Details

sample117.0ms

Algorithm

intervals

Results

26.0ms	31×	body	2560	valid
25.0ms	184×	body	80	valid
24.0ms	35×	body	1280	valid
11.0ms	86×	body	80	nan
6.0ms	12×	body	640	valid
3.0ms	7×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	3×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

69.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
46.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

187 → 187

Iterations

Iter	Nodes
3	4034
2	1423
1	576
0	248

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 261

Calls

4 calls:

46.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
51.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

273 → 273

Iterations

Iter	Nodes
2	2075
1	834
0	355

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize37.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.5b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0b	(- (* b_2 b_2) (* b_2 b_2))
21.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
33×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-+l-`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 204

Calls

4 calls:

123.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
112.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(- (* b_2 b_2) (* b_2 b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
142.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.0ms	(- (* b_2 b_2) (* b_2 b_2))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify895.0ms

Counts

216 → 216

Iterations

Iter	Nodes
2	2029
1	786
0	327

prune2.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.4b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.1b	(/ (* a c) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
21.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`prod-diff` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `flip3--` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-*r/` `associate-/r/` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

4 → 103

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
67.0ms	(/ (* a c) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
201.0ms	(/ (* a c) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify7.0s

Counts

115 → 115

Iterations

Iter	Nodes
3	13026
2	1768
1	471
0	191

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

regimes399.0ms

Accuracy

96% (1.0b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.8b

bsearch303.0ms

Steps

Iters	Range	Point
9	1.7155709022758137e+74	7.648947555279674e+80	7.774374944213099e+79
10	1.6511671529804793e-286	5.373241602768166e-276	1.5270348471001126e-284
10	-1.0499721897563905e+163	-2.2374592669061634e+150	-5.709051322868216e+150

Iters

Range

Point

1.7155709022758137e+74

7.648947555279674e+80

7.774374944213099e+79

1.6511671529804793e-286

5.373241602768166e-276

1.5270348471001126e-284

-1.0499721897563905e+163

-2.2374592669061634e+150

-5.709051322868216e+150

simplify5.0ms

Iterations

Iter	Nodes
2	34
1	34
0	30

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	5873×	body	80	valid
1.1s	1093×	body	2560	valid
532.0ms	864×	body	1280	valid
319.0ms	2898×	body	80	nan
236.0ms	426×	body	640	valid
123.0ms	108×	body	5120	valid
75.0ms	235×	body	320	valid
26.0ms	122×	body	160	valid