Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	181×	body	80	valid
5.0ms	27×	body	2560	valid
5.0ms	31×	body	1280	valid
2.0ms	21×	body	640	valid
2.0ms	81×	body	80	nan
2.0ms	8×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify21.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

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:

42.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify623.0ms

Counts

183 → 183

Iterations

Useful iterations: done (617.0ms)

Iter	Nodes	Cost
0	242	5993
1	536	4313
2	1422	3549
done	5000	3540

prune360.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
2.6b	(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
8.2b	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
21.1b	(sqrt (- (pow b_2 2) (* a c)))

rewrite185.0ms

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:

45.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
71.0ms	(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
48.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
10.0ms	(sqrt (- (pow b_2 2) (* a c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
97.0ms	(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
132.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
58.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify1.0s

Counts

231 → 231

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	335	7469
1	802	6262
2	2353	5369
done	5000	5367

prune609.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

5.4b	(exp (log (sqrt (- (pow b_2 2) (* a c)))))
8.6b	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2))
15.5b	(- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2)
21.1b	(sqrt (- (pow b_2 2) (* a c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
41×	`add-cube-cbrt`
40×	`log-prod` `exp-sum`
27×	`prod-diff`
23×	`sqrt-prod`
21×	`times-frac`
15×	`difference-of-squares`
9×	`fma-neg`
7×	`pow1` `associate-/r*`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u`
3×	`log-pow` `associate-/l*`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 144

Calls

4 calls:

6.0ms	(exp (log (sqrt (- (pow b_2 2) (* a c)))))
56.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2))
59.0ms	(- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2)
9.0ms	(sqrt (- (pow b_2 2) (* a c)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(exp (log (sqrt (- (pow b_2 2) (* a c)))))
129.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2))
70.0ms	(- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2)
58.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify2.2s

Counts

156 → 156

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	235	3995
1	486	2993
2	1233	2410
3	3795	2258
done	5001	2254

prune394.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (pow b_2 2) (* a c))
1.2b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
13.4b	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (* a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
21.1b	(sqrt (- (pow b_2 2) (* a c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

9.0ms	(- (pow b_2 2) (* a c))
45.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
33.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (* a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
12.0ms	(sqrt (- (pow b_2 2) (* a c)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (pow b_2 2) (* a c))
69.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
104.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (* a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
60.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify805.0ms

Counts

127 → 127

Iterations

Useful iterations: done (802.0ms)

Iter	Nodes	Cost
0	212	2496
1	520	2078
2	1570	1636
done	5000	1631

prune318.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes181.0ms

Accuracy

88% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 32.0b

bsearch161.0ms

Steps

Iters	Range	Point
10	1.1889782913455773e+76	6.845935134449847e+90	2.0945334611922723e+90
9	-2.2089175703627385e-287	-1.7683474342019888e-296	-2.57120366754749e-295
9	-3.339096941797073e+59	-6.124320340976488e+51	-5.109856166749479e+57

Iters

Range

Point

1.1889782913455773e+76

6.845935134449847e+90

2.0945334611922723e+90

-2.2089175703627385e-287

-1.7683474342019888e-296

-2.57120366754749e-295

-3.339096941797073e+59

-6.124320340976488e+51

-5.109856166749479e+57

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	59
1	43	59
done	43	59

end0.0ms

sample1.0s

Algorithm

intervals

Results

213.0ms	1059×	body	2560	valid
196.0ms	5842×	body	80	valid
145.0ms	911×	body	1280	valid
90.0ms	2942×	body	80	nan
57.0ms	463×	body	640	valid
24.0ms	103×	body	5120	valid
22.0ms	235×	body	320	valid
7.0ms	109×	body	160	valid