Details

sample65.0ms

Algorithm

intervals

Results

32.0ms	287×	body	80	valid
8.0ms	108×	body	80	nan

simplify191.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	20	38
1	39	38
2	79	37
3	142	37
4	171	37
5	181	37
6	185	37
done	185	37

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize135.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite142.0ms

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:

61.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
143.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.4s

Counts

163 → 163

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	179	6238
1	417	4208
2	1168	3343
3	4792	2690
done	5000	2690

prune659.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize106.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
4.8b	(/ (* a c) b)
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

33.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
10.0ms	(/ (* a c) b)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms	(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
39.0ms	(/ (* a c) b)
167.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	179	1375
1	441	1282
2	1543	1112
done	5000	1102

prune621.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize134.0ms

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))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

86.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms	(- (* b b) (* (* 4.0 a) c))
38.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
76.0ms	(- (* b b) (* (* 4.0 a) c))
117.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

101 → 101

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	157	1641
1	396	1523
2	1365	1304
done	5001	1288

prune449.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize149.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (fma 2.0 (/ a (/ b c)) (* -2 b)) (* 2.0 a))
5.7b	(/ a (/ b c))
24.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
56×	`*-un-lft-identity`
53×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
14×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
10×	`fma-def`
8×	`add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+`

Counts

4 → 139

Calls

4 calls:

41.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (fma 2.0 (/ a (/ b c)) (* -2 b)) (* 2.0 a))
15.0ms	(/ a (/ b c))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms	(/ (fma 2.0 (/ a (/ b c)) (* -2 b)) (* 2.0 a))
23.0ms	(/ a (/ b c))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

151 → 151

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	283	2069
1	646	1916
2	2096	1736
done	5000	1724

prune781.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

regimes324.0ms

Accuracy

91% (1.4b remaining)

Error of 7.3b against oracle of 5.9b and baseline of 21.5b

bsearch456.0ms

Steps

Iters	Range	Point
9	1.7084993271036838e+35	8.915315724770326e+40	8.75372275402518e+40
10	-9.54870507633444e-304	1.3079717882256375e-300	-3.20057348973956e-310
5	-2.3823986784004295e+101	-6.644598008915225e+100	-2.1851923969506957e+101

Iters

Range

Point

1.7084993271036838e+35

8.915315724770326e+40

8.75372275402518e+40

-9.54870507633444e-304

1.3079717882256375e-300

-3.20057348973956e-310

-2.3823986784004295e+101

-6.644598008915225e+100

-2.1851923969506957e+101

simplify10.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	55	162
1	63	162
done	63	162

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	8706×	body	80	valid
348.0ms	2996×	body	80	nan