Details

sample102.0ms

Algorithm

intervals

Results

21.0ms	35×	body	2560	valid
18.0ms	185×	body	80	valid
11.0ms	23×	body	1280	valid
10.0ms	103×	body	80	nan
7.0ms	19×	body	640	valid
1.0ms	7×	body	160	valid
1.0ms	4×	body	320	valid

simplify171.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	64	17
3	115	17
4	142	17
5	152	17
6	156	17
done	156	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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:

69.0ms	(/ (- (- 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)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms	(- (* b b) (* 4.0 (* a c)))
108.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify851.0ms

Counts

89 → 89

Iterations

Useful iterations: done (847.0ms)

Iter	Nodes	Cost
0	155	1748
1	411	1650
2	1618	1476
done	5000	1466

prune534.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

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:

56.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(- (* b b) (* 4.0 (* a c)))
37.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series468.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
62.0ms	(- (* b b) (* 4.0 (* a c)))
120.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
118.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts

137 → 137

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	226	3421
1	588	3066
2	2565	2854
done	5001	2850

prune599.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite175.0ms

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:

130.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
7.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
86.0ms	(- (* b b) (* 4.0 (* a c)))
117.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

100 → 100

Iterations

Useful iterations: 2 (394.0ms)

Iter	Nodes	Cost
0	177	2073
1	509	1920
2	2788	1634
done	5000	1634

prune503.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

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:

75.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
63.0ms	(- (* b b) (* 4.0 (* a c)))
134.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
113.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify800.0ms

Counts

89 → 89

Iterations

Useful iterations: done (795.0ms)

Iter	Nodes	Cost
0	155	1748
1	411	1650
2	1618	1476
done	5000	1466

prune441.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

regimes539.0ms

Accuracy

87.7% (3.6b remaining)

Error of 9.0b against oracle of 5.4b and baseline of 34.4b

bsearch357.0ms

Steps

Iters	Range	Point
9	6.258218916731328e+93	1.8883840965187804e+99	6.637037935235253e+98
7	-1.9525004674970017e-146	-8.640740768077714e-148	-1.571246895950166e-147
10	-6.172175216823688e+56	-1.1198862992811701e+41	-1.532647813487865e+52

Iters

Range

Point

6.258218916731328e+93

1.8883840965187804e+99

6.637037935235253e+98

-1.9525004674970017e-146

-8.640740768077714e-148

-1.571246895950166e-147

-6.172175216823688e+56

-1.1198862992811701e+41

-1.532647813487865e+52

simplify13.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	40	71
1	51	65
2	54	65
done	54	65

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	1114×	body	2560	valid
957.0ms	5781×	body	80	valid
459.0ms	884×	body	1280	valid
387.0ms	2931×	body	80	nan
234.0ms	464×	body	640	valid
71.0ms	110×	body	5120	valid
59.0ms	250×	body	320	valid
21.0ms	127×	body	160	valid