Details

sample288.0ms

Algorithm

intervals

Results

58.0ms	96×	body	80	nan
35.0ms	40×	body	2560	valid
33.0ms	187×	body	80	valid
28.0ms	32×	body	1280	valid
5.0ms	8×	body	640	valid
2.0ms	2×	body	5120	valid
2.0ms	5×	body	320	valid
1.0ms	2×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	34
5	34
4	32
3	30
2	23
1	15
0	10

prune58.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `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 → 118

Calls

4 calls:

83.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
59.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
108.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
54.0ms	(- (* b_2 b_2) (* a c))
131.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

130 → 130

Iterations

Iter	Nodes
3	3582
2	1173
1	458
0	195

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

165.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
54.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
115.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
51.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.6s

Counts

131 → 131

Iterations

Iter	Nodes
3	4056
2	1390
1	523
0	215

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (* b_2 b_2) (* a c))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b_2 b_2) (* a c))
54.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

78 → 78

Iterations

Iter	Nodes
4	3866
3	1385
2	442
1	159
0	67

prune980.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.5b

localize34.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.8b	(/ (- (- (* b_2 b_2) (* a c)) (* b_2 b_2)) a)
19.3b	(- (- (* b_2 b_2) (* a c)) (* b_2 b_2))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`times-frac`
11×	`add-log-exp`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod`
5×	`pow1` `difference-of-squares`
4×	`expm1-log1p-u` `prod-diff` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `flip3--` `fma-neg` `diff-log` `associate--l+` `flip--`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

36.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
70.0ms	(/ (- (- (* b_2 b_2) (* a c)) (* b_2 b_2)) a)
33.0ms	(- (- (* b_2 b_2) (* a c)) (* b_2 b_2))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(/ (- (- (* b_2 b_2) (* a c)) (* b_2 b_2)) a)
27.0ms	(- (- (* b_2 b_2) (* a c)) (* b_2 b_2))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

111 → 111

Iterations

Iter	Nodes
3	5151
2	1294
1	425
0	168

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.4b

regimes323.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 28.9b

bsearch256.0ms

Steps

Iters	Range		Point
9	1.5347927881719531e+137	5.414027326126016e+143	6.5172615559013e+137
4	1.9945656437063767e-299	3.432923155517869e-299	2.08048502174419e-299
10	-1.4013492266633723e+97	-6.399945091756968e+81	-9.20968712670863e+88

simplify6.0ms

Iterations

Iter	Nodes
2	38
1	38
0	32

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	1088×	body	2560	valid
830.0ms	5907×	body	80	valid
617.0ms	916×	body	1280	valid
322.0ms	2906×	body	80	nan
237.0ms	436×	body	640	valid
130.0ms	121×	body	5120	valid
64.0ms	212×	body	320	valid
52.0ms	112×	body	160	valid