Details

sample242.0ms

Algorithm

intervals

Results

70.0ms	278×	body	80	nan
29.0ms	121×	body	320	valid
17.0ms	534×	pre	80	true
12.0ms	85×	body	160	valid
5.0ms	19×	body	640	valid
2.0ms	31×	body	80	valid

simplify149.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.0b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite175.0ms

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:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
35.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
83.0ms	(- (* b b) (* (* 4.0 a) c))
131.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
150.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

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

prune381.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 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)))))

rewrite354.0ms

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:

11.0ms	(- (* b b) (* (* 4.0 a) c))
40.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
170.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
122.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b b) (* (* 4.0 a) c))
130.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
235.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
282.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.2s

Counts

243 → 243

Iterations

Useful iterations: done (2.2s)

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

prune870.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* c (* (* (* 4.0 a) c) (* 4.0 a)))
0.3b	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 4) (* c (* (* (* 4.0 a) c) (* 4.0 a)))) (fma b b (* (* 4.0 a) c))))))
0.3b	(* (* (* 4.0 a) c) (* 4.0 a))
0.4b	(/ (- (pow b 4) (* c (* (* (* 4.0 a) c) (* 4.0 a)))) (fma b b (* (* 4.0 a) c)))

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log` `add-cbrt-cube`
54×	`pow1` `add-sqr-sqrt`
42×	`*-un-lft-identity`
37×	`times-frac` `pow-prod-down` `prod-exp` `cbrt-unprod`
26×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`associate-/r*`
8×	`sqrt-prod` `distribute-lft-out--`
6×	`associate-/l*`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `associate-l` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `associate-r` `clear-num` `associate-/r/` `*-commutative` `flip--` `div-inv`
1×	`flip3-+` `div-sub` `flip-+`

Counts

4 → 150

Calls

4 calls:

271.0ms	(* c (* (* (* 4.0 a) c) (* 4.0 a)))
146.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 4) (* c (* (* (* 4.0 a) c) (* 4.0 a)))) (fma b b (* (* 4.0 a) c))))))
102.0ms	(* (* (* 4.0 a) c) (* 4.0 a))
81.0ms	(/ (- (pow b 4) (* c (* (* (* 4.0 a) c) (* 4.0 a)))) (fma b b (* (* 4.0 a) c)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* c (* (* (* 4.0 a) c) (* 4.0 a)))
363.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 4) (* c (* (* (* 4.0 a) c) (* 4.0 a)))) (fma b b (* (* 4.0 a) c))))))
36.0ms	(* (* (* 4.0 a) c) (* 4.0 a))
130.0ms	(/ (- (pow b 4) (* c (* (* (* 4.0 a) c) (* 4.0 a)))) (fma b b (* (* 4.0 a) c)))

simplify2.3s

Counts

162 → 162

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	260	5275
1	629	4987
2	3088	4451
done	5000	4433

prune656.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 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)))))
0.3b	(* (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
102×	`*-un-lft-identity`
70×	`add-cube-cbrt`
61×	`prod-diff`
51×	`add-exp-log`
46×	`times-frac`
38×	`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`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`neg-mul-1` `associate-r` `associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`diff-log` `div-inv` `associate-/l*`
2×	`sub-neg` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 226

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
94.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
176.0ms	(* (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b b) (* (* 4.0 a) c))
125.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
296.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
240.0ms	(* (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify2.5s

Counts

238 → 238

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	345	9620
1	871	7148
2	3447	5898
done	5000	5812

prune809.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes126.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	22	23
done	22	23

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.2s	8339×	body	80	nan
1.1s	16339×	pre	80	true
870.0ms	3606×	body	320	valid
538.0ms	2912×	body	160	valid
262.0ms	508×	body	640	valid
159.0ms	974×	body	80	valid