Details

sample102.0ms

Algorithm

intervals

Results

35.0ms	143×	body	160	valid
15.0ms	296×	body	80	nan
15.0ms	552×	pre	80	true
9.0ms	55×	body	320	valid
3.0ms	58×	body	80	valid

simplify81.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite175.0ms

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:

22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
33.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(- (* b b) (* (* 4.0 a) c))
142.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
111.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1481	1361
done	5000	1347

prune398.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite245.0ms

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:

9.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
90.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series702.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* (* 4.0 a) c))
146.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
261.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
229.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.2s

Counts

243 → 243

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	340	10026
1	812	7598
2	3228	6483
done	5000	6397

prune957.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 157

Calls

4 calls:

19.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
133.0ms	(* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
204.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series560.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms	(* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
201.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify2.2s

Counts

169 → 169

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	278	7131
1	701	5051
2	3351	3964
done	5001	3878

prune548.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* c (* 4.0 a)) a)
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b	(* (/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ (* c (* 4.0 a)) a))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log`
72×	`add-cbrt-cube`
67×	`prod-exp`
60×	`prod-diff`
59×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
53×	`add-cube-cbrt`
44×	`div-exp`
31×	`sqrt-prod`
29×	`cbrt-unprod`
22×	`cbrt-undiv` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
12×	`times-frac`
10×	`rec-exp` `fma-neg` `1-exp`
9×	`pow1` `associate-l`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-r`
5×	`associate-*r/`
4×	`expm1-log1p-u` `associate-/r` `associate-/r/` `log1p-expm1-u` `div-inv` `associate-/l`
3×	`flip3--` `flip--`
2×	`pow-flip` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `neg-log` `associate-l/` `-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 218

Calls

4 calls:

20.0ms	(/ (* c (* 4.0 a)) a)
51.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
310.0ms	(* (/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ (* c (* 4.0 a)) a))

series482.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (* c (* 4.0 a)) a)
115.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
145.0ms	(/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
204.0ms	(* (/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ (* c (* 4.0 a)) a))

simplify2.3s

Counts

230 → 230

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	343	8860
1	839	6638
2	2985	4879
done	5000	4793

prune768.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes152.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	25
1	23	25
done	23	25

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.3s	8186×	body	80	nan
956.0ms	4842×	body	160	valid
757.0ms	16186×	pre	80	true
369.0ms	1362×	body	320	valid
192.0ms	1796×	body	80	valid