Details

sample90.0ms

Algorithm

intervals

Results

48.0ms	79×	body	1280	valid
17.0ms	150×	body	80	valid
7.0ms	14×	body	640	valid
3.0ms	9×	body	160	valid
1.0ms	4×	body	320	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	27
3	27
2	25
1	21
0	9

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(+ (/ 1/2 (hypot 1 x)) 1/2)
0.0b	(/ 1/2 (hypot 1 x))
2.4b	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
21×	`prod-diff`
20×	`sqrt-prod`
19×	`times-frac`
13×	`fma-def`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `fma-neg` `associate-/l` `distribute-lft-out--`
2×	`flip3-+` `sqrt-div` `flip-+` `hypot-def` `div-inv`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `flip--`

Counts

4 → 125

Calls

4 calls:

23.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
14.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
4.0ms	(/ 1/2 (hypot 1 x))
35.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
65.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
84.0ms	(/ 1/2 (hypot 1 x))
162.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify2.2s

Counts

137 → 137

Iterations

Iter	Nodes
3	3271
2	1145
1	490
0	213

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
1.9b	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `fma-neg` `div-exp` `prod-diff` `div-inv`
2×	`associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--`

Counts

4 → 113

Calls

4 calls:

6.0ms	(/ 1/2 (hypot 1 x))
6.0ms	(/ 1/2 (hypot 1 x))
6.0ms	(/ 1/2 (hypot 1 x))
8.0ms	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ 1/2 (hypot 1 x))
57.0ms	(/ 1/2 (hypot 1 x))
70.0ms	(/ 1/2 (hypot 1 x))
210.0ms	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.1s

Counts

125 → 125

Iterations

Iter	Nodes
3	3040
2	933
1	349
0	149

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.6b	(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.8b	(- (* 1 1) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

136×	`frac-times`
108×	`flip3-+` `sqrt-div` `flip-+`
107×	`pow1`
53×	`pow-prod-up`
44×	`associate-l/` `associate-r/`
34×	`pow-plus`
32×	`sqrt-pow1` `pow1/2`
30×	`add-sqr-sqrt`
28×	`pow-prod-down`
22×	`*-un-lft-identity`
20×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
18×	`times-frac`
13×	`pow-sqr`
11×	`cube-unmult`
8×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate--r+`
2×	`difference-cubes` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `fma-neg` `diff-log` `swap-sqr` `associate-r` `associate-l` `prod-diff` `pow3` `*-commutative` `flip--` `difference-of-squares`

Counts

4 → 240

Calls

4 calls:

4.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(/ 1/2 (hypot 1 x))
98.0ms	(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
116.0ms	(- (* 1 1) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ 1/2 (hypot 1 x))
82.0ms	(/ 1/2 (hypot 1 x))
55.0ms	(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
227.0ms	(- (* 1 1) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))

simplify2.5s

Counts

252 → 252

Iterations

Iter	Nodes
2	4684
1	1129
0	362

prune3.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.5b	(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.8b	(- (* 1 1) (* (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

36×	`sqrt-div`
28×	`frac-times`
27×	`flip3-+` `flip-+`
24×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`pow1` `add-cube-cbrt`
18×	`times-frac`
14×	`associate-*l/`
13×	`add-cbrt-cube` `add-exp-log` `pow-prod-up`
8×	`sqrt-pow1` `pow1/2` `associate-*r/`
7×	`associate-r`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`pow-plus`
4×	`expm1-log1p-u` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `cube-unmult` `div-exp` `div-inv` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `fma-neg` `diff-log` `associate-l` `prod-diff` `*-commutative` `flip--` `distribute-lft-out`

Counts

4 → 140

Calls

4 calls:

7.0ms	(/ 1/2 (hypot 1 x))
7.0ms	(/ 1/2 (hypot 1 x))
120.0ms	(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
224.0ms	(- (* 1 1) (* (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 1/2 (hypot 1 x))
103.0ms	(/ 1/2 (hypot 1 x))
75.0ms	(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
317.0ms	(- (* 1 1) (* (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.4s

Counts

152 → 152

Iterations

Iter	Nodes
2	2335
1	700
0	256

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes218.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 14.6b

bsearch172.0ms

Steps

Iters	Range		Point
5	0.007518985586860445	0.025588075918097277	0.01245245038673954
8	-0.13148120066069036	-0.0002706832727749338	-0.012038844039708093

simplify17.0ms

Iterations

Iter	Nodes
4	75
3	75
2	71
1	61
0	42

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.4s	2861×	body	1280	valid
509.0ms	4069×	body	80	valid
340.0ms	615×	body	640	valid
106.0ms	307×	body	320	valid
34.0ms	148×	body	160	valid