Details

sample145.0ms

Algorithm

intervals

Results

35.0ms	39×	body	2560	valid
28.0ms	188×	body	80	valid
25.0ms	87×	body	80	nan
25.0ms	31×	body	1280	valid
8.0ms	13×	body	640	valid
3.0ms	3×	body	5120	valid
3.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify100.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	115
5	115
4	107
3	83
2	47
1	25
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

34.0ms	(/ (- (sqrt (fma -4 (* a c) (* b b))) b) a)
0.0ms	(fma -4 (* a c) (* b b))
23.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
3.0ms	(sqrt (fma -4 (* a c) (* b b)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (- (sqrt (fma -4 (* a c) (* b b))) b) a)
73.0ms	(fma -4 (* a c) (* b b))
121.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
139.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify2.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	5002
3	2858
2	813
1	335
0	156

prune654.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 29.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* -4 c) a))) b) a)
0.4b	(- (sqrt (fma b b (* (* -4 c) a))) b)
0.5b	(fma b b (* (* -4 c) a))
23.1b	(sqrt (fma b b (* (* -4 c) a)))

rewrite38.0ms

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:

18.0ms	(/ (- (sqrt (fma b b (* (* -4 c) a))) b) a)
15.0ms	(- (sqrt (fma b b (* (* -4 c) a))) b)
0.0ms	(fma b b (* (* -4 c) a))
3.0ms	(sqrt (fma b b (* (* -4 c) a)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (sqrt (fma b b (* (* -4 c) a))) b) a)
112.0ms	(- (sqrt (fma b b (* (* -4 c) a))) b)
62.0ms	(fma b b (* (* -4 c) a))
94.0ms	(sqrt (fma b b (* (* -4 c) a)))

simplify2.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
3	3587
2	1047
1	423
0	180

prune681.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.4b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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:

28.0ms	(/ 1 (/ a (- (sqrt (fma -4 (* a c) (* b b))) b)))
1.0ms	(fma -4 (* a c) (* b b))
17.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
3.0ms	(sqrt (fma -4 (* a c) (* b b)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ 1 (/ a (- (sqrt (fma -4 (* a c) (* b b))) b)))
74.0ms	(fma -4 (* a c) (* b b))
112.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
104.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify2.8s

Counts

204 → 204

Iterations

Iter	Nodes
done	5000
3	4896
2	1645
1	616
0	271

prune802.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma -4 (* a c) (* b b))
1.0b	(+ (sqrt (fma -4 (* a c) (* b b))) b)
14.5b	(/ (fma c (* -4 a) 0) a)
23.1b	(sqrt (fma -4 (* a c) (* b b)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma -4 (* a c) (* b b))
12.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
8.0ms	(/ (fma c (* -4 a) 0) a)
2.0ms	(sqrt (fma -4 (* a c) (* b b)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma -4 (* a c) (* b b))
122.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
46.0ms	(/ (fma c (* -4 a) 0) a)
107.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify1.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5005
3	2461
2	507
1	214
0	117

prune796.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

regimes244.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.6b

bsearch266.0ms

Steps

Iters	Range	Point
10	6.2301214455520334e+75	1.5034565205168897e+88	5.6843076821754435e+85
7	-4.8398086897492375e-295	-7.680997906572533e-297	-9.252735565156383e-297
8	-3.370135567630554e+133	-1.481129451033522e+129	-2.1144981103869975e+131

Iters

Range

Point

6.2301214455520334e+75

1.5034565205168897e+88

5.6843076821754435e+85

-4.8398086897492375e-295

-7.680997906572533e-297

-9.252735565156383e-297

-3.370135567630554e+133

-1.481129451033522e+129

-2.1144981103869975e+131

simplify7.0ms

Iterations

Iter	Nodes
done	44
1	44
0	36

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	1064×	body	2560	valid
846.0ms	5890×	body	80	valid
746.0ms	901×	body	1280	valid
328.0ms	2854×	body	80	nan
299.0ms	447×	body	640	valid
113.0ms	95×	body	5120	valid
74.0ms	207×	body	320	valid
29.0ms	133×	body	160	valid