Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.3% → 95.5%

Time: 7.0s

Alternatives: 13

Speedup: 1.0×

• 25.1% 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: 93.3% 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: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq 10^{+289}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (<= t_1 1e+289) t_1 (+ x (/ z (/ t (- y x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if (t_1 <= 1e+289) {
		tmp = t_1;
	} else {
		tmp = x + (z / (t / (y - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * z) / t)
    if (t_1 <= 1d+289) then
        tmp = t_1
    else
        tmp = x + (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if (t_1 <= 1e+289) {
		tmp = t_1;
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if t_1 <= 1e+289:
		tmp = t_1
	else:
		tmp = x + (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * z) / t))
	tmp = 0.0
	if (t_1 <= 1e+289)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((y - x) * z) / t);
	tmp = 0.0;
	if (t_1 <= 1e+289)
		tmp = t_1;
	else
		tmp = x + (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+289], t$95$1, N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 1.0000000000000001e289

   1. Initial program 97.0%

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

   if 1.0000000000000001e289 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 83.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq 10^{+289}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 2: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \frac{z}{t}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. +-commutative 94.6%

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

   2. remove-double-neg 94.6%

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

   3. unsub-neg 94.6%

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

   4. associate-*r/ 97.1%

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

   5. fma-neg 97.1%

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

   6. remove-double-neg 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 3: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-75} \lor \neg \left(x \leq 1050\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5e-75) (not (<= x 1050.0)))
   (* x (- 1.0 (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5e-75) || !(x <= 1050.0)) {
		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 ((x <= (-2.5d-75)) .or. (.not. (x <= 1050.0d0))) 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 ((x <= -2.5e-75) || !(x <= 1050.0)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5e-75) or not (x <= 1050.0):
		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 ((x <= -2.5e-75) || !(x <= 1050.0))
		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 ((x <= -2.5e-75) || ~((x <= 1050.0)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5e-75], N[Not[LessEqual[x, 1050.0]], $MachinePrecision]], 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 2 regimes

2. if x < -2.49999999999999989e-75 or 1050 < x

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. remove-double-neg 96.6%

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

      3. unsub-neg 96.6%

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

      4. associate-*r/ 99.9%

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

      5. fma-neg 100.0%

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

      6. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 85.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 85.7%

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

      2. associate-*r/ 88.4%

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

      3. *-rgt-identity 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. mul-1-neg 88.4%

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

      6. distribute-lft-in 88.4%

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

      7. mul-1-neg 88.4%

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

      8. unsub-neg 88.4%

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

   6. Simplified 88.4%

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

   if -2.49999999999999989e-75 < x < 1050

   1. Initial program 91.9%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around inf 84.6%

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

      1. associate-*r/ 87.7%

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

   6. Simplified 87.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-75} \lor \neg \left(x \leq 1050\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 4: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-75} \lor \neg \left(x \leq 620\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.2e-75) (not (<= x 620.0)))
   (* x (- 1.0 (/ z t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.2e-75) || !(x <= 620.0)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (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 <= (-3.2d-75)) .or. (.not. (x <= 620.0d0))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y / (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 <= -3.2e-75) || !(x <= 620.0)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.2e-75) or not (x <= 620.0):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.2e-75) || !(x <= 620.0))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.2e-75) || ~((x <= 620.0)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.2e-75], N[Not[LessEqual[x, 620.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999977e-75 or 620 < x

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. remove-double-neg 96.6%

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

      3. unsub-neg 96.6%

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

      4. associate-*r/ 99.9%

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

      5. fma-neg 100.0%

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

      6. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 85.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 85.7%

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

      2. associate-*r/ 88.4%

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

      3. *-rgt-identity 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. mul-1-neg 88.4%

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

      6. distribute-lft-in 88.4%

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

      7. mul-1-neg 88.4%

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

      8. unsub-neg 88.4%

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

   6. Simplified 88.4%

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

   if -3.19999999999999977e-75 < x < 620

   1. Initial program 91.9%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around inf 86.5%

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

      1. associate-*l/ 84.6%

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

      2. associate-/l* 87.7%

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

   6. Applied egg-rr 87.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-75} \lor \neg \left(x \leq 620\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 93.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+183}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 5.8e+183) (+ x (* z (/ (- y x) t))) (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5.8e+183) {
		tmp = x + (z * ((y - x) / 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 (x <= 5.8d+183) then
        tmp = x + (z * ((y - x) / 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 (x <= 5.8e+183) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 5.8e+183:
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 5.8e+183)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / 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 (x <= 5.8e+183)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 5.8e+183], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.8000000000000001e183

   1. Initial program 94.1%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   if 5.8000000000000001e183 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-*r/ 100.0%

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

      5. fma-neg 100.0%

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

      6. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. mul-1-neg 100.0%

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

      8. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+183}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 6: 94.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+185}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.15e+185) (+ x (/ z (/ t (- y x)))) (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.15e+185) {
		tmp = x + (z / (t / (y - x)));
	} 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 (x <= 1.15d+185) then
        tmp = x + (z / (t / (y - x)))
    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 (x <= 1.15e+185) {
		tmp = x + (z / (t / (y - x)));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.15e+185:
		tmp = x + (z / (t / (y - x)))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.15e+185)
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	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 (x <= 1.15e+185)
		tmp = x + (z / (t / (y - x)));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.15e+185], N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.1500000000000001e185

   1. Initial program 94.1%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

      1. *-commutative 93.0%

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

      2. clear-num 93.0%

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

      3. un-div-inv 93.8%

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

   5. Applied egg-rr 93.8%

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

   if 1.1500000000000001e185 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-*r/ 100.0%

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

      5. fma-neg 100.0%

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

      6. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{t}} \]
   5. Step-by-step derivation

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. mul-1-neg 100.0%

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

      8. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+185}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 7: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+60} \lor \neg \left(z \leq 3.2 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.2e+60) (not (<= z 3.2e+18))) (* (/ x t) (- z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.2e+60) || !(z <= 3.2e+18)) {
		tmp = (x / t) * -z;
	} 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 <= (-8.2d+60)) .or. (.not. (z <= 3.2d+18))) then
        tmp = (x / t) * -z
    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 <= -8.2e+60) || !(z <= 3.2e+18)) {
		tmp = (x / t) * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.2e+60) or not (z <= 3.2e+18):
		tmp = (x / t) * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.2e+60) || !(z <= 3.2e+18))
		tmp = Float64(Float64(x / t) * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.2e+60) || ~((z <= 3.2e+18)))
		tmp = (x / t) * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.2e+60], N[Not[LessEqual[z, 3.2e+18]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e60 or 3.2e18 < z

   1. Initial program 90.2%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

      1. *-commutative 99.0%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.0%

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

   5. Applied egg-rr 99.0%

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

   6. Taylor expanded in y around 0 65.5%

      \[\leadsto x + \frac{z}{\color{blue}{-1 \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

   8. Simplified 65.5%

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

      1. associate-/r/ 65.4%

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

      2. associate-*l/ 62.8%

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

      3. remove-double-neg 62.8%

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

      4. distribute-rgt-neg-out 62.8%

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

      5. div-inv 62.7%

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

      6. add-sqr-sqrt 35.9%

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

      7. sqrt-unprod 41.1%

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

      8. sqr-neg 41.1%

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

      9. sqrt-unprod 6.2%

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

      10. add-sqr-sqrt 12.4%

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

      11. cancel-sign-sub-inv 12.4%

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

      12. div-inv 12.4%

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

      13. frac-2neg 12.4%

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

      14. distribute-rgt-neg-out 12.4%

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

      15. remove-double-neg 12.4%

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

      16. associate-*l/ 16.4%

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

      17. associate-/r/ 13.7%

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

      18. div-inv 13.7%

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

      19. clear-num 13.7%

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

      20. add-sqr-sqrt 6.6%

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

   10. Applied egg-rr 65.5%

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

   11. Taylor expanded in z around inf 54.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 54.1%

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

       2. associate-*l/ 55.0%

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

       3. distribute-rgt-neg-in 55.0%

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

   13. Simplified 55.0%

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

   if -8.2e60 < z < 3.2e18

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. remove-double-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. associate-*r/ 98.2%

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

      5. fma-neg 98.2%

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

      6. remove-double-neg 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 57.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+60} \lor \neg \left(z \leq 3.2 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+60)
   (/ x (/ (- t) z))
   (if (<= z 3.8e+18) x (* (/ x t) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+60) {
		tmp = x / (-t / z);
	} else if (z <= 3.8e+18) {
		tmp = x;
	} else {
		tmp = (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 <= (-2.3d+60)) then
        tmp = x / (-t / z)
    else if (z <= 3.8d+18) then
        tmp = x
    else
        tmp = (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 <= -2.3e+60) {
		tmp = x / (-t / z);
	} else if (z <= 3.8e+18) {
		tmp = x;
	} else {
		tmp = (x / t) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+60:
		tmp = x / (-t / z)
	elif z <= 3.8e+18:
		tmp = x
	else:
		tmp = (x / t) * -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+60)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= 3.8e+18)
		tmp = x;
	else
		tmp = Float64(Float64(x / t) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e+60)
		tmp = x / (-t / z);
	elseif (z <= 3.8e+18)
		tmp = x;
	else
		tmp = (x / t) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+60], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+18], x, N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000017e60

   1. Initial program 89.6%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

      1. *-commutative 97.8%

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

      2. clear-num 97.8%

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

      3. un-div-inv 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in y around 0 72.3%

      \[\leadsto x + \frac{z}{\color{blue}{-1 \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   8. Simplified 72.3%

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

      1. associate-/r/ 72.5%

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

      2. associate-*l/ 70.2%

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

      3. remove-double-neg 70.2%

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

      4. distribute-rgt-neg-out 70.2%

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

      5. div-inv 70.2%

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

      6. add-sqr-sqrt 45.8%

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

      7. sqrt-unprod 48.5%

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

      8. sqr-neg 48.5%

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

      9. sqrt-unprod 4.6%

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

      10. add-sqr-sqrt 5.6%

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

      11. cancel-sign-sub-inv 5.6%

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

      12. div-inv 5.6%

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

      13. frac-2neg 5.6%

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

      14. distribute-rgt-neg-out 5.6%

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

      15. remove-double-neg 5.6%

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

      16. associate-*l/ 8.5%

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

      17. associate-/r/ 6.5%

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

      18. div-inv 6.5%

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

      19. clear-num 6.5%

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

      20. add-sqr-sqrt 1.9%

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

   10. Applied egg-rr 72.3%

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

   11. Taylor expanded in z around inf 66.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. associate-*l/ 66.5%

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

       2. *-commutative 66.5%

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

       3. metadata-eval 66.5%

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

       4. distribute-lft-neg-in 66.5%

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

       5. metadata-eval 66.5%

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

       6. associate-*r/ 66.6%

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

       7. times-frac 66.6%

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

       8. neg-mul-1 66.6%

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

       9. neg-mul-1 66.6%

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

       10. distribute-frac-neg 66.6%

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

       11. remove-double-neg 66.6%

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

       12. *-commutative 66.6%

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

       13. associate-/l* 66.6%

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

   13. Simplified 66.6%

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

   if -2.30000000000000017e60 < z < 3.8e18

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. remove-double-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. associate-*r/ 98.2%

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

      5. fma-neg 98.2%

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

      6. remove-double-neg 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 57.8%

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

   if 3.8e18 < z

   1. Initial program 90.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 60.3%

      \[\leadsto x + \frac{z}{\color{blue}{-1 \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 60.3%

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

      2. neg-mul-1 60.3%

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

   8. Simplified 60.3%

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

      1. associate-/r/ 60.1%

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

      2. associate-*l/ 57.2%

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

      3. remove-double-neg 57.2%

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

      4. distribute-rgt-neg-out 57.2%

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

      5. div-inv 57.1%

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

      6. add-sqr-sqrt 28.3%

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

      7. sqrt-unprod 35.5%

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

      8. sqr-neg 35.5%

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

      9. sqrt-unprod 7.4%

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

      10. add-sqr-sqrt 17.6%

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

      11. cancel-sign-sub-inv 17.6%

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

      12. div-inv 17.6%

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

      13. frac-2neg 17.6%

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

      14. distribute-rgt-neg-out 17.6%

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

      15. remove-double-neg 17.6%

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

      16. associate-*l/ 22.3%

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

      17. associate-/r/ 19.1%

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

      18. div-inv 19.1%

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

      19. clear-num 19.1%

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

      20. add-sqr-sqrt 10.2%

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

   10. Applied egg-rr 60.3%

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

   11. Taylor expanded in z around inf 44.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 44.7%

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

       2. associate-*l/ 46.2%

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

       3. distribute-rgt-neg-in 46.2%

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

   13. Simplified 46.2%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \]

Alternative 9: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{-x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.9e+64)
   (/ x (/ (- t) z))
   (if (<= z 1.45e+18) x (/ z (/ t (- x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.9e+64) {
		tmp = x / (-t / z);
	} else if (z <= 1.45e+18) {
		tmp = x;
	} else {
		tmp = z / (t / -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 <= (-4.9d+64)) then
        tmp = x / (-t / z)
    else if (z <= 1.45d+18) then
        tmp = x
    else
        tmp = z / (t / -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.9e+64) {
		tmp = x / (-t / z);
	} else if (z <= 1.45e+18) {
		tmp = x;
	} else {
		tmp = z / (t / -x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.9e+64:
		tmp = x / (-t / z)
	elif z <= 1.45e+18:
		tmp = x
	else:
		tmp = z / (t / -x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.9e+64)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= 1.45e+18)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.9e+64)
		tmp = x / (-t / z);
	elseif (z <= 1.45e+18)
		tmp = x;
	else
		tmp = z / (t / -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.9e+64], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+18], x, N[(z / N[(t / (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9000000000000003e64

   1. Initial program 89.6%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

      1. *-commutative 97.8%

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

      2. clear-num 97.8%

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

      3. un-div-inv 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in y around 0 72.3%

      \[\leadsto x + \frac{z}{\color{blue}{-1 \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   8. Simplified 72.3%

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

      1. associate-/r/ 72.5%

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

      2. associate-*l/ 70.2%

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

      3. remove-double-neg 70.2%

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

      4. distribute-rgt-neg-out 70.2%

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

      5. div-inv 70.2%

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

      6. add-sqr-sqrt 45.8%

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

      7. sqrt-unprod 48.5%

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

      8. sqr-neg 48.5%

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

      9. sqrt-unprod 4.6%

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

      10. add-sqr-sqrt 5.6%

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

      11. cancel-sign-sub-inv 5.6%

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

      12. div-inv 5.6%

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

      13. frac-2neg 5.6%

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

      14. distribute-rgt-neg-out 5.6%

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

      15. remove-double-neg 5.6%

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

      16. associate-*l/ 8.5%

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

      17. associate-/r/ 6.5%

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

      18. div-inv 6.5%

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

      19. clear-num 6.5%

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

      20. add-sqr-sqrt 1.9%

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

   10. Applied egg-rr 72.3%

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

   11. Taylor expanded in z around inf 66.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. associate-*l/ 66.5%

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

       2. *-commutative 66.5%

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

       3. metadata-eval 66.5%

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

       4. distribute-lft-neg-in 66.5%

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

       5. metadata-eval 66.5%

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

       6. associate-*r/ 66.6%

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

       7. times-frac 66.6%

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

       8. neg-mul-1 66.6%

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

       9. neg-mul-1 66.6%

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

       10. distribute-frac-neg 66.6%

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

       11. remove-double-neg 66.6%

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

       12. *-commutative 66.6%

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

       13. associate-/l* 66.6%

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

   13. Simplified 66.6%

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

   if -4.9000000000000003e64 < z < 1.45e18

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. remove-double-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. associate-*r/ 98.2%

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

      5. fma-neg 98.2%

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

      6. remove-double-neg 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 57.8%

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

   if 1.45e18 < z

   1. Initial program 90.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 60.3%

      \[\leadsto x + \frac{z}{\color{blue}{-1 \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 60.3%

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

      2. neg-mul-1 60.3%

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

   8. Simplified 60.3%

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

      1. associate-/r/ 60.1%

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

      2. associate-*l/ 57.2%

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

      3. remove-double-neg 57.2%

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

      4. distribute-rgt-neg-out 57.2%

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

      5. div-inv 57.1%

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

      6. add-sqr-sqrt 28.3%

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

      7. sqrt-unprod 35.5%

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

      8. sqr-neg 35.5%

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

      9. sqrt-unprod 7.4%

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

      10. add-sqr-sqrt 17.6%

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

      11. cancel-sign-sub-inv 17.6%

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

      12. div-inv 17.6%

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

      13. frac-2neg 17.6%

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

      14. distribute-rgt-neg-out 17.6%

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

      15. remove-double-neg 17.6%

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

      16. associate-*l/ 22.3%

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

      17. associate-/r/ 19.1%

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

      18. div-inv 19.1%

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

      19. clear-num 19.1%

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

      20. add-sqr-sqrt 10.2%

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

   10. Applied egg-rr 60.3%

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

   11. Taylor expanded in z around inf 44.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. associate-*r/ 44.7%

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

       2. *-commutative 44.7%

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

       3. neg-mul-1 44.7%

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

       4. distribute-rgt-neg-in 44.7%

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

       5. associate-/l* 46.2%

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

   13. Simplified 46.2%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{-x}}\\ \end{array} \]

Alternative 10: 97.7% 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 94.6%

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

   1. associate-/l* 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 11: 97.6% accurate, 1.0× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.6%

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

   1. +-commutative 94.6%

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

   2. remove-double-neg 94.6%

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

   3. unsub-neg 94.6%

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

   4. associate-*r/ 97.1%

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

   5. fma-neg 97.1%

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

   6. remove-double-neg 97.1%

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

3. Simplified 97.1%

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

   1. fma-udef 97.1%

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

5. Applied egg-rr 97.1%

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

6. Final simplification 97.1%

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

Alternative 12: 65.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (z / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.6%

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

   1. +-commutative 94.6%

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

   2. remove-double-neg 94.6%

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

   3. unsub-neg 94.6%

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

   4. associate-*r/ 97.1%

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

   5. fma-neg 97.1%

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

   6. remove-double-neg 97.1%

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

3. Simplified 97.1%

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

4. Taylor expanded in y around 0 66.0%

   \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{t}} \]
5. Step-by-step derivation

   1. mul-1-neg 66.0%

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

   2. associate-*r/ 67.5%

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

   3. *-rgt-identity 67.5%

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

   4. distribute-rgt-neg-in 67.5%

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

   5. mul-1-neg 67.5%

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

   6. distribute-lft-in 67.5%

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

   7. mul-1-neg 67.5%

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

   8. unsub-neg 67.5%

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

6. Simplified 67.5%

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

7. Final simplification 67.5%

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

Alternative 13: 38.5% 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 94.6%

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

   1. +-commutative 94.6%

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

   2. remove-double-neg 94.6%

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

   3. unsub-neg 94.6%

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

   4. associate-*r/ 97.1%

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

   5. fma-neg 97.1%

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

   6. remove-double-neg 97.1%

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

3. Simplified 97.1%

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

4. Taylor expanded in z around 0 38.6%

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

5. Final simplification 38.6%

   \[\leadsto x \]

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 2024024 
(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)))