Details

sample112.0ms

Algorithm

intervals

Results

21.0ms	36×	body	2560	valid
18.0ms	176×	body	80	valid
17.0ms	33×	body	1280	valid
8.0ms	79×	body	80	nan
7.0ms	19×	body	640	valid
4.0ms	6×	body	5120	valid
3.0ms	10×	body	320	valid
1.0ms	3×	body	160	valid

simplify147.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	156
6	156
5	152
4	142
3	115
2	64
1	28
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

98.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
52.0ms	(- (* b b) (* 4.0 (* a c)))
132.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
139.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify777.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1618
1	411
0	155

prune642.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize22.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
6.9b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

33.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
129.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
52.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series753.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
235.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
279.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	3611
1	648
0	250

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize46.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
2.2b	(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
5.2b	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) a)
24.4b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-cbrt-cube` `add-exp-log`
41×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`times-frac`
24×	`associate-r`
21×	`cbrt-undiv` `div-exp`
19×	`add-cube-cbrt`
16×	`prod-exp` `cbrt-unprod`
8×	`difference-of-squares`
7×	`pow1` `associate-l` `sqrt-prod`
6×	`add-log-exp`
4×	`distribute-lft-out--`
3×	`associate-/r*` `flip3--` `div-inv` `flip--` `associate-/l/`
2×	`frac-times` `sqrt-div` `associate-l/` `associate-r/` `associate-/r/` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 121

Calls

4 calls:

55.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
162.0ms	(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
73.0ms	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) a)
23.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
320.0ms	(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
242.0ms	(/ (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) a)
88.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify512.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
1	787
0	260

prune718.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize27.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
2.2b	(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
5.3b	(* (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) (/ 1 a))
24.4b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-exp-log`
90×	`add-cbrt-cube`
68×	`prod-exp`
49×	`div-exp`
46×	`add-sqr-sqrt`
38×	`cbrt-unprod`
37×	`associate-r`
32×	`*-un-lft-identity`
31×	`times-frac`
28×	`cbrt-undiv`
24×	`add-cube-cbrt`
12×	`pow1`
8×	`associate-l` `difference-of-squares`
7×	`rec-exp` `1-exp` `sqrt-prod`
6×	`frac-times` `associate-*l/` `add-log-exp`
4×	`pow-prod-down` `associate-*r/` `distribute-lft-out--`
3×	`flip3--` `div-inv` `flip--`
2×	`sqrt-div` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `un-div-inv`

Counts

4 → 161

Calls

4 calls:

59.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
112.0ms	(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
195.0ms	(* (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) (/ 1 a))
14.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series747.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
307.0ms	(* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
248.0ms	(* (* (/ (* 4.0 a) 2.0) (/ c (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))) (/ 1 a))
76.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify571.0ms

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
1	1036
0	317

prune850.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes352.0ms

Accuracy

90.2% (2.6b remaining)

Error of 8.0b against oracle of 5.4b and baseline of 32.3b

bsearch279.0ms

Steps

Iters	Range		Point
9	2.1340360609407003e+79	6.102484722804822e+84	6.033691444141405e+84
10	8.852475844905406e-209	2.711563690867585e-195	8.958852798091287e-209
9	-31812840434242.992	-117892343.0362464	-9661478263987.111

simplify5.0ms

Iterations

Iter	Nodes
done	58
1	58
0	44

end0.0ms

sample3.6s

Algorithm

intervals

Results

996.0ms	921×	body	1280	valid
865.0ms	1065×	body	2560	valid
551.0ms	5799×	body	80	valid
269.0ms	2883×	body	80	nan
214.0ms	455×	body	640	valid
55.0ms	239×	body	320	valid
49.0ms	86×	body	5120	valid
18.0ms	111×	body	160	valid