Details

sample102.0ms

Algorithm

intervals

Results

28.0ms	191×	body	80	valid
14.0ms	28×	body	2560	valid
9.0ms	26×	body	1280	valid
9.0ms	19×	body	640	valid
6.0ms	82×	body	80	nan
3.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify578.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	140
7	140
6	138
5	135
4	132
3	113
2	62
1	29
0	14

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize135.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite409.0ms

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-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

230.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
88.0ms	(- (* b b) (* 4.0 (* a c)))
194.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
131.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.1s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	1801
1	605
0	245

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize142.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite485.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in` `add-exp-log`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

282.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
29.0ms	(- (* b b) (* 4.0 (* a c)))
109.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
37.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
79.0ms	(- (* b b) (* 4.0 (* a c)))
136.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
127.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.9s

Counts

181 → 181

Iterations

Iter	Nodes
done	5005
2	1976
1	669
0	271

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize177.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.0b	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.0b	(- (* b b) (* b b))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite956.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
77×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
21×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
13×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `associate-+l-` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

488.0ms	(/ (/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
357.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
41.0ms	(- (* b b) (* b b))
57.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series746.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(/ (/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
301.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(- (* b b) (* b b))
168.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.6s

Counts

170 → 170

Iterations

Iter	Nodes
done	5088
2	2185
1	700
0	276

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

localize192.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (/ (* (* a 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 4.0 (* a c))))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.4b	(/ (* (* a 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 4.0 (* a c)))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite838.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-exp-log`
87×	`add-cbrt-cube`
72×	`prod-exp`
56×	`div-exp`
36×	`cbrt-unprod`
34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`cbrt-undiv`
20×	`times-frac`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`rec-exp` `1-exp`
6×	`pow1` `associate-/r*` `fma-neg` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`flip3--` `flip--`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-*r/` `difference-of-squares` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 175

Calls

4 calls:

270.0ms	(/ 1 (/ (* (* a 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 4.0 (* a c))))
163.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
330.0ms	(/ (* (* a 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 4.0 (* a c)))
51.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series882.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(/ 1 (/ (* (* a 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 4.0 (* a c))))
187.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
248.0ms	(/ (* (* a 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 4.0 (* a c)))
133.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify6.8s

Counts

187 → 187

Iterations

Iter	Nodes
done	5159
2	3689
1	821
0	302

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.7b

regimes920.0ms

Accuracy

90% (3.0b remaining)

Error of 8.4b against oracle of 5.4b and baseline of 35.6b

bsearch413.0ms

Steps

Iters	Range	Point
10	1.0955696400612189e+91	1.0202913897586463e+104	1.7205132563858266e+103
9	-1.8840476054243272e-132	-9.612842247692592e-139	-2.4242286502051438e-135
9	-2.0190258033009663e+27	-4.429449841721669e+19	-3.234164035284793e+22

Iters

Range

Point

1.0955696400612189e+91

1.0202913897586463e+104

1.7205132563858266e+103

-1.8840476054243272e-132

-9.612842247692592e-139

-2.4242286502051438e-135

-2.0190258033009663e+27

-4.429449841721669e+19

-3.234164035284793e+22

simplify18.0ms

Iterations

Iter	Nodes
done	46
1	46
0	37

end0.0ms

sample4.3s

Algorithm

intervals

Results

960.0ms	890×	body	1280	valid
904.0ms	1082×	body	2560	valid
837.0ms	5883×	body	80	valid
696.0ms	2919×	body	80	nan
233.0ms	438×	body	640	valid
80.0ms	112×	body	5120	valid
73.0ms	230×	body	320	valid
24.0ms	124×	body	160	valid