Details

sample88.0ms

Algorithm

intervals

Results

20.0ms	23×	body	1280	valid
15.0ms	35×	body	2560	valid
14.0ms	185×	body	80	valid
7.0ms	103×	body	80	nan
5.0ms	19×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	7×	body	160	valid

simplify117.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
0.6b	(- (* b b) (* a (* 4.0 c)))
2.0b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
22.7b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite156.0ms

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:

101.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
13.0ms	(- (* b b) (* a (* 4.0 c)))
30.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
7.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
69.0ms	(- (* b b) (* a (* 4.0 c)))
119.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
90.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify840.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1700
1	416
0	157

prune520.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
0.6b	(- (* b b) (* a (* 4.0 c)))
2.0b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
22.7b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 125

Calls

4 calls:

60.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
13.0ms	(- (* b b) (* a (* 4.0 c)))
33.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
19.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
88.0ms	(- (* b b) (* a (* 4.0 c)))
113.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
119.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.1s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	2588
1	595
0	228

prune688.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* a 2.0)) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))
0.6b	(- (* b b) (* 4.0 (* c a)))
2.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
22.7b	(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `rec-exp` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `1-exp` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

145.0ms	(* (/ 1 (* a 2.0)) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))
13.0ms	(- (* b b) (* 4.0 (* c a)))
21.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (/ 1 (* a 2.0)) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))
84.0ms	(- (* b b) (* 4.0 (* c a)))
98.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
91.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	2986
1	514
0	179

prune627.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ b (sqrt (- (* b b) (* (* 4.0 c) a))))) (* a 2.0))
0.6b	(- (* b b) (* (* 4.0 c) a))
2.0b	(+ b (sqrt (- (* b b) (* (* 4.0 c) a))))
22.7b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `times-frac` `associate-/l*`
11×	`add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-log-exp`
5×	`pow1` `distribute-lft-out`
3×	`sqrt-prod`
2×	`cbrt-undiv` `neg-mul-1` `flip3-+` `flip3--` `sqrt-div` `div-exp` `flip-+` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `distribute-frac-neg` `cbrt-unprod` `div-inv`

Counts

4 → 82

Calls

4 calls:

137.0ms	(/ (- (+ b (sqrt (- (* b b) (* (* 4.0 c) a))))) (* a 2.0))
12.0ms	(- (* b b) (* (* 4.0 c) a))
15.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 c) a))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (+ b (sqrt (- (* b b) (* (* 4.0 c) a))))) (* a 2.0))
52.0ms	(- (* b b) (* (* 4.0 c) a))
126.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 c) a))))
105.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify978.0ms

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1903
1	438
0	169

prune481.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

regimes427.0ms

Accuracy

87.8% (3.5b remaining)

Error of 8.9b against oracle of 5.4b and baseline of 34.4b

bsearch272.0ms

Steps

Iters	Range	Point
9	6.258218916731328e+93	1.8883840965187804e+99	3.424685282990076e+98
7	-1.9525004674970017e-146	-8.640740768077714e-148	-2.0179410497559054e-147
6	-1.745417689399421e+60	-1.2092396089946692e+59	-7.890025456402397e+59

Iters

Range

Point

6.258218916731328e+93

1.8883840965187804e+99

3.424685282990076e+98

-1.9525004674970017e-146

-8.640740768077714e-148

-2.0179410497559054e-147

-1.745417689399421e+60

-1.2092396089946692e+59

-7.890025456402397e+59

simplify6.0ms

Iterations

Iter	Nodes
done	56
2	56
1	55
0	41

end0.0ms

sample3.5s

Algorithm

intervals

Results

727.0ms	1114×	body	2560	valid
675.0ms	5781×	body	80	valid
577.0ms	464×	body	640	valid
383.0ms	884×	body	1280	valid
271.0ms	2931×	body	80	nan
147.0ms	250×	body	320	valid
112.0ms	110×	body	5120	valid
19.0ms	127×	body	160	valid