Details

sample99.0ms

Algorithm

intervals

Results

53.0ms	82×	body	1280	valid
16.0ms	136×	body	80	valid
10.0ms	20×	body	640	valid
4.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	25
3	25
2	23
1	19
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
2.1b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
21×	`prod-diff`
16×	`sqrt-prod`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`distribute-lft-out` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `associate-/r` `fma-neg` `log1p-expm1-u` `associate-/l` `distribute-lft-out--`
1×	`cbrt-undiv` `hypot-udef` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--`

Counts

3 → 84

Calls

3 calls:

3.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
31.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series286.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ 1/2 (hypot 1 x))
67.0ms	(hypot 1 x)
136.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.7s

Counts

93 → 93

Iterations

Iter	Nodes
3	2351
2	936
1	411
0	186

prune773.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0b	(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
1.6b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`times-frac`
54×	`add-cube-cbrt`
39×	`prod-diff`
32×	`distribute-lft-out`
16×	`sqrt-prod` `difference-of-squares`
8×	`distribute-lft-out--` `add-log-exp`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `div-inv`
3×	`fma-def` `fma-neg`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `hypot-udef` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp`

Counts

4 → 155

Calls

4 calls:

0.0ms	(hypot 1 x)
14.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
45.0ms	(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
7.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series584.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(hypot 1 x)
129.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
318.0ms	(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))
81.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.9s

Counts

167 → 167

Iterations

Iter	Nodes
2	2679
1	892
0	337

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* (* x (* x x)) (* x (* x x)))
0.1b	(* 11/128 (* x x))
21.0b	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) (- 1/8 (* 11/128 (* x x)))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

283×	`pow1`
121×	`pow-prod-up`
79×	`pow-prod-down`
50×	`add-cbrt-cube` `add-exp-log`
33×	`prod-exp` `cbrt-unprod`
31×	`pow-sqr`
22×	`pow-plus`
16×	`pow2`
15×	`cube-unmult`
8×	`add-sqr-sqrt`
7×	`associate-l`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative`
2×	`unswap-sqr`
1×	`swap-sqr` `fma-udef`

Counts

4 → 158

Calls

4 calls:

24.0ms	(* x (* x x))
66.0ms	(* (* x (* x x)) (* x (* x x)))
21.0ms	(* 11/128 (* x x))
0.0ms	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) (- 1/8 (* 11/128 (* x x)))))

series227.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* x (* x x))
79.0ms	(* (* x (* x x)) (* x (* x x)))
31.0ms	(* 11/128 (* x x))
83.0ms	(fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) (- 1/8 (* 11/128 (* x x)))))

simplify1.8s

Counts

170 → 170

Iterations

Iter	Nodes
3	3895
2	830
1	342
0	136

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 14.8b

bsearch1.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	28
1	28
0	23

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.2s	2773×	body	1280	valid
402.0ms	4152×	body	80	valid
265.0ms	637×	body	640	valid
118.0ms	288×	body	320	valid
28.0ms	150×	body	160	valid