Details

sample32.0ms

Algorithm

intervals

Results

15.0ms	87×	body	1280	valid
4.0ms	136×	body	80	valid
3.0ms	20×	body	640	valid
0.0ms	8×	body	160	valid
0.0ms	5×	body	320	valid

simplify11.0ms

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: 15.4b

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	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.4b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(hypot 1.0 x)
10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series619.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ 1.0 (hypot 1.0 x))
55.0ms	(hypot 1.0 x)
108.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
352.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify62.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	539	998
1	2059	745
2	5001	742
done	5001	742

prune243.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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)))))))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
11.0ms	(/ (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))

series1.7s

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1.0 (hypot 1.0 x))
315.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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)))))))
146.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify92.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	867	1615
1	3961	1498
2	5001	1488
done	5001	1488

prune393.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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)))))))
0.0b	(* (sqrt (/ (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)))))))) (sqrt (/ (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)))))))))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

103×	`*-un-lft-identity`
98×	`sqrt-prod`
81×	`add-sqr-sqrt`
78×	`times-frac`
53×	`add-cube-cbrt`
29×	`swap-sqr`
22×	`distribute-lft-out`
21×	`associate-r` `associate-l`
19×	`pow1`
10×	`associate-/r/`
9×	`unswap-sqr`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube`
5×	`flip3-+` `pow-prod-up` `flip-+` `div-inv`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr` `associate-/l*`
2×	`fma-udef`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 165

Calls

4 calls:

13.0ms	(/ (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)))))))
62.0ms	(* (sqrt (/ (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)))))))) (sqrt (/ (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))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series2.7s

Counts

4 → 12

Calls

4 calls:

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)))))))
1.2s	(* (sqrt (/ (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)))))))) (sqrt (/ (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)))))))))
158.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
150.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify140.0ms

Counts

177 → 177

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	827	4476
1	4231	4173
2	5001	4154
done	5001	4154

prune604.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `fma-udef`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

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

series629.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
151.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
158.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
158.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify41.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	197	902
1	817	778
2	5001	740
done	5001	740

prune376.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes285.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.2b

bsearch158.0ms

Steps

Iters	Range		Point
9	9.85435867085541e-08	110.15968793260775	0.0007537839544262188
8	-0.1517943218839364	-1.6640733670284383e-05	-0.002025286736305129

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	114
1	63	114
done	63	114

end0.0ms

sample905.0ms

Algorithm

intervals

Results

508.0ms	2896×	body	1280	valid
119.0ms	4020×	body	80	valid
83.0ms	621×	body	640	valid
27.0ms	292×	body	320	valid
10.0ms	171×	body	160	valid