335
0	146

prune607.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a (* c -4) (* b b))
0.1b	(/ (- (sqrt (fma a (* c -4) (* b b))) b) a)
1.1b	(- (sqrt (fma a (* c -4) (* b b))) b)
22.2b	(sqrt (fma a (* c -4) (* b b)))

rewrite63.0ms

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:

0.0ms	(fma a (* c -4) (* b b))
34.0ms	(/ (- (sqrt (fma a (* c -4) (* b b))) b) a)
23.0ms	(- (sqrt (fma a (* c -4) (* b b))) b)
2.0ms	(sqrt (fma a (* c -4) (* b b)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma a (* c -4) (* b b))
174.0ms	(/ (- (sqrt (fma a (* c -4) (* b b))) b) a)
126.0ms	(- (sqrt (fma a (* c -4) (* b b))) b)
146.0ms	(sqrt (fma a (* c -4) (* b b)))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	2000
3	2000
2	774
1	336
0	157

prune666.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a (* c -4) (* b b))
0.1b	(/ (- (sqrt (* 1 (fma a (* c -4) (* b b)))) b) a)
1.1b	(- (sqrt (* 1 (fma a (* c -4) (* b b)))) b)
22.2b	(sqrt (* 1 (fma a (* c -4) (* b b))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac`
12×	`prod-diff`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`sqrt-prod` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sqrt-pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `fma-udef` `div-inv`

Counts

4 → 99

Calls

4 calls:

1.0ms	(fma a (* c -4) (* b b))
40.0ms	(/ (- (sqrt (* 1 (fma a (* c -4) (* b b)))) b) a)
27.0ms	(- (sqrt (* 1 (fma a (* c -4) (* b b)))) b)
8.0ms	(sqrt (* 1 (fma a (* c -4) (* b b))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(fma a (* c -4) (* b b))
210.0ms	(/ (- (sqrt (* 1 (fma a (* c -4) (* b b)))) b) a)
152.0ms	(- (sqrt (* 1 (fma a (* c -4) (* b b)))) b)
164.0ms	(sqrt (* 1 (fma a (* c -4) (* b b))))

simplify1.2s

Counts

111 → 111

Iterations

Iter	Nodes
done	2006
3	2006
2	797
1	331
0	154

prune551.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma c (* a -4) (* b b))) b)))
0.3b	(fma c (* a -4) (* b b))
1.1b	(- (sqrt (fma c (* a -4) (* b b))) b)
22.2b	(sqrt (fma c (* a -4) (* b b)))

rewrite34.0ms

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:

14.0ms	(/ 1 (/ a (- (sqrt (fma c (* a -4) (* b b))) b)))
0.0ms	(fma c (* a -4) (* b b))
14.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
2.0ms	(sqrt (fma c (* a -4) (* b b)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ 1 (/ a (- (sqrt (fma c (* a -4) (* b b))) b)))
70.0ms	(fma c (* a -4) (* b b))
114.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
119.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.1s

Counts

204 → 204

Iterations

Iter	Nodes
done	2013
3	2013
2	1614
1	613
0	271

prune792.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 9.8b

regimes315.0ms

Accuracy

85.3% (3.2b remaining)

Error of 14.3b against oracle of 11.1b and baseline of 32.9b

bsearch162.0ms

Steps

Iters	Range		Point
7	2.6599168228204088e-39	1.6102415927742825e-37	2.2058723073785985e-38
5	-3.3440263710910746e+131	-9.921521910190385e+130	-1.7512236628315378e+131

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	1106×	body	2560	valid
1.1s	5933×	body	80	valid
477.0ms	842×	body	1280	valid
355.0ms	2940×	body	80	nan
180.0ms	437×	body	640	valid
99.0ms	120×	body	5120	valid
57.0ms	210×	body	320	valid
20.0ms	113×	body	160	valid