Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	93×	body	1280	valid
4.0ms	129×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	6×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite30.0ms

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:

8.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(hypot 1.0 x)
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series792.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1.0 (hypot 1.0 x))
56.0ms	(hypot 1.0 x)
268.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
362.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify62.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	533	1074
1	2023	830
2	5001	827
done	5001	827

prune264.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 15.4b

localize13.0ms

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	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`associate-/r/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 103

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1.0 (hypot 1.0 x))
114.0ms	(/ 1.0 (hypot 1.0 x))
1.2s	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
152.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify88.0ms

Counts

115 → 115

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	764	1571
1	3539	1461
2	5001	1448
done	5001	1448

prune471.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))
1.7b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.7b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
28×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`log-pow`
21×	`exp-prod`
10×	`pow1`
8×	`distribute-lft-out`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-prod` `associate-/r*` `log1p-expm1-u`
3×	`fma-udef`
2×	`exp-sum` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 97

Calls

4 calls:

20.0ms	(/ (log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0ms	(exp (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))
3.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.4s	(/ (log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
226.0ms	(exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))
165.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
163.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

simplify104.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	786	2153
1	3441	1972
2	5001	1959
done	5001	1959

prune384.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ (/ (- 0.5) x) (fma 0.25 (/ 1 (pow x 3)) 0.5))
0.0b	(/ (+ (/ (- 0.5) x) (fma 0.25 (/ 1 (pow x 3)) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.2b	(/ 1 (pow x 3))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

82×	`times-frac`
81×	`*-un-lft-identity`
59×	`add-sqr-sqrt` `add-cube-cbrt`
34×	`fma-def`
16×	`associate-/r*`
15×	`add-exp-log`
12×	`unpow-prod-down` `cube-prod`
11×	`distribute-lft-out`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`add-cbrt-cube`
7×	`div-exp` `associate-/l*`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `sqr-pow`
3×	`pow-to-exp` `neg-mul-1` `rec-exp` `flip3-+` `1-exp` `div-sub` `pow-exp` `flip-+` `div-inv`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `frac-2neg` `clear-num` `associate-/r/` `associate-/l/`
1×	`+-commutative` `associate-+r+` `hypot-udef` `pow-flip` `sum-log` `fma-udef` `inv-pow`

Counts

4 → 178

Calls

4 calls:

0.0ms	(hypot 1.0 x)
32.0ms	(+ (/ (- 0.5) x) (fma 0.25 (/ 1 (pow x 3)) 0.5))
88.0ms	(/ (+ (/ (- 0.5) x) (fma 0.25 (/ 1 (pow x 3)) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
9.0ms	(/ 1 (pow x 3))

series661.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(hypot 1.0 x)
30.0ms	(+ (/ (- 0.5) x) (fma 0.25 (/ 1 (pow x 3)) 0.5))
530.0ms	(/ (+ (/ (- 0.5) x) (fma 0.25 (/ 1 (pow x 3)) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
38.0ms	(/ 1 (pow x 3))

simplify86.0ms

Counts

190 → 190

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	684	1578
1	3479	1384
2	5001	1368
done	5001	1368

prune531.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes238.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 15.3b

bsearch157.0ms

Steps

Iters	Range		Point
10	0.00012253353073063669	15794870057.515802	0.9622875180021904
9	-2.7342232818785663	-5.599255928070541e-06	-0.0004029999773774761

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	49
1	56	49
done	56	49

end0.0ms

sample882.0ms

Algorithm

intervals

Results

494.0ms	2900×	body	1280	valid
122.0ms	3970×	body	80	valid
80.0ms	626×	body	640	valid
30.0ms	334×	body	320	valid
10.0ms	170×	body	160	valid