Details

sample44.0ms

Algorithm

intervals

Results

19.0ms	81×	body	1280	valid
6.0ms	148×	body	80	valid
3.0ms	19×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	42	12
done	42	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `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` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

25.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
14.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
10.0ms	(/ 1.0 (hypot 1.0 x))
16.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

175.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
379.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
109.0ms	(/ 1.0 (hypot 1.0 x))
532.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.4s

Counts

104 → 104

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	223	2270
1	537	1836
2	1584	1593
done	5001	1460

prune469.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))
0.7b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `div-inv`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `sqrt-prod` `flip--` `flip-+`

Counts

4 → 89

Calls

4 calls:

28.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(/ 1.0 (hypot 1.0 x))
17.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series906.0ms

Counts

4 → 12

Calls

4 calls:

430.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
139.0ms	(/ 1.0 (hypot 1.0 x))
152.0ms	(/ 1.0 (hypot 1.0 x))
185.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.3s

Counts

101 → 101

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	191	1467
1	480	1369
2	1585	1266
done	5001	1250

prune447.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.7b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
2.3b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
14×	`log-pow`
13×	`exp-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `rem-log-exp` `prod-diff` `flip--`

Counts

4 → 101

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
9.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1.0 (hypot 1.0 x))
111.0ms	(/ 1.0 (hypot 1.0 x))
148.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
146.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

simplify2.0s

Counts

113 → 113

Iterations

Useful iterations: 3 (954.0ms)

Iter	Nodes	Cost
0	170	1449
1	359	1344
2	1021	1230
3	3285	1200
done	5000	1200

prune610.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.6b	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
2.3b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

56×	`prod-diff`
53×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
46×	`add-cube-cbrt`
37×	`unpow-prod-down`
22×	`sqr-pow`
18×	`times-frac`
14×	`log-pow`
13×	`exp-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `cube-mult` `unpow3` `cube-prod`
7×	`fma-neg`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `log-prod` `associate-/r` `associate-/l`
2×	`cube-div` `pow-pow` `associate-*l/` `pow-exp` `div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--`

Counts

4 → 166

Calls

4 calls:

11.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
59.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
16.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ 1.0 (hypot 1.0 x))
356.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
601.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
155.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

simplify1.9s

Counts

178 → 178

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	343	6553
1	786	4228
2	2358	3288
done	5000	2552

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes474.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch245.0ms

Steps

Iters	Range		Point
8	6.100620313640196e-08	0.0033303272193615503	0.0017743273033383432
9	-7.35943201301068	-4.403108084983288e-07	-0.002150518847943042

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	52	135
1	58	135
done	58	135

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2825×	body	1280	valid
354.0ms	311×	body	320	valid
315.0ms	4098×	body	80	valid
152.0ms	619×	body	640	valid
16.0ms	147×	body	160	valid