Details

sample316.0ms

Algorithm

intervals

Results

73.0ms	82×	body	80	nan
65.0ms	198×	body	80	valid
65.0ms	29×	body	1280	valid
18.0ms	17×	body	2560	valid
7.0ms	13×	body	640	valid
4.0ms	4×	body	5120	valid
4.0ms	10×	body	320	valid
3.0ms	10×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	34
5	34
4	32
3	30
2	23
1	15
0	10

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.2b	(- (* b_2 b_2) (* a c))
2.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 122

Calls

4 calls:

216.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
25.0ms	(- (* b_2 b_2) (* a c))
83.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
54.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
141.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

134 → 134

Iterations

Iter	Nodes
3	3508
2	1174
1	464
0	199

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
1.5b	(fma b_2 b_2 (- (* a c)))
2.9b	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
22.2b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite31.0ms

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:

20.0ms	(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
0.0ms	(fma b_2 b_2 (- (* a c)))
8.0ms	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
1.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
63.0ms	(fma b_2 b_2 (- (* a c)))
154.0ms	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
110.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

simplify1.5s

Counts

126 → 126

Iterations

Iter	Nodes
3	2549
2	919
1	391
0	177

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
1.2b	(- (* b_2 b_2) (* c a))
2.9b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite172.0ms

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*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 200

Calls

4 calls:

85.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
17.0ms	(- (* b_2 b_2) (* c a))
54.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* c a))) b_2)))
43.0ms	(- (* b_2 b_2) (* c a))
128.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
87.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify2.6s

Counts

212 → 212

Iterations

Iter	Nodes
3	5493
2	1948
1	712
0	303

prune2.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.3b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 120

Calls

4 calls:

42.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
83.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
121.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

132 → 132

Iterations

Iter	Nodes
3	2137
2	669
1	259
0	112

prune1.8s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.3b

regimes424.0ms

Accuracy

78% (6.1b remaining)

Error of 11.9b against oracle of 5.8b and baseline of 33.5b

bsearch322.0ms

Steps

Iters	Range		Point
3	1.897422751335727e-16	2.3824489835354504e-16	1.922674299151799e-16
7	4.1266326978064226e-111	9.799836324706106e-110	4.664677641347216e-111
8	9.808312070140145e-191	3.260010576758525e-187	3.207624111695675e-187
10	-4.8388360275630777e+135	-9.113678877832951e+119	-1.3725796156555912e+127

simplify19.0ms

Iterations

Iter	Nodes
3	54
2	54
1	52
0	39

end0.0ms

sample3.9s

Algorithm

intervals

Results

878.0ms	1046×	body	2560	valid
785.0ms	5930×	body	80	valid
665.0ms	882×	body	1280	valid
662.0ms	498×	body	640	valid
357.0ms	2875×	body	80	nan
131.0ms	121×	body	5120	valid
65.0ms	200×	body	320	valid
24.0ms	116×	body	160	valid