Details

sample51.0ms

Algorithm

intervals

Results

28.0ms	85×	body	1280	valid
6.0ms	139×	body	80	valid
4.0ms	20×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	28	12
4	30	12
5	35	12
6	36	12
done	36	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 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)))))
1.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

15.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
28.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
12.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
14.0ms	(/ 1.0 (hypot 1.0 x))
108.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
139.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify4.2s

Counts

78 → 78

Iterations

Useful iterations: 4 (2.4s)

Iter	Nodes	Cost
0	112	1034
1	223	951
2	539	887
3	1386	885
4	4985	881
done	5000	881

prune272.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.2b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/l*` `add-log-exp`
4×	`distribute-lft-out`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `associate-/r/` `flip--` `flip-+` `div-inv` `associate-/l/` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow1/2` `diff-log` `div-sub` `pow-prod-down` `sqrt-prod`

Counts

4 → 90

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
32.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
17.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1.0 (hypot 1.0 x))
248.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
125.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
42.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.2s

Counts

102 → 102

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	163	2352
1	385	2241
2	1282	2071
done	5001	1894

prune396.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.2b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`associate-*r/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/l*` `add-log-exp`
4×	`flip3--` `associate--l+` `frac-sub` `flip--` `associate-/l/` `distribute-lft-out`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`pow1/2` `diff-log` `div-sub` `pow-prod-down` `sqrt-prod`

Counts

4 → 96

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
60.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
25.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
40.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1.0 (hypot 1.0 x))
236.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
114.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
46.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	188	2502
1	452	2399
2	1430	2229
done	5000	2225

prune472.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(* (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.2b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.2b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

795×	`associate-*r/`
352×	`frac-times`
312×	`frac-add`
212×	`flip3--` `flip--`
152×	`associate-*l/`
127×	`flip3-+` `flip-+`
13×	`add-sqr-sqrt`
12×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`cube-div` `sqr-pow`
4×	`associate-r` `difference-of-squares`
3×	`pow-unpow` `associate-l` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
2×	`pow-pow` `sqrt-pow1` `sqrt-div` `frac-sub`
1×	`difference-cubes` `cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `distribute-lft-in` `pow1/2` `diff-log` `unpow3` `cube-prod` `div-exp` `sqrt-prod` `*-commutative` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 303

Calls

4 calls:

15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
334.0ms	(* (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
15.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
22.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series537.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
293.0ms	(* (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
39.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
96.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify2.0s

Counts

315 → 315

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	831	32616
1	3689	29174
done	5001	28670

prune3.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.4b

regimes283.0ms

Accuracy

0% (0.3b remaining)

Error of 14.8b against oracle of 14.5b and baseline of 14.8b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	66
1	33	66
done	33	66

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s	2884×	body	1280	valid
356.0ms	4024×	body	80	valid
186.0ms	623×	body	640	valid
61.0ms	318×	body	320	valid
19.0ms	151×	body	160	valid