Details

sample76.0ms

Algorithm

intervals

Results

16.0ms	130×	body	320	valid
10.0ms	498×	pre	80	true
9.0ms	242×	body	80	nan
6.0ms	18×	body	640	valid
6.0ms	76×	body	160	valid
2.0ms	32×	body	80	valid

simplify71.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite110.0ms

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:

10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
243.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify870.0ms

Counts

102 → 102

Iterations

Useful iterations: done (868.0ms)

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

prune243.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
145.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.3s

Counts

243 → 243

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	340	10026
1	812	7598
2	3228	6483
done	5000	6397

prune515.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
82×	`add-sqr-sqrt`
78×	`times-frac`
60×	`add-cube-cbrt`
41×	`prod-diff`
27×	`associate-/l*`
26×	`distribute-rgt-neg-in`
22×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-lft-neg-in`
11×	`fma-neg` `difference-of-squares`
10×	`sqrt-prod` `add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/`
5×	`neg-mul-1` `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 → 200

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))
55.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
36.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))
149.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
187.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))))

simplify1.3s

Counts

212 → 212

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	328	8474
1	786	6028
2	3208	5145
done	5001	5087

prune535.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

338×	`times-frac`
308×	`add-sqr-sqrt`
297×	`*-un-lft-identity`
192×	`add-cube-cbrt`
107×	`add-exp-log`
85×	`associate-r`
65×	`add-cbrt-cube`
60×	`prod-diff`
56×	`sqrt-prod`
52×	`distribute-lft-out--` `difference-of-squares`
47×	`distribute-rgt-neg-in` `div-exp`
35×	`prod-exp`
30×	`associate-/l*`
25×	`cbrt-undiv`
21×	`distribute-lft-neg-in` `cbrt-unprod`
16×	`associate-/r/`
11×	`div-inv`
10×	`fma-neg` `associate-/r*`
9×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l`
6×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
2×	`frac-2neg` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `pow-flip` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 413

Calls

4 calls:

29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
39.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
64.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
155.0ms	(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series473.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
104.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
125.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
161.0ms	(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify1.6s

Counts

425 → 425

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	517	15231
1	1367	12349
2	4128	10575
done	5000	10489

prune668.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes86.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	18	25
1	24	23
done	24	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

369.0ms	3616×	body	320	valid
280.0ms	16243×	pre	80	true
268.0ms	8243×	body	80	nan
197.0ms	2887×	body	160	valid
70.0ms	517×	body	640	valid
34.0ms	980×	body	80	valid