Details

sample30.0ms

Algorithm

intervals

Results

15.0ms	95×	body	1280	valid
3.0ms	129×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	8×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	26	6
2	33	6
3	35	6
4	41	6
5	44	6
6	44	6
done	44	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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)
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series786.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(hypot 1.0 x)
269.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
103.0ms	(/ 1.0 (hypot 1.0 x))
350.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify57.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	533	1074
1	2023	830
2	5002	827
done	5002	827

prune270.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.1b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 85

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series685.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
104.0ms	(/ 1.0 (hypot 1.0 x))
104.0ms	(/ 1.0 (hypot 1.0 x))
158.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify46.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	430	681
1	1662	625
2	5001	623
done	5001	623

prune366.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
2.1b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-sum`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`log-pow` `fma-udef` `rem-exp-log`

Counts

4 → 85

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series514.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1.0 (hypot 1.0 x))
107.0ms	(/ 1.0 (hypot 1.0 x))
149.0ms	(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
156.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify158.0ms

Counts

97 → 97

Iterations

Useful iterations: 3 (150.0ms)

Iter	Nodes	Cost
0	273	648
1	913	592
2	4559	571
3	5001	565
done	5001	565

prune381.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
0.1b	(exp (log (fma (- 0.5) (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) (* 1.0 1.0))))
2.1b	(fma (- 0.5) (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) (* 1.0 1.0))
19.4b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `log-prod` `exp-sum`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `log-pow` `rem-cbrt-cube` `fma-udef` `rem-exp-log`

Counts

4 → 119

Calls

4 calls:

6.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
3.0ms	(exp (log (fma (- 0.5) (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) (* 1.0 1.0))))
0.0ms	(fma (- 0.5) (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) (* 1.0 1.0))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series631.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
152.0ms	(exp (log (fma (- 0.5) (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) (* 1.0 1.0))))
158.0ms	(fma (- 0.5) (+ 1.0 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))) (* 1.0 1.0))
105.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify62.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	542	994
1	2360	879
2	5001	845
done	5001	845

prune397.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes307.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch121.0ms

Steps

Iters	Range		Point
7	9.529507114303981e-07	0.00021078761332869983	0.00014077003562226292
7	-0.002799490342594777	-2.5466144345707062e-05	-0.0026446657465048055

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	56
1	68	56
2	72	56
3	73	56
4	73	56
done	73	56

end0.0ms

sample792.0ms

Algorithm

intervals

Results

435.0ms	2833×	body	1280	valid
111.0ms	4108×	body	80	valid
71.0ms	607×	body	640	valid
25.0ms	305×	body	320	valid
8.0ms	147×	body	160	valid