Details

sample55.0ms

Algorithm

intervals

Results

12.0ms	279×	body	80	nan
10.0ms	144×	body	160	valid
9.0ms	535×	pre	80	true
4.0ms	112×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
30.1b	(+ (- 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)))
67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify48.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune254.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

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:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
161.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
47.0ms	(- (* b b) (* (* 4.0 a) c))
194.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify156.0ms

Counts

243 → 243

Iterations

Useful iterations: 2 (117.0ms)

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

prune566.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
0.4b	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
0.4b	(* (* a c) (fma b b (* (* 4.0 a) c)))
0.8b	(pow (* (* 4.0 a) c) 3)

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `times-frac`
36×	`difference-of-squares`
34×	`add-cube-cbrt`
21×	`sqr-pow`
19×	`add-exp-log` `add-cbrt-cube`
15×	`pow1`
13×	`associate-/l*`
12×	`distribute-lft-out--`
11×	`associate-/r*`
9×	`unpow-prod-down`
8×	`sqrt-prod`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-r` `pow-exp` `rem-cube-cbrt`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `associate-/r/` `flip--` `fma-udef` `div-inv`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `distribute-lft-in` `flip3-+` `unpow3` `div-sub` `cube-prod` `associate-l` `*-commutative` `flip-+`

Counts

4 → 162

Calls

4 calls:

136.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
50.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
17.0ms	(* (* a c) (fma b b (* (* 4.0 a) c)))
19.0ms	(pow (* (* 4.0 a) c) 3)

series566.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
144.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
63.0ms	(* (* a c) (fma b b (* (* 4.0 a) c)))
60.0ms	(pow (* (* 4.0 a) c) 3)

simplify145.0ms

Counts

174 → 174

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	755	3316
1	3770	3092
2	5001	3091
done	5001	3091

prune821.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
133×	`add-sqr-sqrt`
131×	`*-un-lft-identity`
123×	`add-cube-cbrt`
92×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
19×	`neg-mul-1`
11×	`fma-neg`
10×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `associate-l`
2×	`associate-/r/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `times-frac` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 285

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
97.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
44.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
51.0ms	(- (* b b) (* (* 4.0 a) c))
156.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify154.0ms

Counts

297 → 297

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	797	8337
1	4394	5185
2	5001	5161
done	5001	5161

prune421.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes130.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	15
1	49	15
2	50	15
3	50	15
done	50	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

298.0ms	4452×	body	160	valid
280.0ms	16609×	pre	80	true
272.0ms	8609×	body	80	nan
121.0ms	3548×	body	80	valid