Details

sample130.0ms

Algorithm

intervals

Results

15.0ms	184×	body	80	valid
11.0ms	26×	body	2560	valid
10.0ms	27×	body	1280	valid
6.0ms	22×	body	640	valid
5.0ms	69×	body	80	nan
2.0ms	4×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

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--` `insert-posit16` `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 → 175

Calls

4 calls:

53.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
117.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(- (* b_2 b_2) (* a c))
116.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

187 → 187

Iterations

Iter	Nodes
done	5009
2	1504
1	577
0	248

prune714.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.9b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `distribute-frac-neg` `div-inv`

Counts

4 → 123

Calls

4 calls:

76.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
23.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
99.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
58.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
3	4896
2	1277
1	468
0	203

prune815.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
3	1558
2	467
1	166
0	69

prune609.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.0b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

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` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 71

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	1558
2	467
1	166
0	69

prune571.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.0b

regimes487.0ms

Accuracy

81.5% (5.2b remaining)

Error of 10.8b against oracle of 5.7b and baseline of 33.6b

bsearch170.0ms

Steps

Iters	Range		Point
6	4.8498614244770303e+48	2.0602804194761557e+49	2.0410715251838527e+49
10	-2.8993282234165347e-22	-3.09682517328325e-32	-3.136683434005781e-32

simplify12.0ms

Iterations

Iter	Nodes
done	34
2	34
1	33
0	24

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	921×	body	1280	valid
853.0ms	1100×	body	2560	valid
701.0ms	5778×	body	80	valid
297.0ms	474×	body	640	valid
293.0ms	2930×	body	80	nan
108.0ms	226×	body	320	valid
79.0ms	98×	body	5120	valid
25.0ms	115×	body	160	valid