Details

sample133.0ms

Algorithm

intervals

Results

27.0ms	151×	body	160	valid
23.0ms	271×	body	80	nan
19.0ms	527×	pre	80	true
19.0ms	105×	body	80	valid

simplify153.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
29.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
128.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms	(- (* b b) (* (* 4.0 a) c))
39.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
184.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(- (* b b) (* (* 4.0 a) c))
133.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify2.1s

Counts

102 → 102

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	167	1697
1	450	1588
2	2152	1361
done	5001	1352

prune630.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite342.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

145.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
53.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series828.0ms

Counts

4 → 12

Calls

4 calls:

307.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
139.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(- (* b b) (* (* 4.0 a) c))
305.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify637.0ms

Counts

243 → 243

Iterations

Useful iterations: done (623.0ms)

Iter	Nodes	Cost
0	339	10026
1	862	7622
done	5000	6606

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma b b (- (* c (* 4.0 a)))))
0.2b	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))) (* 2.0 a))
0.2b	(- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))
0.3b	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a)))))))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 230

Calls

4 calls:

3.0ms	(sqrt (fma b b (- (* c (* 4.0 a)))))
117.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))) (* 2.0 a))
31.0ms	(- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))
78.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a)))))))

series939.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (fma b b (- (* c (* 4.0 a)))))
309.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))) (* 2.0 a))
151.0ms	(- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))
346.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a)))))))

simplify3.0s

Counts

242 → 242

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	322	9993
1	794	7593
2	4019	6469
done	5000	6467

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma b b (- (* c (* 4.0 a)))))
0.2b	(- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))
0.3b	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a)))))))
0.3b	(* (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))) (/ 1 (* 2.0 a)))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
71×	`add-cube-cbrt`
60×	`prod-diff`
51×	`add-exp-log`
46×	`times-frac`
41×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
27×	`associate-l` `add-cbrt-cube`
21×	`distribute-lft-neg-in`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
10×	`fma-neg`
8×	`cbrt-undiv` `cbrt-unprod` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-/r*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `flip--` `div-inv` `associate-/l*`
2×	`diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 225

Calls

4 calls:

3.0ms	(sqrt (fma b b (- (* c (* 4.0 a)))))
36.0ms	(- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))
76.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a)))))))
157.0ms	(* (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))) (/ 1 (* 2.0 a)))

series963.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (fma b b (- (* c (* 4.0 a)))))
151.0ms	(- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))
327.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a)))))))
338.0ms	(* (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (fma b b (- (* c (* 4.0 a))))))) (/ 1 (* 2.0 a)))

simplify753.0ms

Counts

237 → 237

Iterations

Useful iterations: done (737.0ms)

Iter	Nodes	Cost
0	327	9587
1	897	7159
done	5000	5997

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes431.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	25
1	26	23
2	34	23
done	34	23

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	16755×	pre	80	true
1.0s	8755×	body	80	nan
973.0ms	4469×	body	160	valid
424.0ms	3531×	body	80	valid