Main:bigenough3 from C

Average Error: 30.1 → 29.4

Time: 27.2s

Precision: binary64

Cost: 13376

Math

\[\sqrt{x + 1} - \sqrt{x} \]

↓

\[\left(\sqrt{1 + x} - \left(\sqrt{x} - -1\right)\right) + 1 \]

FPCore

(FPCore (x) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt x)))

↓

(FPCore (x) :precision binary64 (+ (- (sqrt (+ 1.0 x)) (- (sqrt x) -1.0)) 1.0))

C

double code(double x) {
	return sqrt((x + 1.0)) - sqrt(x);
}

↓

double code(double x) {
	return (sqrt((1.0 + x)) - (sqrt(x) - -1.0)) + 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((x + 1.0d0)) - sqrt(x)
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = (sqrt((1.0d0 + x)) - (sqrt(x) - (-1.0d0))) + 1.0d0
end function

Java

public static double code(double x) {
	return Math.sqrt((x + 1.0)) - Math.sqrt(x);
}

↓

public static double code(double x) {
	return (Math.sqrt((1.0 + x)) - (Math.sqrt(x) - -1.0)) + 1.0;
}

Python

def code(x):
	return math.sqrt((x + 1.0)) - math.sqrt(x)

↓

def code(x):
	return (math.sqrt((1.0 + x)) - (math.sqrt(x) - -1.0)) + 1.0

Julia

function code(x)
	return Float64(sqrt(Float64(x + 1.0)) - sqrt(x))
end

↓

function code(x)
	return Float64(Float64(sqrt(Float64(1.0 + x)) - Float64(sqrt(x) - -1.0)) + 1.0)
end

MATLAB

function tmp = code(x)
	tmp = sqrt((x + 1.0)) - sqrt(x);
end

↓

function tmp = code(x)
	tmp = (sqrt((1.0 + x)) - (sqrt(x) - -1.0)) + 1.0;
end

Wolfram

code[x_] := N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(N[(N[Sqrt[N[(1.0 + x), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[x], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]

Target

Original	30.1
Target	0.2
Herbie	29.4

\[\frac{1}{\sqrt{x + 1} + \sqrt{x}} \]

Derivation

1. Initial program 30.1

   \[\sqrt{x + 1} - \sqrt{x} \]

2. Applied egg-rr 31.3

   \[\leadsto \color{blue}{\frac{1}{\sqrt{x + 1} - \sqrt{x}} \cdot \left(\left(\sqrt{x + 1} - \sqrt{x}\right) \cdot \left(\sqrt{x + 1} - \sqrt{x}\right)\right)} \]

3. Applied egg-rr 29.4

   \[\leadsto \color{blue}{\left(\sqrt{1 + x} - \left(\sqrt{x} - -1\right)\right) + 1} \]

4. Final simplification 29.4

   \[\leadsto \left(\sqrt{1 + x} - \left(\sqrt{x} - -1\right)\right) + 1 \]

Alternatives

Alternative 1
Error	30.1
Cost	13120

\[\sqrt{x + 1} - \sqrt{x} \]

Alternative 2
Error	31.4
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023077 
(FPCore (x)
  :name "Main:bigenough3 from C"
  :precision binary64

  :herbie-target
  (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

  (- (sqrt (+ x 1.0)) (sqrt x)))