Details

sample69.0ms

Algorithm

intervals

Results

30.0ms	76×	body	1280	valid
9.0ms	136×	body	80	valid
9.0ms	28×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	4×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

10.0ms	(sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0))
9.0ms	(+ 0.5 (/ 0.5 (hypot 1.0 x)))
4.0ms	(/ 0.5 (hypot 1.0 x))
11.0ms	(- 1.0 (sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

398.0ms	(sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0))
158.0ms	(+ 0.5 (/ 0.5 (hypot 1.0 x)))
162.0ms	(/ 0.5 (hypot 1.0 x))
510.0ms	(- 1.0 (sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0)))

simplify1.4s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	2386
1	559
0	227

prune526.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 0.5 (hypot 1.0 x))
0.0b	(+ (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) 1.0)
0.0b	(/ (* 1.0 (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) (+ (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) 1.0))
1.3b	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

5.0ms	(/ 0.5 (hypot 1.0 x))
14.0ms	(+ (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) 1.0)
140.0ms	(/ (* 1.0 (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) (+ (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) 1.0))
54.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

series2.8s

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ 0.5 (hypot 1.0 x))
473.0ms	(+ (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) 1.0)
2.0s	(/ (* 1.0 (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) (+ (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) 1.0))
179.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

simplify616.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	5001
1	993
0	348

prune783.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5))
0.0b	(+ (sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (sqrt 1.0))
0.0b	(/ (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (sqrt 1.0)))
1.3b	(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

135×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
45×	`distribute-lft-out`
40×	`sqrt-prod`
37×	`times-frac`
29×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
11×	`add-log-exp`
8×	`difference-of-squares`
7×	`fma-def`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3-+` `fma-neg` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv` `associate--r+`

Counts

4 → 144

Calls

4 calls:

38.0ms	(sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5))
143.0ms	(+ (sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (sqrt 1.0))
221.0ms	(/ (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (sqrt 1.0)))
44.0ms	(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

266.0ms	(sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5))
361.0ms	(+ (sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (sqrt 1.0))
1.4s	(/ (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (sqrt (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (sqrt 1.0)))
184.0ms	(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

simplify2.0s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	4923
1	931
0	328

prune960.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0)))
0.0b	(+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))
0.0b	(+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))
1.3b	(- (/ 1.0 (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))) (/ (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

2388×	`*-un-lft-identity`
1202×	`times-frac`
979×	`distribute-lft-out`
824×	`sqrt-prod`
720×	`prod-diff`
610×	`add-sqr-sqrt`
598×	`add-cube-cbrt`
116×	`associate-/r/`
61×	`flip3-+` `flip-+`
58×	`div-inv`
24×	`fma-neg`
21×	`distribute-lft-out--`
14×	`fma-def`
10×	`add-log-exp`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l*` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`+-commutative` `sum-log` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `flip--` `sub-div`

Counts

4 → 886

Calls

4 calls:

160.0ms	(/ (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0)))
81.0ms	(+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))
105.0ms	(+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))
921.0ms	(- (/ 1.0 (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))) (/ (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))))

series6.1s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0)))
323.0ms	(+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))
326.0ms	(+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))
4.2s	(- (/ 1.0 (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))) (/ (+ 0.5 (/ 0.5 (hypot 1.0 x))) (+ (sqrt (+ 0.5 (/ 0.5 (hypot 1.0 x)))) (sqrt 1.0))))

simplify1.2s

Counts

898 → 898

Iterations

Iter	Nodes
done	5001
1	1937
0	734

prune2.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.2b

regimes284.0ms

Accuracy

98.3% (0.0b remaining)

Error of 13.9b against oracle of 13.9b and baseline of 15.6b

bsearch549.0ms

Steps

Iters	Range		Point
7	7.46228068957284e-06	0.00104763160503943	8.055965450229695e-05
9	-0.0007095347148853646	-4.632829109756021e-12	-2.80323178038379e-08

simplify25.0ms

Iterations

Iter	Nodes
done	130
1	130
0	107

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	2806×	body	1280	valid
799.0ms	4038×	body	80	valid
184.0ms	664×	body	640	valid
69.0ms	150×	body	160	valid
64.0ms	342×	body	320	valid