Details

sample90.0ms

Algorithm

intervals

Results

18.0ms	198×	body	80	valid
17.0ms	31×	body	2560	valid
13.0ms	28×	body	1280	valid
9.0ms	87×	body	80	nan
6.0ms	17×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify161.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.4b	(- (* b b) (* 4 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
24.3b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite89.0ms

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--` `insert-posit16` `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 → 81

Calls

4 calls:

56.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
8.0ms	(- (* b b) (* 4 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
64.0ms	(- (* b b) (* 4 (* a c)))
116.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
97.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1254
1	400
0	154

prune548.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
0.4b	(+ (* b b) (* c (* a -4)))
1.0b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
24.3b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite123.0ms

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×	`insert-posit16`
3×	`distribute-rgt-neg-in`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `diff-log` `div-exp` `flip-+` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 80

Calls

4 calls:

62.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
11.0ms	(+ (* b b) (* c (* a -4)))
35.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
14.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
55.0ms	(+ (* b b) (* c (* a -4)))
91.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
103.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify1.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1334
1	412
0	156

prune457.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
0.4b	(+ (* b b) (* c (* a -4)))
1.0b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
24.3b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite82.0ms

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`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3--` `div-inv` `flip--`
4×	`insert-posit16`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`flip3-+` `sqrt-div` `diff-log` `flip-+`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 128

Calls

4 calls:

35.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
9.0ms	(+ (* b b) (* c (* a -4)))
24.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
12.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
58.0ms	(+ (* b b) (* c (* a -4)))
123.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
84.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify1.8s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	1858
1	585
0	231

prune616.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
0.4b	(- (* b b) (* 4 (* a c)))
7.5b	(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
24.3b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`flip3--` `sqrt-div` `insert-posit16` `flip--`
3×	`div-inv` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `prod-exp` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

16.0ms	(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
8.0ms	(- (* b b) (* 4 (* a c)))
49.0ms	(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
48.0ms	(- (* b b) (* 4 (* a c)))
124.0ms	(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
99.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1406
1	413
0	161

prune603.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

regimes504.0ms

Accuracy

83% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 33.9b

bsearch350.0ms

Steps

Iters	Range		Point
9	6.2301214455520334e+75	1.9082112581546424e+85	1.6691257204922504e+85
4	-2.3602019652593256e-123	-1.5355849018748885e-123	-2.3344326820285623e-123
9	-2.9300981025422624e-27	-1.2024011261401705e-33	-6.936587154412951e-28
8	-1.0943378505721803e-12	-1.4409381956716427e-15	-7.363255598823911e-15

simplify10.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	1057×	body	2560	valid
560.0ms	5842×	body	80	valid
460.0ms	891×	body	1280	valid
426.0ms	2845×	body	80	nan
256.0ms	456×	body	640	valid
71.0ms	114×	body	5120	valid
62.0ms	228×	body	320	valid
21.0ms	117×	body	160	valid