Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	161×	body	160	valid
10.0ms	297×	body	80	nan
9.0ms	553×	pre	80	true
3.0ms	31×	body	320	valid
2.0ms	64×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9
done	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
39.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite111.0ms

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:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
46.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735
done	5001	735

prune263.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`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`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
55.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series474.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
189.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
158.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify146.0ms

Counts

243 → 243

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	832	5099
1	3967	3830
2	5001	3828
done	5001	3828

prune550.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.5b	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b	(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
138×	`times-frac`
96×	`*-un-lft-identity`
60×	`difference-of-squares`
56×	`add-cube-cbrt`
52×	`cbrt-prod`
50×	`sqrt-prod`
42×	`associate-/l*`
20×	`distribute-lft-out--`
19×	`add-exp-log` `add-cbrt-cube`
16×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*` `sqr-pow`
10×	`distribute-rgt-neg-in`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-mult` `cbrt-div` `frac-2neg` `unpow3` `prod-exp` `clear-num` `cbrt-unprod`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `pow-exp` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 217

Calls

4 calls:

91.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
138.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
10.0ms	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
10.0ms	(pow (- (* b b) (* (* 4.0 a) c)) 3)

series482.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
50.0ms	(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
94.0ms	(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify151.0ms

Counts

229 → 229

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	880	4267
1	4566	3879
2	5001	3878
done	5001	3878

prune663.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 (* a c)) a)
0.1b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b	(- (* b b) (* (* 4.0 a) c))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
91×	`*-un-lft-identity`
57×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
17×	`distribute-lft-out`
15×	`associate-/r*` `div-inv`
10×	`cbrt-undiv` `div-exp`
8×	`neg-mul-1` `associate-/l*` `add-log-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `sum-log` `flip--` `associate-/l/`

Counts

4 → 184

Calls

4 calls:

19.0ms	(/ (* 4.0 (* a c)) a)
14.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(- (* b b) (* (* 4.0 a) c))

series295.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (* 4.0 (* a c)) a)
84.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms	(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
46.0ms	(- (* b b) (* (* 4.0 a) c))

simplify109.0ms

Counts

196 → 196

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	839	2756
1	4554	2476
2	5002	2473
done	5002	2473

prune508.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes130.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	35	20
2	35	20
done	35	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

327.0ms	4854×	body	160	valid
281.0ms	16492×	pre	80	true
270.0ms	8492×	body	80	nan
133.0ms	1348×	body	320	valid
60.0ms	1798×	body	80	valid