Details

sample73.0ms

Algorithm

intervals

Results

13.0ms	16×	body	640	valid
12.0ms	43×	body	2560	valid
9.0ms	164×	body	80	valid
8.0ms	32×	body	1280	valid
4.0ms	80×	body	80	nan
3.0ms	8×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	111
5	111
4	102
3	78
2	44
1	24
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `associate-l` `neg-log` `-commutative` `div-inv` `flip--`

Counts

4 → 76

Calls

4 calls:

15.0ms	(* (* 4.0 a) c)
73.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* 4.0 a) c)
130.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
98.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2486
1	473
0	172

prune586.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.8b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
6.9b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

20.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
138.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
69.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
251.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
274.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	3736
1	659
0	254

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.8b	(/ (/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)
6.9b	(/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

518×	`times-frac`
322×	`add-sqr-sqrt`
321×	`*-un-lft-identity`
173×	`add-cube-cbrt`
74×	`distribute-lft-out--` `difference-of-squares`
62×	`associate-/l*`
42×	`div-inv`
40×	`sqrt-prod`
38×	`add-cbrt-cube` `add-exp-log`
37×	`distribute-rgt-neg-in`
19×	`cbrt-undiv` `div-exp`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1`
2×	`clear-num` `frac-2neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 361

Calls

4 calls:

27.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
100.0ms	(/ (/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)
94.0ms	(/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series757.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
221.0ms	(/ (/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)
304.0ms	(/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
119.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

373 → 373

Iterations

Iter	Nodes
done	5001
1	1292
0	499

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.8b	(* (/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 a))
6.9b	(/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
140×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
103×	`add-exp-log`
63×	`add-cbrt-cube`
58×	`add-cube-cbrt`
55×	`associate-l`
45×	`div-exp`
35×	`prod-exp`
32×	`distribute-lft-out--` `difference-of-squares`
26×	`cbrt-undiv`
19×	`sqrt-prod` `cbrt-unprod`
18×	`div-inv`
16×	`distribute-rgt-neg-in`
13×	`associate-r`
8×	`add-log-exp`
7×	`pow1` `associate-/r` `associate-/l`
6×	`unswap-sqr`
5×	`rec-exp` `1-exp`
4×	`flip3--` `associate-/r/` `flip--`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `associate-/l/`

Counts

4 → 234

Calls

4 calls:

33.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
146.0ms	(* (/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 a))
60.0ms	(/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series1.1s

Counts

4 → 12

Calls

4 calls:

469.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
251.0ms	(* (/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 a))
277.0ms	(/ (/ (* 4.0 (* a c)) 2.0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

246 → 246

Iterations

Iter	Nodes
done	5001
1	1164
0	361

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

regimes617.0ms

Accuracy

84.1% (4.3b remaining)

Error of 9.5b against oracle of 5.2b and baseline of 31.9b

bsearch101.0ms

Steps

Iters	Range		Point
2	3.964947473899983e-62	4.720485511979589e-62	4.626043257219638e-62
7	-5.856362438573669e+138	-1.280729871585891e+137	-3.7108875578650606e+138

simplify9.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample3.1s

Algorithm

intervals

Results

983.0ms	1094×	body	2560	valid
584.0ms	5792×	body	80	valid
415.0ms	887×	body	1280	valid
205.0ms	467×	body	640	valid
191.0ms	2874×	body	80	nan
82.0ms	108×	body	5120	valid
54.0ms	243×	body	320	valid
16.0ms	117×	body	160	valid