Details

sample76.0ms

Algorithm

intervals

Results

13.0ms	137×	body	160	valid
13.0ms	281×	body	80	nan
12.0ms	537×	pre	80	true
8.0ms	58×	body	320	valid
3.0ms	61×	body	80	valid

simplify118.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite152.0ms

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:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms	(- (* b b) (* (* 4.0 a) c))
181.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
131.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.2s

Counts

102 → 102

Iterations

Useful iterations: done (1.2s)

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

prune386.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))))
0.3b	(/ (/ (+ 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)))))

rewrite271.0ms

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))
46.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
78.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series629.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* (* 4.0 a) c))
124.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
209.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
233.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.1s

Counts

243 → 243

Iterations

Useful iterations: done (2.1s)

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

prune923.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize41.0ms

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	(* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.4b	(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite431.0ms

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:

9.0ms	(- (* b b) (* (* 4.0 a) c))
61.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms	(* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
203.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series573.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* b b) (* (* 4.0 a) c))
130.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
174.0ms	(* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
190.0ms	(/ (+ 0 (* (* a c) 4.0)) (* (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify2.5s

Counts

169 → 169

Iterations

Useful iterations: done (2.4s)

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

prune571.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* c (* 4.0 a)) a)
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(* (/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ (* c (* 4.0 a)) a))

rewrite483.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-exp-log`
67×	`add-cbrt-cube`
64×	`prod-exp`
61×	`prod-diff`
57×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
51×	`add-cube-cbrt`
40×	`div-exp`
31×	`sqrt-prod`
28×	`cbrt-unprod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
20×	`cbrt-undiv`
11×	`fma-neg`
10×	`add-log-exp`
9×	`times-frac` `associate-l`
8×	`rec-exp` `1-exp`
7×	`neg-mul-1` `associate-r`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `associate-r/` `associate-/r` `flip--` `div-inv`
2×	`sub-neg` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `frac-2neg` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `-commutative` `associate-/l*` `unswap-sqr`

Counts

4 → 202

Calls

4 calls:

40.0ms	(/ (* c (* 4.0 a)) a)
18.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
348.0ms	(* (/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ (* c (* 4.0 a)) a))

series376.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* c (* 4.0 a)) a)
74.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
187.0ms	(* (/ 1 (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ (* c (* 4.0 a)) a))

simplify2.3s

Counts

214 → 214

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	338	8438
1	848	6223
2	3221	4566
done	5000	4481

prune621.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes178.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	23
1	23	21
done	23	21

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.3s	8422×	body	80	nan
1.2s	16422×	pre	80	true
765.0ms	4894×	body	160	valid
306.0ms	1329×	body	320	valid
160.0ms	1777×	body	80	valid