Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	193×	body	80	valid
10.0ms	31×	body	2560	valid
6.0ms	97×	body	80	nan
5.0ms	18×	body	1280	valid
4.0ms	18×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify146.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.6b

localize47.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
0.6b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
23.1b	(sqrt (fma (* -4 a) c (* b b)))

rewrite137.0ms

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:

88.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
36.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))

series360.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
99.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
146.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.6s

Counts

165 → 165

Iterations

Iter	Nodes
done	5042
3	3375
2	1124
1	479
0	211

prune951.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- (sqrt (fma -4 (* c a) (* b b)))) b) a)
0.4b	(fma -4 (* c a) (* b b))
0.6b	(- (- (sqrt (fma -4 (* c a) (* b b)))) b)
23.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
63×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
48×	`prod-diff`
29×	`distribute-rgt-neg-in`
27×	`sqrt-prod`
24×	`distribute-lft-neg-in`
18×	`times-frac`
16×	`fma-neg`
10×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `difference-of-squares`
4×	`expm1-log1p-u` `neg-mul-1` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
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` `fma-udef` `div-inv`

Counts

4 → 156

Calls

4 calls:

80.0ms	(/ (- (- (sqrt (fma -4 (* c a) (* b b)))) b) a)
1.0ms	(fma -4 (* c a) (* b b))
51.0ms	(- (- (sqrt (fma -4 (* c a) (* b b)))) b)
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (- (sqrt (fma -4 (* c a) (* b b)))) b) a)
69.0ms	(fma -4 (* c a) (* b b))
142.0ms	(- (- (sqrt (fma -4 (* c a) (* b b)))) b)
117.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.5s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
3	3368
2	1021
1	434
0	200

prune777.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- (sqrt (fma -4 (* c a) (* b b)))) b) (/ 1 a))
0.4b	(fma -4 (* c a) (* b b))
0.6b	(- (- (sqrt (fma -4 (* c a) (* b b)))) b)
23.1b	(sqrt (fma -4 (* c a) (* b b)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
49×	`add-cube-cbrt`
48×	`prod-diff`
27×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
16×	`fma-neg`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `neg-mul-1` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `difference-of-squares`
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` `fma-udef` `div-inv`

Counts

4 → 157

Calls

4 calls:

80.0ms	(* (- (- (sqrt (fma -4 (* c a) (* b b)))) b) (/ 1 a))
0.0ms	(fma -4 (* c a) (* b b))
40.0ms	(- (- (sqrt (fma -4 (* c a) (* b b)))) b)
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (- (- (sqrt (fma -4 (* c a) (* b b)))) b) (/ 1 a))
64.0ms	(fma -4 (* c a) (* b b))
140.0ms	(- (- (sqrt (fma -4 (* c a) (* b b)))) b)
94.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.7s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
3	3365
2	1198
1	495
0	220

prune809.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.2b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
23.1b	(sqrt (fma (* -4 a) c (* b b)))
23.1b	(sqrt (fma (* -4 a) c (* b b)))
23.1b	(sqrt (fma (* -4 a) c (* b b)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--`

Counts

4 → 139

Calls

4 calls:

25.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
116.0ms	(sqrt (fma (* -4 a) c (* b b)))
127.0ms	(sqrt (fma (* -4 a) c (* b b)))
95.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.6s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
3	1874
2	671
1	317
0	146

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.2b

regimes387.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 33.1b

bsearch178.0ms

Steps

Iters	Range		Point
8	2.5230591910300896e+45	6.095379443414697e+48	5.6488521390017767e+48
8	-1.0278134165845925e-62	-2.127595877901746e-66	-1.1962309819144974e-65

simplify7.0ms

Iterations

Iter	Nodes
done	30
1	30
0	27

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.0s	5849×	body	80	valid
606.0ms	1066×	body	2560	valid
547.0ms	464×	body	640	valid
476.0ms	903×	body	1280	valid
338.0ms	3069×	body	80	nan
85.0ms	218×	body	320	valid
74.0ms	122×	body	5120	valid
16.0ms	114×	body	160	valid