Details

sample91.0ms

Algorithm

intervals

Results

37.0ms	285×	body	80	valid
10.0ms	85×	body	80	nan

simplify448.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	170
7	170
6	168
5	164
4	157
3	134
2	75
1	39
0	20

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize285.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
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` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 155

Calls

4 calls:

52.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
59.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
34.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
143.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
140.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
169.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify8.1s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
3	4536
2	1212
1	434
0	182

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize247.0ms

Local error

Found 4 expressions with local error:

9.1b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`fma-def` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `neg-mul-1` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 80

Calls

4 calls:

35.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
29.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
28.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
32.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series641.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
159.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
156.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
157.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	3217
2	797
1	249
0	92

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize321.0ms

Local error

Found 4 expressions with local error:

10.6b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`sqrt-prod`
2×	`neg-mul-1` `pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 87

Calls

4 calls:

22.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series824.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
227.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
234.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1364
1	443
0	181

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.8b

localize219.0ms

Local error

Found 4 expressions with local error:

22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1/3))))
25.5b	(pow (- (* b b) (* (* 4.0 a) c)) 1/3)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-prod` `pow-unpow` `unpow-prod-down` `flip3--` `sqrt-prod` `flip--`
2×	`cbrt-div` `neg-mul-1` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-pow` `sqrt-pow1` `pow1/2` `unpow1/3` `pow1/3` `neg-log` `pow-exp` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1/3))))
16.0ms	(pow (- (* b b) (* (* 4.0 a) c)) 1/3)

series983.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
259.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
300.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1/3))))
253.0ms	(pow (- (* b b) (* (* 4.0 a) c)) 1/3)

simplify3.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	1580
1	512
0	207

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.8b

regimes977.0ms

Accuracy

84.1% (2.2b remaining)

Error of 8.6b against oracle of 6.5b and baseline of 20.1b

bsearch254.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
6	-2.971125736392027e+46	-1.937449214055594e+45	-2.900769547116861e+46

simplify40.0ms

Iterations

Iter	Nodes
done	51
1	51
0	43

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s	8738×	body	80	valid
338.0ms	2975×	body	80	nan