Details

sample80.0ms

Algorithm

intervals

Results

37.0ms	90×	body	1280	valid
10.0ms	127×	body	80	valid
8.0ms	23×	body	640	valid
3.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	43	12
done	43	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 75

Calls

3 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
22.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.4s

Counts

3 → 9

Calls

3 calls:

198.0ms	(/ 1.0 (hypot 1.0 x))
500.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
687.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.1s

Counts

84 → 84

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	207	2042
1	519	1621
2	2266	1400
done	5001	1384

prune612.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.6b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `div-inv`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `sqrt-prod` `flip--` `flip-+`

Counts

4 → 89

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(/ 1.0 (hypot 1.0 x))
33.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
17.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.1s

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ 1.0 (hypot 1.0 x))
191.0ms	(/ 1.0 (hypot 1.0 x))
495.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
210.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.6s

Counts

101 → 101

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	191	1467
1	506	1371
2	2484	1271
done	5001	1266

prune804.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(exp (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
0.6b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `exp-sum` `flip--`
2×	`sqrt-pow1` `exp-diff` `sqrt-div` `associate-*r/` `log-pow`
1×	`sub-neg` `flip3-+` `pow1/2` `fma-neg` `diff-log` `rem-log-exp` `prod-diff` `pow-prod-down` `sqrt-prod` `flip-+` `rem-exp-log`

Counts

4 → 66

Calls

4 calls:

17.0ms	(log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))
22.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
28.0ms	(exp (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
16.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

455.0ms	(log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))
523.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
201.0ms	(exp (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
206.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.9s

Counts

78 → 78

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	195	1770
1	493	1634
2	2309	1433
done	5000	1410

prune826.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 16.4b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (cbrt (pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3)))
0.5b	(cbrt (pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3))
0.5b	(pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3)
0.6b	(fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
17×	`exp-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`pow1`
6×	`log-pow`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-mult` `pow-unpow` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 89

Calls

4 calls:

24.0ms	(exp (cbrt (pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3)))
6.0ms	(cbrt (pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3))
7.0ms	(pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3)
1.0ms	(fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series2.2s

Counts

4 → 12

Calls

4 calls:

270.0ms	(exp (cbrt (pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3)))
530.0ms	(cbrt (pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3))
1.2s	(pow (log (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) 3)
279.0ms	(fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.0s

Counts

101 → 101

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	180	2503
1	491	2240
2	2554	1860
done	5001	1856

prune785.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes273.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 15.0b

bsearch2.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	73
1	38	73
done	38	73

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	2806×	body	1280	valid
583.0ms	128×	body	160	valid
300.0ms	4080×	body	80	valid
220.0ms	681×	body	640	valid
117.0ms	305×	body	320	valid