Details

sample63.0ms

Algorithm

intervals

Results

26.0ms	94×	body	1280	valid
18.0ms	131×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	2×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot 1.0 x)
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `prod-diff`
10×	`add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg` `sqrt-prod`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
1×	`hypot-udef` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

0.0ms	(hypot 1.0 x)
11.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series609.0ms

Counts

2 → 6

Calls

2 calls:

103.0ms	(hypot 1.0 x)
506.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.6s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	1492
1	361
0	148

prune251.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp`
7×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`fma-def`
2×	`hypot-udef` `associate--r+`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip-+` `flip--` `distribute-lft-out`

Counts

4 → 55

Calls

4 calls:

0.0ms	(hypot 1.0 x)
0.0ms	(hypot 1.0 x)
8.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
11.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series778.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(hypot 1.0 x)
87.0ms	(hypot 1.0 x)
434.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
167.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.9s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	2163
1	449
0	159

prune567.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
36×	`sqrt-prod`
28×	`add-cube-cbrt`
24×	`prod-diff`
19×	`pow1`
12×	`sqrt-div` `swap-sqr`
8×	`sqrt-pow1` `flip3--` `pow1/2` `associate-r` `associate-l` `flip--` `distribute-lft-out--` `add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `difference-of-squares`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-l/` `associate-r/`
1×	`pow2` `hypot-udef` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 139

Calls

4 calls:

0.0ms	(hypot 1.0 x)
38.0ms	(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
6.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
18.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

97.0ms	(hypot 1.0 x)
570.0ms	(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
539.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
535.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.9s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	2116
1	487
0	213

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.1b	(/ (/ 0.25 x) (* x x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
20×	`*-un-lft-identity`
18×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `fma-def` `log1p-expm1-u` `div-inv`
2×	`prod-exp` `cbrt-unprod`
1×	`+-commutative` `hypot-udef` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

3 → 75

Calls

3 calls:

0.0ms	(hypot 1.0 x)
9.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
22.0ms	(/ (/ 0.25 x) (* x x))

series679.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(hypot 1.0 x)
507.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
83.0ms	(/ (/ 0.25 x) (* x x))

simplify2.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	2815
1	546
0	209

prune580.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes564.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 15.2b

bsearch221.0ms

Steps

Iters	Range		Point
11	3.4817375791661903e-26	573579.0075499975	0.9600273501121953
10	-84463.33967257517	-3.2432757514909933e-09	-0.0009508968473805669

simplify11.0ms

Iterations

Iter	Nodes
done	43
1	43
0	39

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	2942×	body	1280	valid
300.0ms	3991×	body	80	valid
206.0ms	623×	body	640	valid
66.0ms	302×	body	320	valid
16.0ms	142×	body	160	valid