Details

sample385.0ms

Algorithm

intervals

Results

110.0ms	187×	body	80	valid
36.0ms	37×	body	2560	valid
24.0ms	24×	body	1280	valid
18.0ms	86×	body	80	nan
12.0ms	18×	body	640	valid
3.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

65.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
40.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	2003
3	2003
2	1029
1	378
0	158

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

93.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* b_2 b_2) (* a c))
31.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
46.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	2003
3	2003
2	1029
1	378
0	158

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 166

Calls

4 calls:

67.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
46.0ms	(- (* b_2 b_2) (* a c))
99.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

178 → 178

Iterations

Iter	Nodes
done	2002
3	2002
2	1691
1	626
0	262

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

8.0ms

(* -1/2 (/ c b_2))

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

(* -1/2 (/ c b_2))

simplify1.1s

Counts

36 → 36

Iterations

Iter	Nodes
done	2000
4	2000
3	1450
2	509
1	173
0	69

prune323.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.3b

regimes472.0ms

Accuracy

84.5% (4.2b remaining)

Error of 9.8b against oracle of 5.6b and baseline of 32.8b

bsearch170.0ms

Steps

Iters	Range		Point
8	5.833527798943191e-77	3.6732813120885656e-72	3.1295384133612364e-73
9	-2.2464591800446616e+91	-3.153507839293123e+86	-1.3599228730895225e+90

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.2s	5892×	body	80	valid
988.0ms	1027×	body	2560	valid
745.0ms	882×	body	1280	valid
534.0ms	235×	body	320	valid
340.0ms	2956×	body	80	nan
265.0ms	463×	body	640	valid
89.0ms	98×	body	5120	valid
28.0ms	105×	body	160	valid