Details

sample115.0ms

Algorithm

intervals

Results

27.0ms	29×	body	2560	valid
23.0ms	198×	body	80	valid
17.0ms	34×	body	1280	valid
9.0ms	94×	body	80	nan
5.0ms	12×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	5120	valid

simplify177.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b	(- (* b b) (* 4.0 (* a c)))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite151.0ms

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:

75.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
109.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms	(- (* b b) (* 4.0 (* a c)))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

169 → 169

Iterations

Iter	Nodes
done	5004
2	1789
1	600
0	241

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b	(- (* b b) (* 4.0 (* a c)))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

136.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
48.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
127.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(- (* b b) (* 4.0 (* a c)))
121.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts

177 → 177

Iterations

Iter	Nodes
done	5004
2	1964
1	664
0	267

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune29.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.4b

localize73.0ms

Local error

Found 4 expressions with local error:

20.0b	(- (* (- b) (- b)) (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

13.0ms	(- (* (- b) (- b)) (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* (- b) (- b)) (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c))))))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
109.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
3	3025
2	705
1	213
0	85

prune575.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

regimes393.0ms

Accuracy

72.8% (7.4b remaining)

Error of 13.2b against oracle of 5.7b and baseline of 33.2b

bsearch265.0ms

Steps

Iters	Range		Point
10	8.767897341253802e-114	4.657027509742155e-104	1.6805103049992592e-106
10	-3.3499769700489724e-75	-6.612186054126484e-88	-3.304421310335197e-75

simplify10.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	5858×	body	80	valid
774.0ms	1086×	body	2560	valid
680.0ms	2954×	body	80	nan
506.0ms	901×	body	1280	valid
165.0ms	481×	body	640	valid
57.0ms	97×	body	5120	valid
52.0ms	191×	body	320	valid
18.0ms	111×	body	160	valid