Details

sample232.0ms

Algorithm

intervals

Results

59.0ms	278×	body	80	nan
25.0ms	121×	body	320	valid
17.0ms	534×	pre	80	true
12.0ms	85×	body	160	valid
5.0ms	19×	body	640	valid
2.0ms	31×	body	80	valid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	70	16
3	127	16
4	140	16
done	140	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.0b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite149.0ms

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:

13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms	(- (* b b) (* (* 4.0 a) c))
143.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
105.0ms	(+ (- 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	1078	1560
done	5001	1408

prune361.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 4.0 a) c))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite268.0ms

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`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `neg-log` `associate-/l/`

Counts

4 → 229

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
50.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms	(/ (/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
90.0ms	(/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series799.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* (* 4.0 a) c))
116.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
289.0ms	(/ (/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
329.0ms	(/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.1s

Counts

241 → 241

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	331	9790
done	5000	7049

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.0b	(- (* b b) (* (* 4.0 a) c))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.4b	(/ (fma (* 4.0 a) c 0) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 283

Calls

4 calls:

161.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms	(- (* b b) (* (* 4.0 a) c))
61.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms	(/ (fma (* 4.0 a) c 0) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series714.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
59.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
394.0ms	(/ (fma (* 4.0 a) c 0) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify5.9s

Counts

295 → 295

Iterations

Useful iterations: done (5.9s)

Iter	Nodes	Cost
0	360	17484
1	4748	9884
done	5000	9883

prune781.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`cbrt-undiv` `div-exp` `add-log-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`neg-mul-1` `times-frac` `associate-/r*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `neg-log` `clear-num` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 165

Calls

4 calls:

21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(- (* b b) (* (* 4.0 a) c))
62.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
130.0ms	(/ (* c (/ (* 4.0 a) (* 2.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
62.0ms	(- (* b b) (* (* 4.0 a) c))
131.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
257.0ms	(/ (* c (/ (* 4.0 a) (* 2.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.7s

Counts

177 → 177

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	286	7286
1	4233	4650
done	5000	4647

prune787.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	23
1	20	23
done	20	23

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.1s	16339×	pre	80	true
1.0s	3606×	body	320	valid
983.0ms	8339×	body	80	nan
503.0ms	2912×	body	160	valid
141.0ms	508×	body	640	valid
73.0ms	974×	body	80	valid