Details

sample114.0ms

Algorithm

intervals

Results

23.0ms	162×	body	160	valid
19.0ms	270×	body	80	nan
18.0ms	526×	pre	80	true
10.0ms	45×	body	320	valid
3.0ms	49×	body	80	valid

simplify92.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	120
5	120
4	112
3	83
2	42
1	22
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
40.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

7.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(* (* 3.0 a) c)
71.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
44.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(* (* 3.0 a) c)
129.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	2777
1	472
0	167

prune707.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b))))
0.3b	(* (* 3.0 c) a)
0.3b	(/ (+ (- (* b b) (* b b)) (* (* 3.0 c) a)) (- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b)))))
0.4b	(/ (/ (+ (- (* b b) (* b b)) (* (* 3.0 c) a)) (- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b))))) (* 3.0 a))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 237

Calls

4 calls:

17.0ms	(- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b))))
28.0ms	(* (* 3.0 c) a)
105.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 c) a)) (- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b)))))
166.0ms	(/ (/ (+ (- (* b b) (* b b)) (* (* 3.0 c) a)) (- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b))))) (* 3.0 a))

series551.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b))))
28.0ms	(* (* 3.0 c) a)
233.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 c) a)) (- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b)))))
185.0ms	(/ (/ (+ (- (* b b) (* b b)) (* (* 3.0 c) a)) (- (- b) (sqrt (fma 3.0 (* a (- c)) (* b b))))) (* 3.0 a))

simplify2.1s

Counts

249 → 249

Iterations

Iter	Nodes
done	5000
2	4469
1	892
0	354

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (fma 3.0 (* (- a) c) (* b b))))
0.3b	(* (* 3.0 a) (- c))
0.3b	(/ (* (* 3.0 a) (- c)) (- (- (+ b (sqrt (fma 3.0 (* (- a) c) (* b b)))))))
0.4b	(/ (/ (* (* 3.0 a) (- c)) (- (- (+ b (sqrt (fma 3.0 (* (- a) c) (* b b))))))) (* 3.0 a))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
83×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
72×	`*-un-lft-identity`
50×	`add-cbrt-cube` `add-exp-log`
38×	`add-sqr-sqrt` `add-cube-cbrt`
35×	`associate-/l*`
29×	`associate-/r*`
17×	`cbrt-undiv` `div-exp` `distribute-lft-out`
16×	`prod-exp` `cbrt-unprod`
13×	`neg-mul-1`
12×	`distribute-neg-frac`
10×	`associate-r`
9×	`pow1`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
3×	`fma-def` `pow-prod-down` `distribute-frac-neg` `distribute-rgt-neg-out`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 222

Calls

4 calls:

6.0ms	(+ b (sqrt (fma 3.0 (* (- a) c) (* b b))))
20.0ms	(* (* 3.0 a) (- c))
93.0ms	(/ (* (* 3.0 a) (- c)) (- (- (+ b (sqrt (fma 3.0 (* (- a) c) (* b b)))))))
98.0ms	(/ (/ (* (* 3.0 a) (- c)) (- (- (+ b (sqrt (fma 3.0 (* (- a) c) (* b b))))))) (* 3.0 a))

series667.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ b (sqrt (fma 3.0 (* (- a) c) (* b b))))
23.0ms	(* (* 3.0 a) (- c))
249.0ms	(/ (* (* 3.0 a) (- c)) (- (- (+ b (sqrt (fma 3.0 (* (- a) c) (* b b)))))))
258.0ms	(/ (/ (* (* 3.0 a) (- c)) (- (- (+ b (sqrt (fma 3.0 (* (- a) c) (* b b))))))) (* 3.0 a))

simplify554.0ms

Counts

234 → 234

Iterations

Iter	Nodes
done	5000
1	949
0	321

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 3.0 (* c (- a)) (* b b))
0.1b	(+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b)
0.4b	(/ (/ (* 3.0 a) (/ (+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b) (- c))) (* 3.0 a))
0.4b	(/ (* 3.0 a) (/ (+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b) (- c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

341×	`times-frac`
182×	`*-un-lft-identity`
100×	`add-sqr-sqrt` `add-cube-cbrt`
57×	`add-cbrt-cube` `add-exp-log`
50×	`associate-/l*`
48×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
45×	`associate-/r*`
41×	`distribute-lft-out`
28×	`cbrt-undiv` `div-exp`
16×	`neg-mul-1`
11×	`prod-exp` `cbrt-unprod`
8×	`div-inv`
6×	`fma-def` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`associate-/r/` `sqrt-prod`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `fma-udef` `associate-/l/`

Counts

4 → 272

Calls

4 calls:

1.0ms	(fma 3.0 (* c (- a)) (* b b))
13.0ms	(+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b)
58.0ms	(/ (/ (* 3.0 a) (/ (+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b) (- c))) (* 3.0 a))
47.0ms	(/ (* 3.0 a) (/ (+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b) (- c)))

series751.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma 3.0 (* c (- a)) (* b b))
130.0ms	(+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b)
225.0ms	(/ (/ (* 3.0 a) (/ (+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b) (- c))) (* 3.0 a))
300.0ms	(/ (* 3.0 a) (/ (+ (sqrt (fma 3.0 (* c (- a)) (* b b))) b) (- c)))

simplify777.0ms

Counts

284 → 284

Iterations

Iter	Nodes
done	5001
1	1182
0	406

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes295.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
3	24
2	23
1	20
0	15

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	16480×	pre	80	true
767.0ms	4824×	body	160	valid
758.0ms	8480×	body	80	nan
363.0ms	1370×	body	320	valid
160.0ms	1806×	body	80	valid