Details

sample142.0ms

Algorithm

intervals

Results

41.0ms	29×	body	1280	valid
11.0ms	41×	body	2560	valid
8.0ms	179×	body	80	valid
4.0ms	92×	body	80	nan
3.0ms	17×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify52.0ms

Counts

1 → 1

Iterations

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

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.2b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite220.0ms

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--` `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 → 118

Calls

4 calls:

89.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
92.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
109.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms	(- (* b_2 b_2) (* a c))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1377
1	490
0	195

prune746.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.2b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite235.0ms

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` `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 → 119

Calls

4 calls:

136.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
142.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

131 → 131

Iterations

Iter	Nodes
done	5002
2	1584
1	555
0	215

prune673.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize50.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* b_2 b_2) (* a c))
2.2b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	1495
2	455
1	161
0	67

prune508.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

localize422.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

10.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))
113.0ms	(sqrt (- (* b_2 b_2) (* a c)))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	1495
2	455
1	161
0	67

prune529.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

regimes384.0ms

Accuracy

85.5% (4.2b remaining)

Error of 10.1b against oracle of 5.9b and baseline of 34.9b

bsearch224.0ms

Steps

Iters	Range		Point
10	8.767897341253802e-114	4.657027509742155e-104	4.6129908231112306e-104
9	-6.117539429929052e+154	-3.6285784997486435e+148	-3.6803290429888884e+148

simplify10.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample2.9s

Algorithm

intervals

Results

807.0ms	2952×	body	80	nan
657.0ms	1119×	body	2560	valid
469.0ms	5807×	body	80	valid
292.0ms	899×	body	1280	valid
117.0ms	453×	body	640	valid
90.0ms	106×	body	5120	valid
41.0ms	213×	body	320	valid
16.0ms	125×	body	160	valid