Details

sample188.0ms

Algorithm

intervals

Results

18.0ms	45×	body	1280	valid
17.0ms	184×	body	80	valid
13.0ms	25×	body	2560	valid
5.0ms	17×	body	640	valid
5.0ms	69×	body	80	nan
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

75.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
95.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(- (* b_2 b_2) (* a c))
114.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.2s

Counts

112 → 112

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	164	1638
1	385	1535
2	1102	1355
3	3175	1340
done	5001	1332

prune512.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
3.5b	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.2b	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
29×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `associate-/r/`
9×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`distribute-rgt-neg-in` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 140

Calls

4 calls:

20.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
83.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b_2 b_2) (* a c))
194.0ms	(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
253.0ms	(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

152 → 152

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	246	3374
1	609	3147
2	2094	2882
done	5000	2811

prune573.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite152.0ms

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-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 170

Calls

4 calls:

46.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
130.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
47.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.4s

Counts

182 → 182

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	235	5947
1	503	4258
2	1245	3498
3	4133	2945
done	5000	2945

prune501.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (fma a (- c) (pow b_2 2)))) a)
0.4b	(+ (- b_2) (sqrt (fma a (- c) (pow b_2 2))))
22.9b	(sqrt (fma a (- c) (pow b_2 2)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out`
8×	`distribute-rgt-neg-in`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1`
3×	`distribute-lft-neg-in` `expm1-log1p-u` `associate-/r*` `sqrt-prod` `log1p-expm1-u`
2×	`neg-sub0` `associate-+l-` `flip3-+` `sum-log` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

3 → 82

Calls

3 calls:

58.0ms	(/ (+ (- b_2) (sqrt (fma a (- c) (pow b_2 2)))) a)
27.0ms	(+ (- b_2) (sqrt (fma a (- c) (pow b_2 2))))
3.0ms	(sqrt (fma a (- c) (pow b_2 2)))

series380.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(/ (+ (- b_2) (sqrt (fma a (- c) (pow b_2 2)))) a)
119.0ms	(+ (- b_2) (sqrt (fma a (- c) (pow b_2 2))))
115.0ms	(sqrt (fma a (- c) (pow b_2 2)))

simplify2.7s

Counts

91 → 91

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	129	1346
1	292	1261
2	759	1117
3	1944	1109
done	5000	1098

prune338.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.2b

regimes237.0ms

Accuracy

96.1% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.6b

bsearch173.0ms

Steps

Iters	Range	Point
2	5.341589198600723e+134	5.967668210703041e+134	5.4198490751135124e+134
10	-1.2529167750641135e-296	-2.859335985249397e-307	-1.1350926615485409e-302
10	-2.386196042261592e+160	-1.0923850232644114e+143	-1.119811545308531e+143

Iters

Range

Point

5.341589198600723e+134

5.967668210703041e+134

5.4198490751135124e+134

-1.2529167750641135e-296

-2.859335985249397e-307

-1.1350926615485409e-302

-2.386196042261592e+160

-1.0923850232644114e+143

-1.119811545308531e+143

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	37	57
1	44	53
done	44	53

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	1056×	body	2560	valid
465.0ms	5847×	body	80	valid
354.0ms	926×	body	1280	valid
218.0ms	2938×	body	80	nan
165.0ms	477×	body	640	valid
87.0ms	113×	body	5120	valid
72.0ms	209×	body	320	valid
13.0ms	108×	body	160	valid