Details

sample130.0ms

Algorithm

intervals

Results

23.0ms	5×	body	5120	valid
18.0ms	187×	body	80	valid
18.0ms	29×	body	2560	valid
12.0ms	25×	body	1280	valid
10.0ms	103×	body	80	nan
6.0ms	16×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify158.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite185.0ms

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-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

123.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
10.0ms	(- (* b b) (* (* 4.0 a) c))
32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
70.0ms	(- (* b b) (* (* 4.0 a) c))
129.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	167	1697
1	451	1588
2	2113	1361
done	5000	1352

prune556.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize29.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.7b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 232

Calls

4 calls:

37.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
81.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
216.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
267.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts

244 → 244

Iterations

Useful iterations: 2 (848.0ms)

Iter	Nodes	Cost
0	335	10067
1	848	7629
2	4744	6524
done	5000	6524

prune810.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.3b	(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms	(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
196.0ms	(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

164 → 164

Iterations

Useful iterations: 2 (617.0ms)

Iter	Nodes	Cost
0	262	6878
1	691	4800
2	4730	3785
done	5000	3785

prune574.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.8b	(/ (* c (* 4.0 a)) a)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms	(/ (* c (* 4.0 a)) a)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b b) (* (* 4.0 a) c))
99.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* c (* 4.0 a)) a)
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

160 → 160

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	235	6114
1	592	4164
2	2813	3208
done	5001	3124

prune531.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.8b

regimes253.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.3b against oracle of 5.2b and baseline of 29.1b

bsearch248.0ms

Steps

Iters	Range	Point
9	9.357224410271438e+98	8.450543925883448e+104	3.3851047918136536e+104
5	-1.1108143199726668e-179	-3.7489462845636843e-180	-3.7940081798688815e-180
9	-2.0222087628911114e+145	-2.5898121549119986e+137	-1.9144452663620863e+138

Iters

Range

Point

9.357224410271438e+98

8.450543925883448e+104

3.3851047918136536e+104

-1.1108143199726668e-179

-3.7489462845636843e-180

-3.7940081798688815e-180

-2.0222087628911114e+145

-2.5898121549119986e+137

-1.9144452663620863e+138

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	64
1	46	64
done	46	64

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	5854×	body	80	valid
503.0ms	1075×	body	2560	valid
406.0ms	918×	body	1280	valid
230.0ms	2889×	body	80	nan
132.0ms	457×	body	640	valid
43.0ms	110×	body	5120	valid
33.0ms	210×	body	320	valid
12.0ms	108×	body	160	valid