Details

sample90.0ms

Algorithm

intervals

Results

15.0ms	31×	body	2560	valid
15.0ms	35×	body	1280	valid
14.0ms	172×	body	80	valid
7.0ms	20×	body	640	valid
7.0ms	82×	body	80	nan
3.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify460.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	72
2	42
1	24
0	14

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize136.0ms

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)))

rewrite355.0ms

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:

202.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
127.0ms	(- (* b b) (* (* 4.0 a) c))
187.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
175.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1368
1	414
0	158

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize184.0ms

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)))

rewrite501.0ms

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:

316.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
39.0ms	(- (* b b) (* (* 4.0 a) c))
97.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
109.0ms	(- (* b b) (* (* 4.0 a) c))
186.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
133.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.5s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1842
1	489
0	185

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize138.0ms

Local error

Found 4 expressions with local error:

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

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

216.0ms	(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) (* 2.0 a))
39.0ms	(- (* b b) (* a (* c 4.0)))
126.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
46.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) (* 2.0 a))
98.0ms	(- (* b b) (* a (* c 4.0)))
147.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
139.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify3.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1258
1	402
0	158

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

localize185.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (- (* b b) (* a (* c 4.0))))) (sqrt (sqrt (- (* b b) (* a (* c 4.0))))))
12.2b	(- (* (sqrt (sqrt (- (* b b) (* a (* c 4.0))))) (sqrt (sqrt (- (* b b) (* a (* c 4.0)))))) b)
22.2b	(sqrt (- (* b b) (* a (* c 4.0))))
22.2b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3--` `associate-r` `associate-l` `pow-prod-up` `flip--` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `insert-posit16`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares`

Counts

4 → 130

Calls

4 calls:

219.0ms	(* (sqrt (sqrt (- (* b b) (* a (* c 4.0))))) (sqrt (sqrt (- (* b b) (* a (* c 4.0))))))
162.0ms	(- (* (sqrt (sqrt (- (* b b) (* a (* c 4.0))))) (sqrt (sqrt (- (* b b) (* a (* c 4.0)))))) b)
36.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
40.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (sqrt (sqrt (- (* b b) (* a (* c 4.0))))) (sqrt (sqrt (- (* b b) (* a (* c 4.0))))))
149.0ms	(- (* (sqrt (sqrt (- (* b b) (* a (* c 4.0))))) (sqrt (sqrt (- (* b b) (* a (* c 4.0)))))) b)
108.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
136.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify5.5s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
3	2701
2	885
1	338
0	158

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.0b

regimes777.0ms

Accuracy

85.9% (4.1b remaining)

Error of 9.6b against oracle of 5.5b and baseline of 34.5b

bsearch157.0ms

Steps

Iters	Range		Point
6	1.6664801848567985e-94	1.3864776888564433e-93	1.1804820682342164e-93
9	-2.0274263258127503e+155	-2.0044150779320932e+149	-2.3213399824345094e+149

simplify13.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.2s	1056×	body	2560	valid
606.0ms	5744×	body	80	valid
578.0ms	257×	body	320	valid
546.0ms	978×	body	1280	valid
432.0ms	2913×	body	80	nan
203.0ms	454×	body	640	valid
101.0ms	138×	body	5120	valid
25.0ms	119×	body	160	valid