Details

sample39.0ms

Algorithm

intervals

Results

18.0ms	281×	body	80	valid
4.0ms	77×	body	80	nan

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	18
1	67	18
2	123	18
3	160	18
4	175	18
5	177	18
6	177	18
done	177	18

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize87.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite81.0ms

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×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 151

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	418	3056
1	1471	2008
2	5001	1917
done	5001	1917

prune434.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.4b

localize89.0ms

Local error

Found 4 expressions with local error:

4.3b	(expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.7b	(- (- b) (expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`prod-diff`
28×	`add-cube-cbrt`
13×	`distribute-rgt-neg-in`
12×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `neg-mul-1` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--` `expm1-udef`
1×	`associate--l-` `neg-sub0` `sub-neg` `expm1-log1p` `neg-log` `associate--r-` `difference-of-squares`

Counts

4 → 105

Calls

4 calls:

0.0ms	(expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(- (- b) (expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms	(- (- b) (expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	378	2192
1	1229	1213
2	5001	1163
done	5001	1163

prune388.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize91.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
6.2b	(/ (* a c) b)
24.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`times-frac`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`flip3--` `flip--`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `neg-log`

Counts

4 → 156

Calls

4 calls:

29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
15.0ms	(/ (* a c) b)
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
20.0ms	(/ (* a c) b)
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	651	3102
1	2707	2019
2	5002	1941
done	5002	1941

prune434.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

43.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify69.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	545	3278
1	2114	2181
2	5002	2098
done	5002	2098

prune389.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

regimes201.0ms

Accuracy

95.9% (0.6b remaining)

Error of 6.8b against oracle of 6.2b and baseline of 21.6b

bsearch199.0ms

Steps

Iters	Range	Point
5	3.355600980676121e+98	1.2784432988208537e+99	5.2633913525772375e+98
8	-2.2416054230608577e-248	-1.872794966336752e-252	-6.7247162669225565e-252
6	-1.0975144697592171e+114	-1.919867654883946e+113	-1.085320093966694e+114

Iters

Range

Point

3.355600980676121e+98

1.2784432988208537e+99

5.2633913525772375e+98

-2.2416054230608577e-248

-1.872794966336752e-252

-6.7247162669225565e-252

-1.0975144697592171e+114

-1.919867654883946e+113

-1.085320093966694e+114

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	82
1	74	82
2	74	82
done	74	82

end0.0ms

sample882.0ms

Algorithm

intervals

Results

429.0ms	8707×	body	80	valid
130.0ms	2850×	body	80	nan