Details

sample109.0ms

Algorithm

intervals

Results

22.0ms	112×	body	320	valid
19.0ms	274×	body	80	nan
17.0ms	530×	pre	80	true
13.0ms	95×	body	160	valid
4.0ms	13×	body	640	valid
3.0ms	36×	body	80	valid

simplify173.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	75
2	40
1	22
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b	(* (* 3.0 a) c)
26.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite157.0ms

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:

11.0ms	(- (* b b) (* (* 3.0 a) c))
93.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(* (* 3.0 a) c)
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* (* 3.0 a) c))
194.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
33.0ms	(* (* 3.0 a) c)
115.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.9s

Counts

105 → 105

Iterations

Iter	Nodes
done	5002
2	1578
1	461
0	167

prune619.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(* (* 3.0 a) c)
0.3b	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(/ (/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-cbrt-cube` `add-exp-log`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`associate-/r*` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `pow-prod-down` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-l` `*-commutative` `associate-+l-`
1×	`flip3-+` `flip-+`

Counts

4 → 167

Calls

4 calls:

15.0ms	(* (* 3.0 a) c)
25.0ms	(* (* 3.0 a) c)
173.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
166.0ms	(/ (/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series483.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 3.0 a) c)
34.0ms	(* (* 3.0 a) c)
223.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
186.0ms	(/ (/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify2.2s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	2099
1	667
0	247

prune955.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(* (* 3.0 a) c)
0.3b	(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

120×	`prod-diff`
89×	`add-sqr-sqrt` `*-un-lft-identity`
85×	`add-cube-cbrt`
62×	`distribute-rgt-in` `distribute-lft-in`
61×	`sqrt-prod`
37×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
28×	`add-cbrt-cube` `add-exp-log`
19×	`pow1`
13×	`associate-r`
12×	`neg-mul-1` `prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `-commutative` `associate-/l`
2×	`sub-neg` `flip3--` `associate-/r/` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `div-sub` `associate-+l-` `flip-+` `div-inv`

Counts

4 → 220

Calls

4 calls:

14.0ms	(* (* 3.0 a) c)
17.0ms	(* (* 3.0 a) c)
119.0ms	(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
130.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 3.0 a) c)
25.0ms	(* (* 3.0 a) c)
191.0ms	(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
196.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))

simplify2.4s

Counts

232 → 232

Iterations

Iter	Nodes
done	5012
2	2703
1	1023
0	344

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.2b	(* (* 3.0 a) c)
0.2b	(* (* 3.0 a) c)
0.3b	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (* 3.0 a))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

50.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.0ms	(* (* 3.0 a) c)
13.0ms	(* (* 3.0 a) c)
112.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (* 3.0 a))

series184.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
33.0ms	(* (* 3.0 a) c)
24.0ms	(* (* 3.0 a) c)
15.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (* 3.0 a))

simplify1.4s

Counts

168 → 168

Iterations

Iter	Nodes
done	5078
2	1478
1	539
0	220

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes383.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.0s	16109×	pre	80	true
731.0ms	8109×	body	80	nan
675.0ms	3545×	body	320	valid
581.0ms	3048×	body	160	valid
208.0ms	516×	body	640	valid
92.0ms	891×	body	80	valid