Details

sample189.0ms

Algorithm

intervals

Results

22.0ms	37×	body	2560	valid
18.0ms	187×	body	80	valid
11.0ms	24×	body	1280	valid
10.0ms	86×	body	80	nan
6.0ms	18×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite193.0ms

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:

83.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
18.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
45.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

134 → 134

Iterations

Iter	Nodes
done	2015
3	2015
2	1393
1	494
0	199

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite210.0ms

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:

112.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
9.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
58.0ms	(- (* b_2 b_2) (* a c))
132.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

134 → 134

Iterations

Iter	Nodes
done	2015
3	2015
2	1393
1	494
0	199

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

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:

62.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
66.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

212 → 212

Iterations

Iter	Nodes
done	2000
2	2000
1	742
0	303

prune2.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

112.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
15.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
61.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

135 → 135

Iterations

Iter	Nodes
done	2001
3	2001
2	1630
1	559
0	219

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.3b

regimes449.0ms

Accuracy

84.6% (4.2b remaining)

Error of 9.8b against oracle of 5.7b and baseline of 32.8b

bsearch165.0ms

Steps

Iters	Range		Point
8	5.833527798943191e-77	3.6732813120885656e-72	3.1295384133612364e-73
9	-2.2464591800446616e+91	-3.153507839293123e+86	-1.3599228730895225e+90

simplify7.0ms

Iterations

Iter	Nodes
done	26
1	26
0	23

end0.0ms

sample4.2s

Algorithm

intervals

Results

890.0ms	5892×	body	80	valid
843.0ms	2956×	body	80	nan
812.0ms	1027×	body	2560	valid
689.0ms	882×	body	1280	valid
281.0ms	463×	body	640	valid
156.0ms	235×	body	320	valid
113.0ms	98×	body	5120	valid
30.0ms	105×	body	160	valid