Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	39×	body	2560	valid
7.0ms	183×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	84×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	120	17
4	144	17
5	150	17
6	153	17
done	153	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

43.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
53.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify773.0ms

Counts

169 → 169

Iterations

Useful iterations: done (767.0ms)

Iter	Nodes	Cost
0	243	6690
1	607	4755
2	1990	3760
done	5000	3759

prune382.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

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:

41.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
53.0ms	(- (* b b) (* 4.0 (* a c)))
86.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify823.0ms

Counts

183 → 183

Iterations

Useful iterations: done (816.0ms)

Iter	Nodes	Cost
0	246	7041
1	584	5094
2	1838	4140
done	5000	4139

prune399.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

50.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 a))
53.0ms	(- (* b b) (* 4.0 (* a c)))
86.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts

181 → 181

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	265	6947
1	650	4904
2	2237	3878
done	5000	3877

prune411.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 257

Calls

4 calls:

26.0ms	(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series323.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
52.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

269 → 269

Iterations

Useful iterations: 2 (305.0ms)

Iter	Nodes	Cost
0	353	9970
1	809	7637
2	2816	6393
done	5000	6393

prune449.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes200.0ms

Accuracy

82.6% (4.9b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 33.6b

bsearch81.0ms

Steps

Iters	Range		Point
9	1.790439840991813e+53	4.6520850645607246e+61	1.3316184968738608e+61
2	-4.223797038045246e-104	-3.7861133082378615e-104	-4.1690865718193236e-104

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	47
1	41	45
2	43	45
done	43	45

end0.0ms

sample1.1s

Algorithm

intervals

Results

250.0ms	1069×	body	2560	valid
229.0ms	5865×	body	80	valid
158.0ms	828×	body	1280	valid
107.0ms	2882×	body	80	nan
72.0ms	477×	body	640	valid
36.0ms	110×	body	5120	valid
27.0ms	248×	body	320	valid
8.0ms	113×	body	160	valid