Details

sample77.0ms

Algorithm

intervals

Results

16.0ms	35×	body	2560	valid
14.0ms	185×	body	80	valid
8.0ms	23×	body	1280	valid
7.0ms	103×	body	80	nan
5.0ms	19×	body	640	valid
1.0ms	7×	body	160	valid
1.0ms	4×	body	320	valid

simplify18.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 171

Calls

4 calls:

97.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
6.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
49.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2152
1	583
0	244

prune800.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 257

Calls

4 calls:

45.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
6.0ms	(- (* b_2 b_2) (* a c))
48.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
67.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

269 → 269

Iterations

Iter	Nodes
done	5000
2	4146
1	850
0	351

prune964.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.6b	(- (* b_2 b_2) (* a c))
5.6b	(- (- (/ b_2 a)) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

980×	`times-frac`
767×	`*-un-lft-identity`
766×	`add-sqr-sqrt`
757×	`add-cube-cbrt`
661×	`prod-diff`
303×	`distribute-rgt-neg-in`
300×	`distribute-lft-neg-in`
286×	`sqrt-prod`
79×	`div-inv`
31×	`fma-neg`
23×	`neg-mul-1`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log` `difference-of-squares`
2×	`sub-neg` `distribute-neg-frac` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-exp` `neg-log` `frac-sub` `sub-div`

Counts

4 → 793

Calls

4 calls:

28.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
8.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(- (- (/ b_2 a)) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
59.0ms	(- (* b_2 b_2) (* a c))
131.0ms	(- (- (/ b_2 a)) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
123.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

805 → 805

Iterations

Iter	Nodes
done	5000
1	1902
0	850

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
0.8b	(fma b_2 b_2 (- (* a c)))
1.8b	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
22.7b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`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`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `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 → 163

Calls

4 calls:

45.0ms	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
1.0ms	(fma b_2 b_2 (- (* a c)))
23.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
2.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (- b_2) (sqrt (fma b_2 b_2 (- (* a c))))) a)
58.0ms	(fma b_2 b_2 (- (* a c)))
102.0ms	(- (- b_2) (sqrt (fma b_2 b_2 (- (* a c)))))
95.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

simplify1.4s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	1761
1	502
0	222

prune712.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

regimes490.0ms

Accuracy

88% (3.5b remaining)

Error of 8.9b against oracle of 5.4b and baseline of 34.4b

bsearch266.0ms

Steps

Iters	Range	Point
8	1.9371672431899034e+133	9.06569062969358e+135	3.569161879972515e+135
7	-1.9525004674970017e-146	-8.640740768077714e-148	-1.571246895950166e-147
10	-6.172175216823688e+56	-1.1198862992811701e+41	-1.532647813487865e+52

Iters

Range

Point

1.9371672431899034e+133

9.06569062969358e+135

3.569161879972515e+135

-1.9525004674970017e-146

-8.640740768077714e-148

-1.571246895950166e-147

-6.172175216823688e+56

-1.1198862992811701e+41

-1.532647813487865e+52

simplify8.0ms

Iterations

Iter	Nodes
done	53
3	53
2	51
1	46
0	40

end0.0ms

sample2.9s

Algorithm

intervals

Results

673.0ms	2929×	body	80	nan
547.0ms	5778×	body	80	valid
471.0ms	1115×	body	2560	valid
308.0ms	885×	body	1280	valid
208.0ms	463×	body	640	valid
86.0ms	111×	body	5120	valid
46.0ms	254×	body	320	valid
14.0ms	124×	body	160	valid