Details

sample107.0ms

Algorithm

intervals

Results

21.0ms	31×	body	2560	valid
21.0ms	176×	body	80	valid
18.0ms	30×	body	1280	valid
14.0ms	85×	body	80	nan
7.0ms	16×	body	640	valid
5.0ms	6×	body	5120	valid
3.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify171.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.2b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
60×	`prod-diff`
57×	`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`
7×	`neg-mul-1` `associate-/l*` `add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
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` `div-inv`

Counts

3 → 156

Calls

3 calls:

27.0ms	(/ (- (- 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)))

series396.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
118.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
138.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.3s

Counts

165 → 165

Iterations

Iter	Nodes
done	2000
3	2000
2	1124
1	479
0	211

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
1.2b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`prod-diff`
53×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
12×	`add-exp-log`
11×	`times-frac`
10×	`fma-neg`
8×	`add-cbrt-cube`
7×	`neg-mul-1` `associate-l` `add-log-exp`
6×	`pow1`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `unswap-sqr`
2×	`frac-times` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

3 → 154

Calls

3 calls:

51.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series374.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
134.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
104.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.3s

Counts

163 → 163

Iterations

Iter	Nodes
done	2000
3	2000
2	1322
1	541
0	230

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (* -2 (/ c b)) 2)
0.0b	(* -2 (/ c b))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`times-frac` `associate-r`
12×	`*-un-lft-identity` `add-cube-cbrt`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-l*`
2×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l` `associate-/l/`

Counts

2 → 62

Calls

2 calls:

11.0ms	(/ (* -2 (/ c b)) 2)
9.0ms	(* -2 (/ c b))

series52.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(/ (* -2 (/ c b)) 2)
31.0ms	(* -2 (/ c b))

simplify931.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	2004
3	2004
2	838
1	282
0	112

prune600.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b	(expm1 (log1p (/ (- c) b)))
2.2b	(log1p (/ (- c) b))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`expm1-log1p-u`
2×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

2 → 24

Calls

2 calls:

0.0ms	(expm1 (log1p (/ (- c) b)))
0.0ms	(log1p (/ (- c) b))

series201.0ms

Counts

2 → 6

Calls

2 calls:

128.0ms	(expm1 (log1p (/ (- c) b)))
73.0ms	(log1p (/ (- c) b))

simplify1.1s

Counts

30 → 30

Iterations

Iter	Nodes
done	2015
5	2015
4	1380
3	483
2	173
1	85
0	46

prune317.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.6b

regimes526.0ms

Accuracy

81.4% (5.1b remaining)

Error of 10.8b against oracle of 5.6b and baseline of 33.3b

bsearch230.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	2.559678284282607e+69
9	-2.273288360947074e-131	-1.9680749876012584e-137	-2.2415082771065304e-131

simplify11.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.3s	5790×	body	80	valid
1.2s	956×	body	1280	valid
1.0s	1048×	body	2560	valid
506.0ms	2938×	body	80	nan
324.0ms	454×	body	640	valid
97.0ms	98×	body	5120	valid
86.0ms	220×	body	320	valid
28.0ms	105×	body	160	valid