Details

sample33.0ms

Algorithm

intervals

Results

15.0ms	282×	body	80	valid
4.0ms	86×	body	80	nan

simplify94.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	20	38
1	36	38
2	66	37
3	122	37
4	151	37
5	165	37
6	166	37
done	166	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize250.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify613.0ms

Counts

163 → 163

Iterations

Useful iterations: done (607.0ms)

Iter	Nodes	Cost
0	179	6238
1	429	4258
2	1338	3343
done	5000	3332

prune432.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.1b

localize116.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.3b	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
4.5b	(/ (* a c) b)
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

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`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 153

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
3.0ms	(/ (* a c) b)
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
19.0ms	(/ (* a c) b)
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify745.0ms

Counts

165 → 165

Iterations

Useful iterations: 2 (179.0ms)

Iter	Nodes	Cost
0	253	6265
1	600	4346
2	2128	3374
done	5000	3374

prune441.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.3b

localize113.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.8b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
52×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`pow1` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `neg-log` `*-commutative`

Counts

4 → 143

Calls

4 calls:

7.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 4.0 a) c)
46.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify747.0ms

Counts

155 → 155

Iterations

Useful iterations: 2 (153.0ms)

Iter	Nodes	Cost
0	212	5999
1	498	4070
2	1695	3162
done	5001	3162

prune367.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

localize113.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

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:

26.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
50.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify727.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (169.0ms)

Iter	Nodes	Cost
0	233	6633
1	567	4689
2	1911	3699
done	5000	3699

prune417.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

regimes182.0ms

Accuracy

89.2% (1.6b remaining)

Error of 7.7b against oracle of 6.1b and baseline of 21.2b

bsearch282.0ms

Steps

Iters	Range		Point
9	1.790439840991813e+53	4.6520850645607246e+61	2.8436139815832302e+57
10	-4.825160222524179e-304	4.983370065797432e-302	-1.2159818839962e-310
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify15.0ms

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	58	189
1	72	189
done	72	189

end0.0ms

sample841.0ms

Algorithm

intervals

Results

458.0ms	8732×	body	80	valid
137.0ms	2890×	body	80	nan