Details

sample107.0ms

Algorithm

intervals

Results

65.0ms	279×	body	80	valid
18.0ms	84×	body	80	nan

simplify193.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	160
7	160
6	159
5	152
4	140
3	108
2	63
1	36
0	20

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize153.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

659×	`add-sqr-sqrt`
289×	`sqrt-prod`
270×	`prod-diff`
265×	`*-un-lft-identity`
216×	`unswap-sqr`
182×	`difference-of-squares`
113×	`add-cube-cbrt`
108×	`associate-l`
89×	`distribute-rgt-neg-in`
87×	`distribute-lft-neg-in`
74×	`distribute-lft-out--`
36×	`swap-sqr` `*-commutative`
29×	`neg-mul-1`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `distribute-lft-out`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 407

Calls

4 calls:

412.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
254.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
190.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
197.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
108.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
86.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
94.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.3s

Counts

419 → 419

Iterations

Iter	Nodes
done	5000
2	1921
1	771
0	344

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize139.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4 a) c))
0.9b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1042×	`add-sqr-sqrt`
600×	`prod-diff`
460×	`*-un-lft-identity`
411×	`associate-l`
317×	`unswap-sqr`
300×	`add-cube-cbrt`
289×	`sqrt-prod`
197×	`difference-of-squares`
159×	`associate-r`
108×	`swap-sqr`
92×	`*-commutative`
85×	`distribute-rgt-neg-in`
84×	`distribute-lft-neg-in`
80×	`distribute-lft-out--`
28×	`neg-mul-1`
25×	`fma-neg`
10×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 760

Calls

4 calls:

169.0ms	(- (* b b) (* (* 4 a) c))
420.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
212.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
195.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b b) (* (* 4 a) c))
122.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
110.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
108.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.6s

Counts

772 → 772

Iterations

Iter	Nodes
done	5000
2	3520
1	1561
0	691

prune4.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize161.0ms

Local error

Found 4 expressions with local error:

8.1b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
72×	`sqrt-prod`
54×	`*-un-lft-identity` `unswap-sqr`
45×	`difference-of-squares`
29×	`associate-l`
18×	`distribute-lft-out--`
10×	`fma-def` `add-cube-cbrt`
9×	`swap-sqr` `*-commutative`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
5×	`distribute-rgt-neg-in`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `neg-mul-1` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 147

Calls

4 calls:

1.4s	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
231.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
280.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
187.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
93.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
120.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
80.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.9s

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
3	3995
2	1054
1	342
0	138

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize174.0ms

Local error

Found 4 expressions with local error:

9.7b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

4608×	`sqrt-prod`
3648×	`add-sqr-sqrt`
2716×	`*-un-lft-identity`
1769×	`associate-l`
1640×	`prod-diff`
1173×	`unswap-sqr`
1098×	`swap-sqr`
982×	`distribute-lft-out--`
906×	`difference-of-squares`
632×	`add-cube-cbrt`
497×	`distribute-rgt-neg-in`
495×	`distribute-lft-neg-in`
300×	`associate-r`
200×	`*-commutative`
165×	`neg-mul-1`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
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`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 1809

Calls

4 calls:

2.1s	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
213.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
249.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
203.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
91.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify4.0s

Counts

1821 → 1821

Iterations

Iter	Nodes
done	5000
2	4225
1	2034
0	892

prune6.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

regimes439.0ms

Accuracy

88.9% (1.5b remaining)

Error of 7.1b against oracle of 5.7b and baseline of 18.8b

bsearch326.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	7.052614559736995e+62
9	-1.3801743424438113e+48	-9.460060253608456e+39	-1.3607986211035491e+48

simplify19.0ms

Iterations

Iter	Nodes
done	54
1	54
0	45

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.7s	8750×	body	80	valid
553.0ms	3007×	body	80	nan