Details

sample211.0ms

Algorithm

intervals

Results

65.0ms	118×	body	320	valid
18.0ms	249×	body	80	nan
16.0ms	505×	pre	80	true
13.0ms	91×	body	160	valid
9.0ms	20×	body	640	valid
3.0ms	27×	body	80	valid

simplify135.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (23.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize23.0ms

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))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite185.0ms

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)))
11.0ms	(- (* b b) (* (* 4.0 a) c))
110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
46.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms	(- (* b b) (* (* 4.0 a) c))
183.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
148.0ms	(+ (- 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

prune367.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* 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)))))

rewrite364.0ms

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:

67.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(- (* b b) (* (* 4.0 a) c))
139.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
114.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series747.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms	(- (* b b) (* (* 4.0 a) c))
202.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
317.0ms	(/ (+ 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	3236	6483
done	5001	6397

prune866.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
82×	`add-sqr-sqrt`
78×	`times-frac`
60×	`add-cube-cbrt`
41×	`prod-diff`
27×	`associate-/l*`
26×	`distribute-rgt-neg-in`
22×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-lft-neg-in`
11×	`fma-neg` `difference-of-squares`
10×	`sqrt-prod` `add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/`
5×	`neg-mul-1` `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 → 200

Calls

4 calls:

37.0ms	(- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))
22.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
47.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))))

series629.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))
55.0ms	(- (* b b) (* (* 4.0 a) c))
191.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
258.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))))

simplify2.2s

Counts

212 → 212

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	328	8474
1	786	6028
2	3206	5145
done	5000	5087

prune974.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

16.0ms	(- (* b b) (* 4.0 (* a c)))
0.0ms	(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
45.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
46.0ms	(/ (+ 0 (* (* a c) 4.0)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* 4.0 (* a c)))
245.0ms	(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
324.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
427.0ms	(/ (+ 0 (* (* a c) 4.0)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c)))))))

simplify1.4s

Counts

117 → 117

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	223	3857
1	573	3551
2	2281	2698
done	5001	2695

prune709.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes175.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	20	29
1	23	27
done	23	27

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.3s	3634×	body	320	valid
1.0s	2967×	body	160	valid
683.0ms	8051×	body	80	nan
592.0ms	16051×	pre	80	true
280.0ms	500×	body	640	valid
67.0ms	899×	body	80	valid