Details

sample57.0ms

Algorithm

intervals

Results

27.0ms	87×	body	1280	valid
8.0ms	136×	body	80	valid
5.0ms	20×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	8×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 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))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-/r` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `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 → 60

Calls

4 calls:

9.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(hypot 1.0 x)
19.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
8.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series180.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(hypot 1.0 x)
48.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
115.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.4s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	101	854
1	205	801
2	486	737
3	1145	735
4	3645	733
done	5000	733

prune236.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.9b

localize13.0ms

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
35.0ms	(/ (- (* 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)))))))
12.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
130.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
228.0ms	(/ (- (* 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)))))))
59.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	149	2415
1	354	2319
2	1206	2115
done	5000	1912

prune414.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.9b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

21.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
11.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
75.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
95.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
225.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
56.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify2.2s

Counts

102 → 102

Iterations

Useful iterations: 3 (657.0ms)

Iter	Nodes	Cost
0	142	2450
1	361	2364
2	958	2202
3	2627	2200
done	5001	2200

prune368.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.9b

localize19.0ms

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	(/ (exp (log (- 0.5 (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.1b	(exp (log (- 0.5 (/ 0.5 (hypot 1.0 x)))))
1.9b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

11.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
85.0ms	(/ (exp (log (- 0.5 (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
15.0ms	(exp (log (- 0.5 (/ 0.5 (hypot 1.0 x)))))
11.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
202.0ms	(/ (exp (log (- 0.5 (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
40.0ms	(exp (log (- 0.5 (/ 0.5 (hypot 1.0 x)))))
55.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify1.5s

Counts

124 → 124

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	177	3349
1	319	2990
2	764	2773
3	2039	2771
done	5000	2739

prune393.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.9b

regimes265.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	16	33
done	16	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

694.0ms	2896×	body	1280	valid
176.0ms	4020×	body	80	valid
125.0ms	621×	body	640	valid
39.0ms	292×	body	320	valid
14.0ms	171×	body	160	valid