Details

sample103.0ms

Algorithm

intervals

Results

57.0ms	90×	body	1280	valid
16.0ms	129×	body	80	valid
9.0ms	18×	body	640	valid
5.0ms	14×	body	320	valid
1.0ms	5×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

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:

8.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
4.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
49.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
101.0ms	(/ 1/2 (hypot 1 x))
72.0ms	(hypot 1 x)
175.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify2.0s

Counts

120 → 120

Iterations

Iter	Nodes
3	2575
2	1069
1	476
0	212

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
1.2b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-/r` `fma-neg` `associate-/l`
2×	`hypot-udef` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `flip--` `distribute-lft-out--`

Counts

4 → 112

Calls

4 calls:

12.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
11.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ 1/2 (hypot 1 x))
60.0ms	(hypot 1 x)
62.0ms	(hypot 1 x)
83.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.3s

Counts

124 → 124

Iterations

Iter	Nodes
3	3540
2	1329
1	530
0	217

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
1.2b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-/r` `fma-neg` `associate-/l`
2×	`hypot-udef` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `flip--` `distribute-lft-out--`

Counts

4 → 112

Calls

4 calls:

7.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
13.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1/2 (hypot 1 x))
59.0ms	(hypot 1 x)
54.0ms	(hypot 1 x)
112.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.2s

Counts

124 → 124

Iterations

Iter	Nodes
3	3540
2	1329
1	530
0	217

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- 1/2 (/ 1/2 (hypot 1 x)))) (cbrt (- 1/2 (/ 1/2 (hypot 1 x)))))
1.2b	(- 1/2 (/ 1/2 (hypot 1 x)))
1.2b	(- 1/2 (/ 1/2 (hypot 1 x)))
1.2b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
137×	`*-un-lft-identity`
117×	`prod-diff` `add-cube-cbrt`
88×	`times-frac`
32×	`cbrt-prod`
14×	`difference-of-squares`
12×	`cbrt-div`
11×	`pow1` `swap-sqr`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `associate-r` `associate-l` `div-inv` `flip--` `distribute-lft-out--`
6×	`pow1/3` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 242

Calls

4 calls:

51.0ms	(* (cbrt (- 1/2 (/ 1/2 (hypot 1 x)))) (cbrt (- 1/2 (/ 1/2 (hypot 1 x)))))
7.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
10.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
7.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* (cbrt (- 1/2 (/ 1/2 (hypot 1 x)))) (cbrt (- 1/2 (/ 1/2 (hypot 1 x)))))
98.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
77.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
84.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.4s

Counts

254 → 254

Iterations

Iter	Nodes
3	3984
2	1558
1	618
0	265

prune3.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes117.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b 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	2863×	body	1280	valid
372.0ms	4051×	body	80	valid
283.0ms	635×	body	640	valid
88.0ms	310×	body	320	valid
26.0ms	141×	body	160	valid