Details

sample133.0ms

Algorithm

intervals

Results

20.0ms	5×	body	5120	valid
19.0ms	31×	body	2560	valid
18.0ms	172×	body	80	valid
17.0ms	35×	body	1280	valid
8.0ms	20×	body	640	valid
8.0ms	82×	body	80	nan
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify328.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	96
7	96
6	95
5	93
4	85
3	70
2	42
1	24
0	14

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize187.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`insert-posit16`
3×	`distribute-rgt-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*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 74

Calls

4 calls:

182.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
21.0ms	(- (* b b) (* 4.0 (* a c)))
57.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series608.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
83.0ms	(- (* b b) (* 4.0 (* a c)))
153.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
136.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify8.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5003
3	4858
2	1309
1	411
0	156

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.8b

localize146.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sum-log` `distribute-rgt-neg-in` `flip3--` `sqrt-div` `1-exp` `associate-*l/` `flip--`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `associate-+l-` `div-inv` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

229.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
39.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
31.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
102.0ms	(- (* b b) (* 4.0 (* a c)))
151.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
128.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5005
2	1763
1	486
0	183

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.8b

localize177.0ms

Local error

Found 4 expressions with local error:

2.3b	(/ (/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.8b	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
18.5b	(- (* b b) (* b b))
22.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite809.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
21×	`distribute-lft-out--` `difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`insert-posit16` `div-inv`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `associate-+l-` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `diff-log` `flip-+`

Counts

4 → 158

Calls

4 calls:

420.0ms	(/ (/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
316.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.0ms	(- (* b b) (* b b))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series906.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(/ (/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
452.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(- (* b b) (* b b))
137.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify5.1s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	2184
1	685
0	269

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

localize200.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.2b	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
22.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite596.0ms

Algorithm

rewrite-expression-head

Rules

152×	`times-frac`
121×	`add-sqr-sqrt`
109×	`*-un-lft-identity`
94×	`add-exp-log`
85×	`associate-r`
68×	`add-cube-cbrt`
58×	`add-cbrt-cube`
39×	`div-exp`
35×	`prod-exp`
21×	`cbrt-undiv` `cbrt-unprod`
20×	`distribute-lft-out--` `difference-of-squares`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in` `add-log-exp`
7×	`pow1` `associate-l`
6×	`flip3--` `associate-/r/` `flip--`
5×	`div-inv`
4×	`rec-exp` `1-exp` `insert-posit16` `unswap-sqr`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 189

Calls

4 calls:

23.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
426.0ms	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
40.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (* b b) (* 4.0 (* a c)))
142.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
338.0ms	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
155.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify8.3s

Counts

201 → 201

Iterations

Iter	Nodes
done	5005
2	4048
1	1135
0	358

prune2.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.7b

regimes908.0ms

Accuracy

85.5% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 34.9b

bsearch201.0ms

Steps

Iters	Range		Point
6	1.6664801848567985e-94	1.3864776888564433e-93	1.3635892865650846e-93
7	-8.18523145413159e+143	-2.8208844788355687e+142	-5.517926393801403e+142

simplify45.0ms

Iterations

Iter	Nodes
done	38
1	38
0	29

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.2s	5744×	body	80	valid
890.0ms	1056×	body	2560	valid
706.0ms	454×	body	640	valid
573.0ms	978×	body	1280	valid
303.0ms	2913×	body	80	nan
110.0ms	138×	body	5120	valid
84.0ms	257×	body	320	valid
24.0ms	119×	body	160	valid