Details

sample127.0ms

Algorithm

intervals

Results

36.0ms	31×	body	1280	valid
21.0ms	37×	body	2560	valid
17.0ms	182×	body	80	valid
10.0ms	22×	body	640	valid
8.0ms	89×	body	80	nan
2.0ms	9×	body	320	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	5120	valid

simplify602.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	140
7	140
6	138
5	135
4	132
3	113
2	62
1	29
0	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite221.0ms

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-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

125.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
54.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
122.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
58.0ms	(- (* b b) (* 4.0 (* a c)))
103.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5004
2	1789
1	600
0	241

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.4b	(- (* b b) (* 4.0 (* a c)))
6.1b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
141×	`prod-diff`
101×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
51×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
33×	`distribute-lft-neg-in`
28×	`div-inv`
15×	`fma-neg`
11×	`neg-mul-1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `prod-exp` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 240

Calls

4 calls:

16.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
7.0ms	(- (* b b) (* 4.0 (* a c)))
105.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series526.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
64.0ms	(- (* b b) (* 4.0 (* a c)))
149.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts

252 → 252

Iterations

Iter	Nodes
done	5000
2	2164
1	854
0	354

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize62.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
15.8b	(- (/ (- b) (* 2.0 a)) (* (/ (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) a)))
23.6b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.6b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

20×	`times-frac`
15×	`fma-neg` `prod-diff`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `pow1` `cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`frac-sub`
2×	`frac-times` `neg-mul-1` `sub-neg` `pow1/3` `diff-log` `div-inv`
1×	`associate--l-` `neg-sub0` `div-sub` `associate-l/` `associate-r/` `sub-div`

Counts

4 → 93

Calls

4 calls:

15.0ms	(- (* b b) (* 4.0 (* a c)))
63.0ms	(- (/ (- b) (* 2.0 a)) (* (/ (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) a)))
5.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
5.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* b b) (* 4.0 (* a c)))
231.0ms	(- (/ (- b) (* 2.0 a)) (* (/ (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) a)))
138.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
142.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1789
1	568
0	219

prune942.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.2b

localize88.0ms

Local error

Found 4 expressions with local error:

22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.6b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.6b	(cbrt (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`cbrt-div`
9×	`add-sqr-sqrt` `flip3--` `flip--`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `sqrt-prod`
4×	`cbrt-prod` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-l/` `associate-r/`

Counts

4 → 68

Calls

4 calls:

9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
36.0ms	(cbrt (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c))))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
80.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
115.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
169.0ms	(cbrt (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c))))))

simplify2.3s

Counts

80 → 80

Iterations

Iter	Nodes
done	5002
3	2218
2	660
1	253
0	129

prune779.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.2b

regimes564.0ms

Accuracy

84.9% (4.3b remaining)

Error of 10.5b against oracle of 6.2b and baseline of 34.5b

bsearch166.0ms

Steps

Iters	Range		Point
5	2.6243927093659187e+107	5.901159163981397e+107	3.038903409991338e+107
9	-1.0952546209266604e-55	-7.034794544076098e-65	-9.332433396832084e-58

simplify8.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.0s	5891×	body	80	valid
692.0ms	1016×	body	2560	valid
420.0ms	892×	body	1280	valid
367.0ms	2883×	body	80	nan
226.0ms	461×	body	640	valid
107.0ms	98×	body	5120	valid
58.0ms	220×	body	320	valid
19.0ms	118×	body	160	valid