Details

sample89.0ms

Algorithm

intervals

Results

12.0ms	185×	body	80	valid
9.0ms	35×	body	2560	valid
5.0ms	24×	body	1280	valid
3.0ms	76×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify53.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

72.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
81.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Counts: 103 → 103

prune264.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

49.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
42.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Counts: 189 → 189

prune310.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
528×	`add-sqr-sqrt`
527×	`*-un-lft-identity`
355×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-rgt-neg-in` `div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/r*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 468

Calls

4 calls:

63.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
38.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Counts: 480 → 480

prune696.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cbrt 1) a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
22×	`associate-l`
21×	`times-frac`
19×	`add-cube-cbrt`
11×	`cbrt-prod`
10×	`add-log-exp`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`diff-log`
2×	`distribute-rgt-in` `frac-times` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `associate-*r/` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 100

Calls

4 calls:

94.0ms	(* (/ (cbrt 1) a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (cbrt 1) a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
43.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Counts: 112 → 112

prune324.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.7b

regimes314.0ms

Accuracy

89.3% (3.1b remaining)

Error of 8.4b against oracle of 5.4b and baseline of 34.1b

bsearch218.0ms

Steps

Iters	Range	Point
8	9.012561940608131e+125	4.309422734686771e+129	3.1300482469197902e+128
9	1.5935168845766596e-213	1.1953111840417005e-206	1.626652957185991e-213
10	-1.6145330241135586e+155	-4.1230913930237915e+136	-5.978111652548667e+136

Iters

Range

Point

9.012561940608131e+125

4.309422734686771e+129

3.1300482469197902e+128

1.5935168845766596e-213

1.1953111840417005e-206

1.626652957185991e-213

-1.6145330241135586e+155

-4.1230913930237915e+136

-5.978111652548667e+136

simplify1.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

661.0ms	1059×	body	2560	valid
453.0ms	5897×	body	80	valid
263.0ms	915×	body	1280	valid
191.0ms	2932×	body	80	nan
76.0ms	463×	body	640	valid
30.0ms	243×	body	320	valid
28.0ms	85×	body	5120	valid
9.0ms	104×	body	160	valid