Details

sample99.0ms

Algorithm

intervals

Results

25.0ms	193×	body	80	valid
19.0ms	30×	body	2560	valid
14.0ms	26×	body	1280	valid
10.0ms	99×	body	80	nan
6.0ms	12×	body	640	valid
4.0ms	5×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify134.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.2b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.6b	(fma (* a c) -4 (* b b))
24.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite55.0ms

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:

35.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
15.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.0ms	(fma (* a c) -4 (* b b))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
97.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
69.0ms	(fma (* a c) -4 (* b b))
103.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify863.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	2000
2	718
1	319
0	156

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
0.2b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.6b	(fma (* a c) -4 (* b b))
24.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 115

Calls

4 calls:

45.0ms	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
8.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.0ms	(fma (* a c) -4 (* b b))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
108.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
65.0ms	(fma (* a c) -4 (* b b))
92.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.2s

Counts

127 → 127

Iterations

Iter	Nodes
3	2506
2	963
1	380
0	175

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.2b

localize42.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (fma (* a c) -4 (* b b))) b)
2.2b	(/ (/ (fma -4 (* a c) 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
10.8b	(/ (fma -4 (* a c) 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
24.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite44.0ms

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:

6.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
19.0ms	(/ (/ (fma -4 (* a c) 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
15.0ms	(/ (fma -4 (* a c) 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series777.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
278.0ms	(/ (/ (fma -4 (* a c) 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
292.0ms	(/ (fma -4 (* a c) 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
104.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.7s

Counts

178 → 178

Iterations

Iter	Nodes
3	6246
2	1441
1	555
0	246

prune2.0s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 17.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(fma (* a c) -4 (* b b))
24.5b	(sqrt (fma (* a c) -4 (* b b)))
24.5b	(sqrt (fma (* a c) -4 (* b b)))
24.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (* a c) -4 (* 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)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma (* a c) -4 (* b b))
85.0ms	(sqrt (fma (* a c) -4 (* b b)))
81.0ms	(sqrt (fma (* a c) -4 (* b b)))
87.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify7.5s

Counts

71 → 71

Iterations

Iter	Nodes
5	10076
4	1719
3	412
2	119
1	59
0	40

prune1.0s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 17.8b

regimes506.0ms

Accuracy

94.1% (0.9b remaining)

Error of 18.2b against oracle of 17.2b and baseline of 33.2b

bsearch299.0ms

Steps

Iters	Range		Point
6	9.393510413029077e+92	1.3693909217968502e+94	1.1941771483955193e+94
9	-4.397101713511905e-269	-3.9837954536011494e-278	-1.488368069126177e-277

simplify11.0ms

Iterations

Iter	Nodes
2	33
1	33
0	30

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.1s	1029×	body	2560	valid
951.0ms	2862×	body	80	nan
892.0ms	5860×	body	80	valid
663.0ms	889×	body	1280	valid
309.0ms	469×	body	640	valid
138.0ms	107×	body	5120	valid
79.0ms	199×	body	320	valid
37.0ms	141×	body	160	valid