Details

sample110.0ms

Algorithm

intervals

Results

62.0ms	93×	body	1280	valid
15.0ms	125×	body	80	valid
14.0ms	26×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
6	114
5	111
4	89
3	69
2	43
1	21
0	9

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(hypot 1 x)
0.0b	(/ 1/2 (hypot 1 x))
1.7b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

14.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0ms	(hypot 1 x)
7.0ms	(/ 1/2 (hypot 1 x))
55.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
76.0ms	(hypot 1 x)
98.0ms	(/ 1/2 (hypot 1 x))
137.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.7s

Counts

120 → 120

Iterations

Iter	Nodes
done	2003
3	2003
2	1331
1	495
0	212

prune519.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

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))
1.2b	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite35.0ms

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:

7.0ms	(/ 1/2 (hypot 1 x))
7.0ms	(/ 1/2 (hypot 1 x))
7.0ms	(/ 1/2 (hypot 1 x))
10.0ms	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 1/2 (hypot 1 x))
85.0ms	(/ 1/2 (hypot 1 x))
83.0ms	(/ 1/2 (hypot 1 x))
195.0ms	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.1s

Counts

125 → 125

Iterations

Iter	Nodes
done	2008
3	2008
2	1124
1	366
0	149

prune784.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(/ 1/2 (hypot 1 x))
0.1b	(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
1.7b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

0.0ms	(hypot 1 x)
7.0ms	(/ 1/2 (hypot 1 x))
49.0ms	(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
50.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(hypot 1 x)
86.0ms	(/ 1/2 (hypot 1 x))
180.0ms	(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
167.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	2001
3	2001
2	1144
1	480
0	233

prune607.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* (* x x) x)
0.3b	(* (* (* x x) (* x x)) -11/128)
17.0b	(fma (* (* (* x x) x) (* (* x x) x)) 69/1024 (* (* (* x x) (* x x)) -11/128))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

60×	`pow1`
32×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`pow-plus` `pow-prod-up`
10×	`add-sqr-sqrt`
9×	`associate-r`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`pow2` `expm1-log1p-u` `pow-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative` `unswap-sqr`
2×	`pow3`
1×	`fma-udef`

Counts

4 → 104

Calls

4 calls:

32.0ms	(* (* x x) x)
30.0ms	(* (* x x) x)
113.0ms	(* (* (* x x) (* x x)) -11/128)
0.0ms	(fma (* (* (* x x) x) (* (* x x) x)) 69/1024 (* (* (* x x) (* x x)) -11/128))

series415.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* x x) x)
49.0ms	(* (* x x) x)
70.0ms	(* (* (* x x) (* x x)) -11/128)
227.0ms	(fma (* (* (* x x) x) (* (* x x) x)) 69/1024 (* (* (* x x) (* x x)) -11/128))

simplify1.4s

Counts

116 → 116

Iterations

Iter	Nodes
done	2012
3	2012
2	833
1	302
0	103

prune399.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes157.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 14.7b

bsearch1.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.3s	2787×	body	1280	valid
653.0ms	4079×	body	80	valid
390.0ms	651×	body	640	valid
115.0ms	324×	body	320	valid
36.0ms	159×	body	160	valid