Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.5% → 96.9%

Time: 7.9s

Alternatives: 12

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot z}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (/ (* (- y x) z) t)))

C

double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((y - x) * z) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}

Python

def code(x, y, z, t):
	return x + (((y - x) * z) / t)

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(y - x) * z) / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((y - x) * z) / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot z}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (/ (* (- y x) z) t)))

C

double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((y - x) * z) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}

Python

def code(x, y, z, t):
	return x + (((y - x) * z) / t)

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(y - x) * z) / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((y - x) * z) / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+302}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z (- y x)) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+302)))
     (* (- y x) (/ z t))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+302)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((z * (y - x)) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+302)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((z * (y - x)) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+302):
		tmp = (y - x) * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(z * Float64(y - x)) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+302))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((z * (y - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+302)))
		tmp = (y - x) * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+302]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -inf.0 or 2.0000000000000002e302 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 80.2%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in t around 0 80.2%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]
   3. Step-by-step derivation

      1. *-commutative 80.2%

         \[\leadsto \frac{\color{blue}{z \cdot \left(y - x\right)}}{t} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 2.0000000000000002e302

   1. Initial program 99.2%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{z \cdot \left(y - x\right)}{t} \leq -\infty \lor \neg \left(x + \frac{z \cdot \left(y - x\right)}{t} \leq 2 \cdot 10^{+302}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+16) (fma (/ (- y x) t) z x) (fma (/ z t) (- y x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+16) {
		tmp = fma(((y - x) / t), z, x);
	} else {
		tmp = fma((z / t), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+16)
		tmp = fma(Float64(Float64(y - x) / t), z, x);
	else
		tmp = fma(Float64(z / t), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e+16], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e16

   1. Initial program 92.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. +-commutative 92.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t} + x} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{y - x}{t} \cdot z} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)} \]

   if -5e16 < z

   1. Initial program 94.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. +-commutative 94.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t} + x} \]

      2. *-commutative 94.0%

         \[\leadsto \frac{\color{blue}{z \cdot \left(y - x\right)}}{t} + x \]

      3. associate-*l/ 98.5%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} + x \]

      4. fma-def 98.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)} \]

   3. Simplified 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \end{array} \]

Alternative 3: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{z}{t \cdot \frac{1}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+137) (+ x (/ z (* t (/ 1.0 (- y x))))) (fma (/ z t) (- y x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+137) {
		tmp = x + (z / (t * (1.0 / (y - x))));
	} else {
		tmp = fma((z / t), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+137)
		tmp = Float64(x + Float64(z / Float64(t * Float64(1.0 / Float64(y - x)))));
	else
		tmp = fma(Float64(z / t), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+137], N[(x + N[(z / N[(t * N[(1.0 / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e137

   1. Initial program 91.7%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. flip-- 78.2%

         \[\leadsto x + \frac{\color{blue}{\frac{y \cdot y - x \cdot x}{y + x}} \cdot z}{t} \]

      2. associate-*l/ 67.4%

         \[\leadsto x + \frac{\color{blue}{\frac{\left(y \cdot y - x \cdot x\right) \cdot z}{y + x}}}{t} \]

   3. Applied egg-rr 67.4%

      \[\leadsto x + \frac{\color{blue}{\frac{\left(y \cdot y - x \cdot x\right) \cdot z}{y + x}}}{t} \]
   4. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto x + \frac{\frac{\color{blue}{z \cdot \left(y \cdot y - x \cdot x\right)}}{y + x}}{t} \]

      2. associate-/l* 78.2%

         \[\leadsto x + \frac{\color{blue}{\frac{z}{\frac{y + x}{y \cdot y - x \cdot x}}}}{t} \]

      3. difference-of-squares 82.7%

         \[\leadsto x + \frac{\frac{z}{\frac{y + x}{\color{blue}{\left(y + x\right) \cdot \left(y - x\right)}}}}{t} \]

      4. associate-/r* 91.7%

         \[\leadsto x + \frac{\frac{z}{\color{blue}{\frac{\frac{y + x}{y + x}}{y - x}}}}{t} \]

      5. +-commutative 91.7%

         \[\leadsto x + \frac{\frac{z}{\frac{\frac{\color{blue}{x + y}}{y + x}}{y - x}}}{t} \]

      6. +-commutative 91.7%

         \[\leadsto x + \frac{\frac{z}{\frac{\frac{x + y}{\color{blue}{x + y}}}{y - x}}}{t} \]

   5. Simplified 91.7%

      \[\leadsto x + \frac{\color{blue}{\frac{z}{\frac{\frac{x + y}{x + y}}{y - x}}}}{t} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 91.7%

         \[\leadsto x + \color{blue}{1 \cdot \frac{\frac{z}{\frac{\frac{x + y}{x + y}}{y - x}}}{t}} \]

      2. associate-/l/ 99.6%

         \[\leadsto x + 1 \cdot \color{blue}{\frac{z}{t \cdot \frac{\frac{x + y}{x + y}}{y - x}}} \]

      3. *-inverses 99.6%

         \[\leadsto x + 1 \cdot \frac{z}{t \cdot \frac{\color{blue}{1}}{y - x}} \]

   7. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{1 \cdot \frac{z}{t \cdot \frac{1}{y - x}}} \]

   if -1e137 < z

   1. Initial program 94.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. +-commutative 94.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t} + x} \]

      2. *-commutative 94.0%

         \[\leadsto \frac{\color{blue}{z \cdot \left(y - x\right)}}{t} + x \]

      3. associate-*l/ 98.6%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} + x \]

      4. fma-def 98.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)} \]

   3. Simplified 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{z}{t \cdot \frac{1}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \end{array} \]

Alternative 4: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= y -5.8e+77)
     t_1
     (if (<= y -2.4e-16)
       (* (- y x) (/ z t))
       (if (<= y 3e-41) (* x (- 1.0 (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (y <= -5.8e+77) {
		tmp = t_1;
	} else if (y <= -2.4e-16) {
		tmp = (y - x) * (z / t);
	} else if (y <= 3e-41) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (y <= (-5.8d+77)) then
        tmp = t_1
    else if (y <= (-2.4d-16)) then
        tmp = (y - x) * (z / t)
    else if (y <= 3d-41) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (y <= -5.8e+77) {
		tmp = t_1;
	} else if (y <= -2.4e-16) {
		tmp = (y - x) * (z / t);
	} else if (y <= 3e-41) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	tmp = 0
	if y <= -5.8e+77:
		tmp = t_1
	elif y <= -2.4e-16:
		tmp = (y - x) * (z / t)
	elif y <= 3e-41:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (y <= -5.8e+77)
		tmp = t_1;
	elseif (y <= -2.4e-16)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	elseif (y <= 3e-41)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (y <= -5.8e+77)
		tmp = t_1;
	elseif (y <= -2.4e-16)
		tmp = (y - x) * (z / t);
	elseif (y <= 3e-41)
		tmp = x * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+77], t$95$1, If[LessEqual[y, -2.4e-16], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-41], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000003e77 or 2.99999999999999989e-41 < y

   1. Initial program 89.7%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in y around inf 86.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 67.1%

         \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   4. Simplified 94.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   if -5.8000000000000003e77 < y < -2.40000000000000005e-16

   1. Initial program 95.5%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in t around 0 91.4%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]
   3. Step-by-step derivation

      1. *-commutative 91.4%

         \[\leadsto \frac{\color{blue}{z \cdot \left(y - x\right)}}{t} \]

      2. associate-*l/ 95.7%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} \]

   4. Applied egg-rr 95.7%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} \]

   if -2.40000000000000005e-16 < y < 2.99999999999999989e-41

   1. Initial program 96.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in x around inf 85.4%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right) \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 85.4%

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

      2. distribute-lft-in 85.4%

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

      3. *-rgt-identity 85.4%

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

      4. mul-1-neg 85.4%

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

      5. distribute-rgt-neg-in 85.4%

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

      6. unsub-neg 85.4%

         \[\leadsto \color{blue}{x - x \cdot \frac{z}{t}} \]

   4. Simplified 85.4%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{t}} \]

   5. Taylor expanded in x around 0 85.4%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+77}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-16}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e+77)
   (+ x (/ y (/ t z)))
   (if (<= y -3.5e-16)
     (* (- y x) (/ z t))
     (if (<= y 2.8e-40) (* x (- 1.0 (/ z t))) (+ x (* y (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+77) {
		tmp = x + (y / (t / z));
	} else if (y <= -3.5e-16) {
		tmp = (y - x) * (z / t);
	} else if (y <= 2.8e-40) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d+77)) then
        tmp = x + (y / (t / z))
    else if (y <= (-3.5d-16)) then
        tmp = (y - x) * (z / t)
    else if (y <= 2.8d-40) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+77) {
		tmp = x + (y / (t / z));
	} else if (y <= -3.5e-16) {
		tmp = (y - x) * (z / t);
	} else if (y <= 2.8e-40) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e+77:
		tmp = x + (y / (t / z))
	elif y <= -3.5e-16:
		tmp = (y - x) * (z / t)
	elif y <= 2.8e-40:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e+77)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (y <= -3.5e-16)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	elseif (y <= 2.8e-40)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e+77)
		tmp = x + (y / (t / z));
	elseif (y <= -3.5e-16)
		tmp = (y - x) * (z / t);
	elseif (y <= 2.8e-40)
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e+77], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-16], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-40], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.8000000000000003e77

   1. Initial program 84.2%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. flip-- 51.9%

         \[\leadsto x + \frac{\color{blue}{\frac{y \cdot y - x \cdot x}{y + x}} \cdot z}{t} \]

      2. associate-*l/ 45.2%

         \[\leadsto x + \frac{\color{blue}{\frac{\left(y \cdot y - x \cdot x\right) \cdot z}{y + x}}}{t} \]

   3. Applied egg-rr 45.2%

      \[\leadsto x + \frac{\color{blue}{\frac{\left(y \cdot y - x \cdot x\right) \cdot z}{y + x}}}{t} \]
   4. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto x + \frac{\frac{\color{blue}{z \cdot \left(y \cdot y - x \cdot x\right)}}{y + x}}{t} \]

      2. associate-/l* 51.8%

         \[\leadsto x + \frac{\color{blue}{\frac{z}{\frac{y + x}{y \cdot y - x \cdot x}}}}{t} \]

      3. difference-of-squares 56.8%

         \[\leadsto x + \frac{\frac{z}{\frac{y + x}{\color{blue}{\left(y + x\right) \cdot \left(y - x\right)}}}}{t} \]

      4. associate-/r* 84.2%

         \[\leadsto x + \frac{\frac{z}{\color{blue}{\frac{\frac{y + x}{y + x}}{y - x}}}}{t} \]

      5. +-commutative 84.2%

         \[\leadsto x + \frac{\frac{z}{\frac{\frac{\color{blue}{x + y}}{y + x}}{y - x}}}{t} \]

      6. +-commutative 84.2%

         \[\leadsto x + \frac{\frac{z}{\frac{\frac{x + y}{\color{blue}{x + y}}}{y - x}}}{t} \]

   5. Simplified 84.2%

      \[\leadsto x + \frac{\color{blue}{\frac{z}{\frac{\frac{x + y}{x + y}}{y - x}}}}{t} \]

   6. Taylor expanded in x around 0 84.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 95.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z}}} \]

   8. Simplified 95.6%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z}}} \]

   if -5.8000000000000003e77 < y < -3.50000000000000017e-16

   1. Initial program 95.5%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in t around 0 91.4%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]
   3. Step-by-step derivation

      1. *-commutative 91.4%

         \[\leadsto \frac{\color{blue}{z \cdot \left(y - x\right)}}{t} \]

      2. associate-*l/ 95.7%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} \]

   4. Applied egg-rr 95.7%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} \]

   if -3.50000000000000017e-16 < y < 2.8e-40

   1. Initial program 96.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in x around inf 85.4%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right) \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 85.4%

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

      2. distribute-lft-in 85.4%

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

      3. *-rgt-identity 85.4%

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

      4. mul-1-neg 85.4%

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

      5. distribute-rgt-neg-in 85.4%

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

      6. unsub-neg 85.4%

         \[\leadsto \color{blue}{x - x \cdot \frac{z}{t}} \]

   4. Simplified 85.4%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{t}} \]

   5. Taylor expanded in x around 0 85.4%

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

   if 2.8e-40 < y

   1. Initial program 93.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in y around inf 87.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 67.8%

         \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   4. Simplified 93.9%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-16}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+132}:\\ \;\;\;\;x + \frac{z}{t \cdot \frac{1}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e+132)
   (+ x (/ z (* t (/ 1.0 (- y x)))))
   (+ x (/ (- y x) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e+132) {
		tmp = x + (z / (t * (1.0 / (y - x))));
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9d+132)) then
        tmp = x + (z / (t * (1.0d0 / (y - x))))
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e+132) {
		tmp = x + (z / (t * (1.0 / (y - x))));
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9e+132:
		tmp = x + (z / (t * (1.0 / (y - x))))
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e+132)
		tmp = Float64(x + Float64(z / Float64(t * Float64(1.0 / Float64(y - x)))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9e+132)
		tmp = x + (z / (t * (1.0 / (y - x))));
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9e+132], N[(x + N[(z / N[(t * N[(1.0 / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999944e132

   1. Initial program 91.7%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. flip-- 78.2%

         \[\leadsto x + \frac{\color{blue}{\frac{y \cdot y - x \cdot x}{y + x}} \cdot z}{t} \]

      2. associate-*l/ 67.4%

         \[\leadsto x + \frac{\color{blue}{\frac{\left(y \cdot y - x \cdot x\right) \cdot z}{y + x}}}{t} \]

   3. Applied egg-rr 67.4%

      \[\leadsto x + \frac{\color{blue}{\frac{\left(y \cdot y - x \cdot x\right) \cdot z}{y + x}}}{t} \]
   4. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto x + \frac{\frac{\color{blue}{z \cdot \left(y \cdot y - x \cdot x\right)}}{y + x}}{t} \]

      2. associate-/l* 78.2%

         \[\leadsto x + \frac{\color{blue}{\frac{z}{\frac{y + x}{y \cdot y - x \cdot x}}}}{t} \]

      3. difference-of-squares 82.7%

         \[\leadsto x + \frac{\frac{z}{\frac{y + x}{\color{blue}{\left(y + x\right) \cdot \left(y - x\right)}}}}{t} \]

      4. associate-/r* 91.7%

         \[\leadsto x + \frac{\frac{z}{\color{blue}{\frac{\frac{y + x}{y + x}}{y - x}}}}{t} \]

      5. +-commutative 91.7%

         \[\leadsto x + \frac{\frac{z}{\frac{\frac{\color{blue}{x + y}}{y + x}}{y - x}}}{t} \]

      6. +-commutative 91.7%

         \[\leadsto x + \frac{\frac{z}{\frac{\frac{x + y}{\color{blue}{x + y}}}{y - x}}}{t} \]

   5. Simplified 91.7%

      \[\leadsto x + \frac{\color{blue}{\frac{z}{\frac{\frac{x + y}{x + y}}{y - x}}}}{t} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 91.7%

         \[\leadsto x + \color{blue}{1 \cdot \frac{\frac{z}{\frac{\frac{x + y}{x + y}}{y - x}}}{t}} \]

      2. associate-/l/ 99.6%

         \[\leadsto x + 1 \cdot \color{blue}{\frac{z}{t \cdot \frac{\frac{x + y}{x + y}}{y - x}}} \]

      3. *-inverses 99.6%

         \[\leadsto x + 1 \cdot \frac{z}{t \cdot \frac{\color{blue}{1}}{y - x}} \]

   7. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{1 \cdot \frac{z}{t \cdot \frac{1}{y - x}}} \]

   if -8.99999999999999944e132 < z

   1. Initial program 94.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   3. Simplified 98.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{t}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+132}:\\ \;\;\;\;x + \frac{z}{t \cdot \frac{1}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 7: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-16} \lor \neg \left(y \leq 2.7 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.9e-16) (not (<= y 2.7e-18)))
   (* y (/ z t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-16) || !(y <= 2.7e-18)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.9d-16)) .or. (.not. (y <= 2.7d-18))) then
        tmp = y * (z / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-16) || !(y <= 2.7e-18)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.9e-16) or not (y <= 2.7e-18):
		tmp = y * (z / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.9e-16) || !(y <= 2.7e-18))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.9e-16) || ~((y <= 2.7e-18)))
		tmp = y * (z / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.9e-16], N[Not[LessEqual[y, 2.7e-18]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.89999999999999977e-16 or 2.69999999999999989e-18 < y

   1. Initial program 90.2%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in t around 0 68.9%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   3. Taylor expanded in y around inf 61.9%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.5%

         \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   5. Simplified 68.5%

      \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   if -3.89999999999999977e-16 < y < 2.69999999999999989e-18

   1. Initial program 97.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in x around inf 85.3%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right) \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 85.3%

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

      2. distribute-lft-in 85.3%

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

      3. *-rgt-identity 85.3%

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

      4. mul-1-neg 85.3%

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

      5. distribute-rgt-neg-in 85.3%

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

      6. unsub-neg 85.3%

         \[\leadsto \color{blue}{x - x \cdot \frac{z}{t}} \]

   4. Simplified 85.3%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{t}} \]

   5. Taylor expanded in x around 0 85.3%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-16} \lor \neg \left(y \leq 2.7 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 8: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.96 \cdot 10^{-16} \lor \neg \left(y \leq 2.7 \cdot 10^{-18}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.96e-16) (not (<= y 2.7e-18)))
   (* (- y x) (/ z t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.96e-16) || !(y <= 2.7e-18)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.96d-16)) .or. (.not. (y <= 2.7d-18))) then
        tmp = (y - x) * (z / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.96e-16) || !(y <= 2.7e-18)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.96e-16) or not (y <= 2.7e-18):
		tmp = (y - x) * (z / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.96e-16) || !(y <= 2.7e-18))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.96e-16) || ~((y <= 2.7e-18)))
		tmp = (y - x) * (z / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.96e-16], N[Not[LessEqual[y, 2.7e-18]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.96000000000000005e-16 or 2.69999999999999989e-18 < y

   1. Initial program 90.2%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in t around 0 68.9%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]
   3. Step-by-step derivation

      1. *-commutative 68.9%

         \[\leadsto \frac{\color{blue}{z \cdot \left(y - x\right)}}{t} \]

      2. associate-*l/ 77.8%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} \]

   4. Applied egg-rr 77.8%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(y - x\right)} \]

   if -1.96000000000000005e-16 < y < 2.69999999999999989e-18

   1. Initial program 97.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in x around inf 85.3%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right) \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 85.3%

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

      2. distribute-lft-in 85.3%

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

      3. *-rgt-identity 85.3%

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

      4. mul-1-neg 85.3%

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

      5. distribute-rgt-neg-in 85.3%

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

      6. unsub-neg 85.3%

         \[\leadsto \color{blue}{x - x \cdot \frac{z}{t}} \]

   4. Simplified 85.3%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{t}} \]

   5. Taylor expanded in x around 0 85.3%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.96 \cdot 10^{-16} \lor \neg \left(y \leq 2.7 \cdot 10^{-18}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 9: 54.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-45} \lor \neg \left(z \leq 8.8 \cdot 10^{-66}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e-45) (not (<= z 8.8e-66))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e-45) || !(z <= 8.8e-66)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.5d-45)) .or. (.not. (z <= 8.8d-66))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e-45) || !(z <= 8.8e-66)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e-45) or not (z <= 8.8e-66):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e-45) || !(z <= 8.8e-66))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.5e-45) || ~((z <= 8.8e-66)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e-45], N[Not[LessEqual[z, 8.8e-66]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000041e-45 or 8.8000000000000004e-66 < z

   1. Initial program 90.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in t around 0 74.6%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   3. Taylor expanded in y around inf 49.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 55.2%

         \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   if -8.50000000000000041e-45 < z < 8.8000000000000004e-66

   1. Initial program 98.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in z around 0 70.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-45} \lor \neg \left(z \leq 8.8 \cdot 10^{-66}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 54.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.1e-45) (* z (/ y t)) (if (<= z 7e-66) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e-45) {
		tmp = z * (y / t);
	} else if (z <= 7e-66) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.1d-45)) then
        tmp = z * (y / t)
    else if (z <= 7d-66) then
        tmp = x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e-45) {
		tmp = z * (y / t);
	} else if (z <= 7e-66) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.1e-45:
		tmp = z * (y / t)
	elif z <= 7e-66:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.1e-45)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 7e-66)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.1e-45)
		tmp = z * (y / t);
	elseif (z <= 7e-66)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.1e-45], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-66], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1000000000000001e-45

   1. Initial program 94.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in t around 0 81.0%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   3. Taylor expanded in y around inf 56.8%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   4. Step-by-step derivation

      1. associate-*l/ 59.0%

         \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]

      2. *-commutative 59.0%

         \[\leadsto \color{blue}{z \cdot \frac{y}{t}} \]

   5. Simplified 59.0%

      \[\leadsto \color{blue}{z \cdot \frac{y}{t}} \]

   if -3.1000000000000001e-45 < z < 7.0000000000000001e-66

   1. Initial program 98.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in z around 0 70.0%

      \[\leadsto \color{blue}{x} \]

   if 7.0000000000000001e-66 < z

   1. Initial program 86.5%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]

   2. Taylor expanded in t around 0 68.0%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]

   3. Taylor expanded in y around inf 41.2%

      \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 52.2%

         \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 11: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{\frac{t}{z}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (/ (- y x) (/ t z))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) / (t / z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) / (t / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - x) / (t / z));
}

Python

def code(x, y, z, t):
	return x + ((y - x) / (t / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) / Float64(t / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - x) / (t / z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.6%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Step-by-step derivation

   1. associate-/l* 97.0%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

3. Simplified 97.0%

   \[\leadsto \color{blue}{x + \frac{y - x}{\frac{t}{z}}} \]

4. Final simplification 97.0%

   \[\leadsto x + \frac{y - x}{\frac{t}{z}} \]

Alternative 12: 37.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 93.6%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]

2. Taylor expanded in z around 0 38.0%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 38.0%

   \[\leadsto x \]

Developer target: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))