Details

sample61.0ms

Algorithm

intervals

Results

12.0ms	36×	body	2560	valid
11.0ms	189×	body	80	valid
7.0ms	25×	body	1280	valid
5.0ms	104×	body	80	nan
3.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite172.0ms

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:

88.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
53.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
88.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	1505
1	573
0	244

prune918.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

128.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
53.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
120.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
52.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	1786
1	639
0	263

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite139.0ms

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:

77.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
107.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	1505
1	573
0	244

prune781.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
16.0b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* c a)) a)
20.3b	(- (* b_2 b_2) (* b_2 b_2))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `sqrt-prod` `flip--` `associate-/l`
2×	`sub-neg` `fma-neg` `sqrt-div` `diff-log` `prod-diff` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `div-sub` `div-exp` `associate-+l-` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* c a)) a)
13.0ms	(- (* b_2 b_2) (* b_2 b_2))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series136.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* c a)) a)
1.0ms	(- (* b_2 b_2) (* b_2 b_2))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

97 → 97

Iterations

Iter	Nodes
done	5036
3	2534
2	774
1	346
0	149

prune496.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

regimes596.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.6b

bsearch161.0ms

Steps

Iters	Range	Point
6	5.84949006905106e+100	6.027833473435204e+101	3.355858625783055e+101
9	-1.4598085821258646e-291	-1.0697531889019586e-297	-1.0850002786366243e-297
6	-1.7989235910837076e+89	-1.4585470499056154e+88	-1.7633154797394035e+89

Iters

Range

Point

5.84949006905106e+100

6.027833473435204e+101

3.355858625783055e+101

-1.4598085821258646e-291

-1.0697531889019586e-297

-1.0850002786366243e-297

-1.7989235910837076e+89

-1.4585470499056154e+88

-1.7633154797394035e+89

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	29

end0.0ms

sample2.6s

Algorithm

intervals

Results

553.0ms	2885×	body	80	nan
519.0ms	5821×	body	80	valid
456.0ms	1063×	body	2560	valid
340.0ms	950×	body	1280	valid
147.0ms	475×	body	640	valid
121.0ms	116×	body	5120	valid
71.0ms	239×	body	320	valid
12.0ms	105×	body	160	valid