Details

sample58.0ms

Algorithm

intervals

Results

12.0ms	27×	body	2560	valid
11.0ms	202×	body	80	valid
9.0ms	35×	body	1280	valid
4.0ms	86×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	45	13
4	47	13
done	47	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

39.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
76.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify617.0ms

Counts

183 → 183

Iterations

Useful iterations: done (612.0ms)

Iter	Nodes	Cost
0	242	5993
1	536	4313
2	1422	3549
done	5001	3540

prune340.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b	(/ (/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.3b	(/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 219

Calls

4 calls:

20.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(/ (/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
28.0ms	(/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
143.0ms	(/ (/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
183.0ms	(/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

231 → 231

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	342	7455
1	823	6251
2	2480	5351
done	5000	5349

prune547.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.8b	(* (/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
10.3b	(/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
52×	`times-frac`
47×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
23×	`sqrt-prod`
18×	`prod-diff` `add-cbrt-cube`
16×	`difference-of-squares`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--`
7×	`pow1`
6×	`fma-neg` `associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `cbrt-unprod` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 173

Calls

4 calls:

21.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
60.0ms	(* (/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
26.0ms	(/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
149.0ms	(* (/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
183.0ms	(/ (+ (* a c) (* b_2 (- b_2 b_2))) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify981.0ms

Counts

185 → 185

Iterations

Useful iterations: done (975.0ms)

Iter	Nodes	Cost
0	288	4937
1	793	4056
2	2239	3228
done	5001	3226

prune451.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0b	(/ (fma a c 0) a)
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
9×	`times-frac`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-/r` `flip--` `associate-/l`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out--`

Counts

4 → 103

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms	(/ (fma a c 0) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(/ (fma a c 0) a)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

115 → 115

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	176	1788
1	356	1513
2	933	1264
3	3532	1188
done	5001	1187

prune266.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

regimes154.0ms

Accuracy

96% (0.9b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 28.8b

bsearch116.0ms

Steps

Iters	Range	Point
8	2.1878188410446244e+107	3.8616146939177386e+111	2.8568501197790958e+109
9	2.1745589989703455e-245	7.342308417195682e-240	2.5402182456312607e-243
6	-2.0136180636941443e+142	-1.4127342237564056e+141	-2.61268387266151e+141

Iters

Range

Point

2.1878188410446244e+107

3.8616146939177386e+111

2.8568501197790958e+109

2.1745589989703455e-245

7.342308417195682e-240

2.5402182456312607e-243

-2.0136180636941443e+142

-1.4127342237564056e+141

-2.61268387266151e+141

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	49
1	35	49
done	35	49

end0.0ms

sample1.0s

Algorithm

intervals

Results

214.0ms	1110×	body	2560	valid
192.0ms	5789×	body	80	valid
142.0ms	885×	body	1280	valid
92.0ms	2997×	body	80	nan
54.0ms	449×	body	640	valid
27.0ms	102×	body	5120	valid
26.0ms	256×	body	320	valid
8.0ms	124×	body	160	valid