Details

sample70.0ms

Algorithm

intervals

Results

34.0ms	87×	body	1280	valid
9.0ms	130×	body	80	valid
6.0ms	20×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid

simplify71.0ms

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	42	12
done	42	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))))
2.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `hypot-udef` `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

4 → 85

Calls

4 calls:

0.0ms	(hypot 1.0 x)
5.0ms	(/ 1.0 (hypot 1.0 x))
21.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
10.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

68.0ms	(hypot 1.0 x)
133.0ms	(/ 1.0 (hypot 1.0 x))
300.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
504.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts

97 → 97

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	225	2149
1	536	1724
2	1590	1489
done	5001	1355

prune459.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
2.1b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite44.0ms

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:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series784.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
130.0ms	(/ 1.0 (hypot 1.0 x))
122.0ms	(/ 1.0 (hypot 1.0 x))
148.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	191	1467
1	480	1369
2	1585	1266
done	5001	1250

prune554.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
2.1b	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
18.2b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `clear-num` `flip--` `rem-cbrt-cube`

Counts

4 → 137

Calls

4 calls:

11.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
15.0ms	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series713.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ 1.0 (hypot 1.0 x))
257.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
157.0ms	(- (* 1.0 1.0) (* (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) 0.5))
146.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify1.6s

Counts

149 → 149

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	227	2365
1	596	1929
2	1989	1722
done	5000	1687

prune610.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (* 0.5 (+ (pow 1.0 3) (pow (/ 1.0 (hypot 1.0 x)) 3)))) (sqrt (fma 1.0 1.0 (* (/ 1.0 (hypot 1.0 x)) (- (/ 1.0 (hypot 1.0 x)) 1.0)))))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
2.1b	(- (/ 1.0 (hypot 1.0 x)) 1.0)
2.1b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
79×	`*-un-lft-identity` `times-frac`
77×	`add-cube-cbrt`
40×	`prod-diff`
22×	`sqrt-prod`
14×	`fma-neg`
13×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`div-inv`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`pow-unpow`
2×	`cbrt-undiv` `sub-neg` `flip3--` `sqrt-div` `diff-log` `associate-*r/` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt` `difference-of-squares`
1×	`cube-div` `cube-mult` `pow-to-exp` `sqrt-undiv` `pow-pow` `frac-2neg` `flip3-+` `unpow3` `clear-num` `flip-+` `distribute-lft-out--` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

48.0ms	(/ (sqrt (* 0.5 (+ (pow 1.0 3) (pow (/ 1.0 (hypot 1.0 x)) 3)))) (sqrt (fma 1.0 1.0 (* (/ 1.0 (hypot 1.0 x)) (- (/ 1.0 (hypot 1.0 x)) 1.0)))))
7.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
31.0ms	(- (/ 1.0 (hypot 1.0 x)) 1.0)
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series8.5s

Counts

4 → 12

Calls

4 calls:

7.6s	(/ (sqrt (* 0.5 (+ (pow 1.0 3) (pow (/ 1.0 (hypot 1.0 x)) 3)))) (sqrt (fma 1.0 1.0 (* (/ 1.0 (hypot 1.0 x)) (- (/ 1.0 (hypot 1.0 x)) 1.0)))))
263.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
564.0ms	(- (/ 1.0 (hypot 1.0 x)) 1.0)
147.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.3s

Counts

196 → 196

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	520	6977
1	1496	5921
done	5000	5218

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes323.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.4b

bsearch292.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.002020724333725315
7	-0.006495210018506858	-0.00021785999598854965	-0.002558345731073738

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	197
1	65	197
done	65	197

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.5s	2825×	body	1280	valid
310.0ms	4040×	body	80	valid
220.0ms	665×	body	640	valid
51.0ms	309×	body	320	valid
18.0ms	161×	body	160	valid