Details

sample77.0ms

Algorithm

intervals

Results

14.0ms	153×	body	160	valid
13.0ms	286×	body	80	nan
12.0ms	542×	pre	80	true
6.0ms	41×	body	320	valid
3.0ms	62×	body	80	valid

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	119	16
5	128	16
done	128	16

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
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×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(- (* b b) (* (* 4.0 a) c))
149.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
118.0ms	(+ (- 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	452	1588
2	2113	1361
done	5000	1352

prune624.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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

rewrite260.0ms

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-cbrt-cube` `add-exp-log`
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×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`clear-num` `sub-neg` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

47.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(- (* b b) (* (* 4.0 a) c))
107.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
83.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms	(- (* b b) (* (* 4.0 a) c))
231.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
256.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify557.0ms

Counts

243 → 243

Iterations

Useful iterations: done (542.0ms)

Iter	Nodes	Cost
0	339	10026
1	860	7622
done	5000	6606

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
28×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-prod` `associate-/l/`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef`

Counts

4 → 104

Calls

4 calls:

1.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
0.0ms	(fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* (* 4.0 a) c))))))
51.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* (* 4.0 a) c))))))) (* 2.0 a))
37.0ms	(/ (+ 0 (* c (* 4.0 a))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* (* 4.0 a) c)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

145.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
307.0ms	(fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* (* 4.0 a) c))))))
444.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* (* 4.0 a) c))))))) (* 2.0 a))
377.0ms	(/ (+ 0 (* c (* 4.0 a))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (fma b b (- (* (* 4.0 a) c)))))))

simplify1.7s

Counts

116 → 116

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	216	3823
1	553	3536
2	2992	2674
done	5000	2671

prune954.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-l`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `times-frac` `flip3--` `div-exp` `pow-prod-down` `flip--` `associate-/l*`
2×	`diff-log` `associate-/r/` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `neg-log` `-commutative` `flip-+` `div-inv`

Counts

4 → 160

Calls

4 calls:

1.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
63.0ms	(* (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))) (* a 2.0))
16.0ms	(- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))
48.0ms	(/ (+ 0 (* c (* 4.0 a))) (* (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))) (* a 2.0)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))
172.0ms	(* (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))) (* a 2.0))
121.0ms	(- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))
238.0ms	(/ (+ 0 (* c (* 4.0 a))) (* (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))) (* a 2.0)))

simplify1.8s

Counts

172 → 172

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	254	7163
1	655	5114
2	3636	4020
done	5000	4019

prune642.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes317.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	20	29
1	27	27
2	38	27
3	40	27
done	40	27

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	8376×	body	80	nan
911.0ms	4835×	body	160	valid
679.0ms	16376×	pre	80	true
370.0ms	1392×	body	320	valid
128.0ms	1773×	body	80	valid