Details

sample45.0ms

Algorithm

intervals

Results

23.0ms	101×	body	1280	valid
5.0ms	26×	body	640	valid
5.0ms	108×	body	80	valid
2.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
2.8b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
21×	`prod-diff`
20×	`sqrt-prod`
10×	`times-frac`
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-def` `fma-neg` `associate-/l` `distribute-lft-out--`
2×	`flip3-+` `sqrt-div` `flip-+` `hypot-def`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `div-inv` `flip--`

Counts

4 → 115

Calls

4 calls:

27.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
10.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
4.0ms	(/ 1/2 (hypot 1 x))
82.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
76.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
86.0ms	(/ 1/2 (hypot 1 x))
176.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify3.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
3	4713
2	1398
1	507
0	213

prune562.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

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 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1) (+ 1/2 (/ 1/2 (hypot 1 x)))))
2.3b	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite521.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

5.0ms	(/ 1/2 (hypot 1 x))
5.0ms	(/ 1/2 (hypot 1 x))
499.0ms	(/ (- 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) (+ 1/2 (/ 1/2 (hypot 1 x)))))
9.0ms	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ 1/2 (hypot 1 x))
97.0ms	(/ 1/2 (hypot 1 x))
1.2s	(/ (- 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) (+ 1/2 (/ 1/2 (hypot 1 x)))))
212.0ms	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify4.6s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	4353
1	1069
0	354

prune917.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* (* x x) (* x x)))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
18.0b	(fma (* (* x x) (* (* x x) (* x x))) 69/1024 (* -11/128 (* (* x x) (* x x))))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

848×	`pow1`
370×	`pow-prod-up`
175×	`pow-prod-down`
153×	`pow-sqr`
140×	`pow-plus`
99×	`pow2`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`cube-unmult` `fma-udef`

Counts

4 → 337

Calls

4 calls:

152.0ms	(* (* x x) (* (* x x) (* x x)))
61.0ms	(* (* x x) (* x x))
50.0ms	(* (* x x) (* x x))
0.0ms	(fma (* (* x x) (* (* x x) (* x x))) 69/1024 (* -11/128 (* (* x x) (* x x))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* x x) (* (* x x) (* x x)))
50.0ms	(* (* x x) (* x x))
53.0ms	(* (* x x) (* x x))
196.0ms	(fma (* (* x x) (* (* x x) (* x x))) 69/1024 (* -11/128 (* (* x x) (* x x))))

simplify2.1s

Counts

349 → 349

Iterations

Iter	Nodes
done	5000
3	1410
2	575
1	307
0	138

prune376.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (* x x) (* x x)) (+ (* (* x x) 69/1024) -11/128))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) 69/1024)
1.2b	(log (exp (* (* (* x x) (* x x)) (+ (* (* x x) 69/1024) -11/128))))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

139×	`pow1`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
36×	`pow-prod-up`
24×	`prod-exp` `cbrt-unprod`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
5×	`log-prod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `log-pow` `*-commutative` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `exp-sum` `associate-*r/`
1×	`exp-prod` `flip3-+` `exp-to-pow` `swap-sqr` `rem-log-exp` `flip-+`

Counts

4 → 142

Calls

4 calls:

193.0ms	(* (* (* x x) (* x x)) (+ (* (* x x) 69/1024) -11/128))
30.0ms	(* (* x x) (* x x))
33.0ms	(* (* x x) 69/1024)
7.0ms	(log (exp (* (* (* x x) (* x x)) (+ (* (* x x) 69/1024) -11/128))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (* (* x x) (* x x)) (+ (* (* x x) 69/1024) -11/128))
40.0ms	(* (* x x) (* x x))
30.0ms	(* (* x x) 69/1024)
183.0ms	(log (exp (* (* (* x x) (* x x)) (+ (* (* x x) 69/1024) -11/128))))

simplify2.0s

Counts

154 → 154

Iterations

Iter	Nodes
done	5001
2	1536
1	451
0	154

prune473.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes103.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 14.6b

bsearch1.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s	2850×	body	1280	valid
285.0ms	638×	body	640	valid
274.0ms	4068×	body	80	valid
68.0ms	304×	body	320	valid
19.0ms	140×	body	160	valid