Details

sample315.0ms

Algorithm

intervals

Results

21.0ms	42×	body	2560	valid
16.0ms	173×	body	80	valid
10.0ms	25×	body	1280	valid
6.0ms	69×	body	80	nan
6.0ms	18×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify155.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite305.0ms

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:

124.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
81.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
281.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1414	3549
done	5001	3001

prune572.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (pow b_2 2) (* a c))
2.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
10.8b	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
24.4b	(sqrt (- (pow b_2 2) (* a c)))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
117×	`*-un-lft-identity`
85×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
8×	`fma-neg` `prod-diff`
7×	`flip3--` `flip--`
6×	`unpow-prod-down` `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` `unpow2` `sqr-pow`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 208

Calls

4 calls:

32.0ms	(- (pow b_2 2) (* a c))
181.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
111.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
24.0ms	(sqrt (- (pow b_2 2) (* a c)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (pow b_2 2) (* a c))
217.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
330.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
106.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify1.6s

Counts

220 → 220

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	332	5836
1	769	5059
2	2431	4856
done	5000	4842

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize34.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (pow b_2 2) (* a c))
2.5b	(* (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) (/ 1 a))
10.8b	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
24.4b	(sqrt (- (pow b_2 2) (* a c)))

rewrite487.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
52×	`times-frac`
37×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`fma-neg` `prod-diff` `prod-exp`
7×	`pow1` `distribute-lft-out--`
6×	`unpow-prod-down` `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/` `unpow2` `sqr-pow`
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 → 162

Calls

4 calls:

38.0ms	(- (pow b_2 2) (* a c))
232.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) (/ 1 a))
167.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
37.0ms	(sqrt (- (pow b_2 2) (* a c)))

series1.0s

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (pow b_2 2) (* a c))
616.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) (/ 1 a))
249.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
83.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify3.9s

Counts

174 → 174

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	278	3714
1	721	3155
2	2280	2836
done	5000	2656

prune696.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (pow b_2 2) (* a c))) b_2))
0.4b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
1.2b	(- (pow b_2 2) (* a c))
24.4b	(sqrt (- (pow b_2 2) (* a c)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

81.0ms	(/ c (- (sqrt (- (pow b_2 2) (* a c))) b_2))
114.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
37.0ms	(- (pow b_2 2) (* a c))
35.0ms	(sqrt (- (pow b_2 2) (* a c)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(/ c (- (sqrt (- (pow b_2 2) (* a c))) b_2))
134.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
61.0ms	(- (pow b_2 2) (* a c))
74.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify2.9s

Counts

143 → 143

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	202	2544
1	433	2228
2	960	1987
3	3269	1887
done	5000	1887

prune490.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.2b

regimes282.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.6b

bsearch246.0ms

Steps

Iters	Range	Point
5	1.7897742140858872e+53	5.1194650287633095e+53	5.031608061939103e+53
9	9.448397398655464e-278	1.4829972419072586e-270	8.216265756828381e-276
9	-1.4642911230069481e+159	-8.435593739772907e+149	-3.5132588248780117e+152

Iters

Range

Point

1.7897742140858872e+53

5.1194650287633095e+53

5.031608061939103e+53

9.448397398655464e-278

1.4829972419072586e-270

8.216265756828381e-276

-1.4642911230069481e+159

-8.435593739772907e+149

-3.5132588248780117e+152

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	54
1	40	54
done	40	54

end0.0ms

sample3.1s

Algorithm

intervals

Results

761.0ms	2938×	body	80	nan
598.0ms	1104×	body	2560	valid
497.0ms	5843×	body	80	valid
368.0ms	860×	body	1280	valid
208.0ms	492×	body	640	valid
57.0ms	107×	body	5120	valid
43.0ms	226×	body	320	valid
14.0ms	106×	body	160	valid