Details

sample47.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
8.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
4.0ms	9×	body	320	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	106	16
5	114	16
done	114	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

7.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 4.0 a) c)
50.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify668.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (129.0ms)

Iter	Nodes	Cost
0	161	1863
1	390	1562
2	1524	1315
done	5000	1315

prune301.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0) a)
0.8b	(- (pow b 2) (* 4.0 (* a c)))
1.3b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
138×	`times-frac`
112×	`*-un-lft-identity`
86×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`prod-diff` `difference-of-squares`
22×	`associate-/l*`
14×	`fma-neg`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`unpow-prod-down`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 197

Calls

4 calls:

76.0ms	(/ (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0) a)
10.0ms	(- (pow b 2) (* 4.0 (* a c)))
51.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
11.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0) a)
45.0ms	(- (pow b 2) (* 4.0 (* a c)))
83.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
76.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.4s

Counts

209 → 209

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	334	5195
1	802	4799
2	3136	4441
done	5000	4440

prune588.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma b b (- (* (* a c) 4.0)))) b) (/ (/ 1 2.0) a))
1.0b	(fma b b (- (* (* a c) 4.0)))
1.3b	(- (sqrt (fma b b (- (* (* a c) 4.0)))) b)
21.1b	(sqrt (fma b b (- (* (* a c) 4.0))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`times-frac`
60×	`*-un-lft-identity`
55×	`add-cube-cbrt`
43×	`associate-r`
19×	`add-exp-log`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`add-cbrt-cube`
7×	`pow1`
6×	`fma-neg` `div-exp` `associate-l` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `flip3--` `flip--` `cbrt-unprod`
2×	`frac-times` `associate-*l/` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `fma-udef`

Counts

4 → 143

Calls

4 calls:

38.0ms	(* (- (sqrt (fma b b (- (* (* a c) 4.0)))) b) (/ (/ 1 2.0) a))
0.0ms	(fma b b (- (* (* a c) 4.0)))
10.0ms	(- (sqrt (fma b b (- (* (* a c) 4.0)))) b)
1.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (- (sqrt (fma b b (- (* (* a c) 4.0)))) b) (/ (/ 1 2.0) a))
59.0ms	(fma b b (- (* (* a c) 4.0)))
92.0ms	(- (sqrt (fma b b (- (* (* a c) 4.0)))) b)
84.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))

simplify1.4s

Counts

155 → 155

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	283	3455
1	737	3002
2	2866	2574
done	5001	2573

prune450.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
1.3b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (pow b 2) (* 4.0 (* a c))))
21.1b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

50.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
51.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
10.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))
11.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
85.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
76.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))
70.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify684.0ms

Counts

128 → 128

Iterations

Useful iterations: done (680.0ms)

Iter	Nodes	Cost
0	112	2856
1	270	2306
2	941	1916
done	5000	1706

prune379.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes195.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 33.8b

bsearch101.0ms

Steps

Iters	Range		Point
8	1.3679096689958957e-81	5.608239720335765e-77	3.84613441880261e-81
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	38
1	31	38
done	31	38

end0.0ms

sample1.2s

Algorithm

intervals

Results

256.0ms	1074×	body	2560	valid
245.0ms	5844×	body	80	valid
179.0ms	907×	body	1280	valid
112.0ms	2890×	body	80	nan
69.0ms	452×	body	640	valid
34.0ms	234×	body	320	valid
30.0ms	102×	body	5120	valid
9.0ms	119×	body	160	valid