Details

sample124.0ms

Algorithm

intervals

Results

36.0ms	28×	body	1280	valid
24.0ms	35×	body	2560	valid
21.0ms	184×	body	80	valid
9.0ms	86×	body	80	nan
6.0ms	15×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	8×	body	320	valid
2.0ms	5×	body	160	valid

simplify144.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize26.0ms

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))
1.7b	(- (sqrt (fma (* a c) -4 (* b b))) b)
24.6b	(sqrt (fma (* a c) -4 (* b b)))

rewrite58.0ms

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:

38.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
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)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
80.0ms	(fma (* a c) -4 (* b b))
112.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
112.0ms	(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

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (fma (* a c) -4 (* b b))) b)
3.1b	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
11.7b	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
24.6b	(sqrt (fma (* a c) -4 (* b b)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
101×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 166

Calls

4 calls:

13.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
28.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
10.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
311.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
265.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
117.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.4s

Counts

178 → 178

Iterations

Iter	Nodes
done	2002
3	2002
2	1434
1	557
0	246

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 17.3b

localize64.0ms

Local error

Found 4 expressions with local error:

6.6b	(/ (/ (fma (* a c) -4 0) (sqrt (+ (sqrt (fma (* a c) -4 (* b b))) b))) a)
8.2b	(/ (fma (* a c) -4 0) (sqrt (+ (sqrt (fma (* a c) -4 (* b b))) b)))
24.6b	(sqrt (fma (* a c) -4 (* b b)))
24.6b	(sqrt (fma (* a c) -4 (* b b)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
138×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
106×	`add-cube-cbrt`
70×	`sqrt-prod`
30×	`associate-/l*`
16×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r*` `sqrt-div` `associate-/r/`
6×	`pow1` `div-inv`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 209

Calls

4 calls:

31.0ms	(/ (/ (fma (* a c) -4 0) (sqrt (+ (sqrt (fma (* a c) -4 (* b b))) b))) a)
10.0ms	(/ (fma (* a c) -4 0) (sqrt (+ (sqrt (fma (* a c) -4 (* b b))) b)))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series1.8s

Counts

4 → 12

Calls

4 calls:

928.0ms	(/ (/ (fma (* a c) -4 0) (sqrt (+ (sqrt (fma (* a c) -4 (* b b))) b))) a)
639.0ms	(/ (fma (* a c) -4 0) (sqrt (+ (sqrt (fma (* a c) -4 (* b b))) b)))
119.0ms	(sqrt (fma (* a c) -4 (* b b)))
142.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.5s

Counts

221 → 221

Iterations

Iter	Nodes
done	2007
3	2007
2	1731
1	719
0	317

prune3.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 17.3b

localize80.0ms

Local error

Found 4 expressions with local error:

7.0b	(/ (fma (* a c) -4 0) (cbrt (+ (sqrt (fma (* a c) -4 (* b b))) b)))
24.6b	(sqrt (fma (* a c) -4 (* b b)))
24.6b	(sqrt (fma (* a c) -4 (* b b)))
24.6b	(sqrt (fma (* a c) -4 (* b b)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
21×	`times-frac`
16×	`cbrt-prod`
9×	`sqrt-prod`
7×	`pow1` `associate-/r*`
6×	`add-exp-log`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`cbrt-div` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 96

Calls

4 calls:

10.0ms	(/ (fma (* a c) -4 0) (cbrt (+ (sqrt (fma (* a c) -4 (* b b))) b)))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series6.4s

Counts

4 → 12

Calls

4 calls:

5.8s	(/ (fma (* a c) -4 0) (cbrt (+ (sqrt (fma (* a c) -4 (* b b))) b)))
83.0ms	(sqrt (fma (* a c) -4 (* b b)))
448.0ms	(sqrt (fma (* a c) -4 (* b b)))
97.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	2011
4	2011
3	1347
2	461
1	234
0	133

prune1.8s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 17.3b

regimes476.0ms

Accuracy

95.1% (0.8b remaining)

Error of 17.7b against oracle of 16.9b and baseline of 33.4b

bsearch284.0ms

Steps

Iters	Range		Point
8	6.45623811977989e+97	1.5556153764929518e+101	3.1351721739575554e+98
7	5.341724598133588e-164	3.634876864120329e-162	4.3423124612709e-163

simplify7.0ms

Iterations

Iter	Nodes
done	38
1	38
0	33

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.1s	915×	body	1280	valid
1.0s	5836×	body	80	valid
980.0ms	1126×	body	2560	valid
490.0ms	2976×	body	80	nan
262.0ms	417×	body	640	valid
111.0ms	119×	body	5120	valid
80.0ms	236×	body	320	valid
30.0ms	115×	body	160	valid