Details

sample267.0ms

Algorithm

intervals

Results

86.0ms	105×	body	320	valid
25.0ms	282×	body	80	nan
24.0ms	538×	pre	80	true
20.0ms	105×	body	160	valid
8.0ms	20×	body	640	valid
3.0ms	26×	body	80	valid

simplify111.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize16.0ms

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))
27.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite220.0ms

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:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
134.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
61.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
63.0ms	(- (* b b) (* (* 4.0 a) c))
198.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
158.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.9s

Counts

102 → 102

Iterations

Useful iterations: done (1.9s)

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

prune341.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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

rewrite265.0ms

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:

48.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
118.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series766.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms	(- (* b b) (* (* 4.0 a) c))
294.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
242.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify2.2s

Counts

243 → 243

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	340	10026
1	812	7598
2	3231	6483
done	5000	6397

prune795.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
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)) (* 2.0 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
135×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
125×	`add-cube-cbrt`
92×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
15×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
7×	`associate-r`
6×	`pow1` `associate-*r/`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `times-frac` `diff-log` `div-exp` `associate-l` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `flip3-+` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 285

Calls

4 calls:

111.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
48.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(- (* b b) (* (* 4.0 a) c))
189.0ms	(/ (+ 0 (* (* a c) 4.0)) (* 2.0 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
116.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms	(- (* b b) (* (* 4.0 a) c))
241.0ms	(/ (+ 0 (* (* a c) 4.0)) (* 2.0 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify2.3s

Counts

297 → 297

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	375	17014
1	776	11181
2	3134	8606
done	5000	8353

prune692.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

90.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
17.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(+ (- (* a b)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
62.0ms	(/ (+ 0 (* (* a c) 4.0)) (* 2.0 (+ (- (* a b)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a))))

series663.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
59.0ms	(- (* b b) (* (* 4.0 a) c))
172.0ms	(+ (- (* a b)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
323.0ms	(/ (+ 0 (* (* a c) 4.0)) (* 2.0 (+ (- (* a b)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) a))))

simplify1.9s

Counts

115 → 115

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	203	2373
1	552	2195
2	2715	1813
done	5000	1812

prune609.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	19	25
1	26	23
done	26	23

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	3715×	body	320	valid
1.3s	16258×	pre	80	true
876.0ms	8258×	body	80	nan
471.0ms	2936×	body	160	valid
169.0ms	455×	body	640	valid
68.0ms	894×	body	80	valid