Details

sample30.0ms

Algorithm

intervals

Results

15.0ms	95×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	30	12
4	32	12
5	38	12
6	41	12
done	41	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize8.0ms

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)))))
3.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite16.0ms

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)
2.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series806.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(hypot 1.0 x)
102.0ms	(/ 1.0 (hypot 1.0 x))
271.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
373.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify601.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (280.0ms)

Iter	Nodes	Cost
0	225	2149
1	531	1724
2	1608	1489
done	5001	1489

prune263.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

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)))))
3.1b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite17.0ms

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:

2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series597.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1.0 (hypot 1.0 x))
108.0ms	(/ 1.0 (hypot 1.0 x))
269.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
116.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify593.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (255.0ms)

Iter	Nodes	Cost
0	191	1467
1	477	1369
2	1556	1266
done	5000	1266

prune341.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
3.1b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
11×	`pow1`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `cube-prod`
6×	`sqrt-div` `associate-*r/` `add-log-exp`
5×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `pow-pow` `sqrt-pow1` `log1p-expm1-u`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `pow-prod-down` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `pow1/3` `diff-log` `prod-diff` `pow-exp` `sqrt-pow2` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 91

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
12.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
3.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

281.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
281.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
705.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
118.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify762.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (316.0ms)

Iter	Nodes	Cost
0	231	2366
1	625	1930
2	2368	1824
done	5000	1824

prune360.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
0.0b	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
3.1b	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
56×	`prod-diff`
52×	`unpow-prod-down`
50×	`add-cube-cbrt`
43×	`sqr-pow`
30×	`times-frac` `difference-of-squares`
15×	`cube-prod`
14×	`cbrt-prod`
10×	`associate-/l*`
9×	`cube-mult` `unpow3`
8×	`pow1`
7×	`add-exp-log` `fma-neg` `add-cbrt-cube`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`cube-div` `expm1-log1p-u` `pow-pow` `sqrt-div` `associate-*r/` `sqrt-prod` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r*`
2×	`cbrt-div` `flip3--` `sqrt-pow1` `flip3-+` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `pow1/2` `pow1/3` `diff-log` `div-sub` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sqrt-pow2` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 204

Calls

4 calls:

31.0ms	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
2.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
8.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
16.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series3.6s

Counts

4 → 12

Calls

4 calls:

2.2s	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
280.0ms	(cbrt (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))
714.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
432.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify487.0ms

Counts

216 → 216

Iterations

Useful iterations: done (475.0ms)

Iter	Nodes	Cost
0	574	11886
1	1480	9169
done	5000	8771

prune912.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes195.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.5b

bsearch155.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.0017653455068687579
7	-0.0009113054925467739	-1.3606912768451591e-05	-0.0008764990404917051

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	148
1	62	148
done	62	148

end0.0ms

sample825.0ms

Algorithm

intervals

Results

480.0ms	2872×	body	1280	valid
121.0ms	4044×	body	80	valid
80.0ms	621×	body	640	valid
26.0ms	295×	body	320	valid
10.0ms	168×	body	160	valid