Details

sample85.0ms

Algorithm

intervals

Results

17.0ms	542×	pre	80	true
15.0ms	158×	body	160	valid
14.0ms	286×	body	80	nan
7.0ms	47×	body	320	valid
3.0ms	51×	body	80	valid

simplify133.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite210.0ms

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:

23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(- (* b b) (* (* 4.0 a) c))
116.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(- (* b b) (* (* 4.0 a) c))
165.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
123.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1481	1361
done	5000	1347

prune331.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.4b	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite247.0ms

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:

36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
83.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms	(- (* b b) (* (* 4.0 a) c))
198.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
271.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.0s

Counts

243 → 243

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	340	10026
1	812	7598
2	3236	6483
done	5001	6397

prune786.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
0.3b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

338×	`times-frac`
263×	`add-sqr-sqrt`
252×	`*-un-lft-identity`
151×	`add-cube-cbrt`
107×	`add-exp-log`
85×	`associate-r`
65×	`add-cbrt-cube`
50×	`distribute-lft-out--` `difference-of-squares`
47×	`div-exp`
35×	`prod-exp`
30×	`associate-/l*`
25×	`cbrt-undiv` `distribute-rgt-neg-in` `sqrt-prod`
21×	`cbrt-unprod`
16×	`associate-/r/`
11×	`div-inv`
10×	`associate-/r*`
9×	`flip3--` `flip--`
7×	`pow1` `associate-l`
6×	`rec-exp` `1-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sub-neg` `pow-flip` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 339

Calls

4 calls:

46.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
264.0ms	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
111.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)

series570.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
53.0ms	(- (* b b) (* (* 4.0 a) c))
204.0ms	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
173.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)

simplify2.5s

Counts

351 → 351

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	447	10246
1	1255	9231
2	4323	8253
done	5001	8251

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (/ (* c (* 4.0 a)) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b	(* (/ (/ (* c (* 4.0 a)) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 a))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
164×	`*-un-lft-identity`
159×	`times-frac`
103×	`add-exp-log`
98×	`add-cube-cbrt`
63×	`add-cbrt-cube`
61×	`prod-diff`
55×	`associate-l`
46×	`sqrt-prod`
45×	`div-exp`
37×	`distribute-rgt-neg-in`
35×	`prod-exp`
32×	`distribute-lft-out--` `difference-of-squares`
26×	`cbrt-undiv`
21×	`distribute-lft-neg-in`
19×	`cbrt-unprod`
18×	`div-inv`
13×	`associate-r`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1` `associate-/r` `associate-/l`
6×	`pow1` `unswap-sqr`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg`
1×	`associate--l-` `neg-sub0` `frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `associate-/l/`

Counts

4 → 311

Calls

4 calls:

32.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(/ (/ (* c (* 4.0 a)) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
180.0ms	(* (/ (/ (* c (* 4.0 a)) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 a))

series758.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
57.0ms	(- (* b b) (* (* 4.0 a) c))
250.0ms	(/ (/ (* c (* 4.0 a)) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
315.0ms	(* (/ (/ (* c (* 4.0 a)) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 a))

simplify3.3s

Counts

323 → 323

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	447	12346
1	1236	10078
2	4255	8407
done	5001	8405

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes165.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	25
1	26	25
done	26	25

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	4878×	body	160	valid
718.0ms	8393×	body	80	nan
630.0ms	16393×	pre	80	true
384.0ms	1311×	body	320	valid
130.0ms	1811×	body	80	valid