Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.9% → 95.3%

Time: 9.3s

Alternatives: 13

Speedup: 1.0×

• 24.9% 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: 92.9% 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: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.2 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 4.2e-95) (+ x (/ (* (- y x) z) t)) (+ x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.2e-95) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = x + (z * ((y - x) / 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 <= 4.2d-95) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = x + (z * ((y - x) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.2e-95) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 4.2e-95:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 4.2e-95)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 4.2e-95)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 4.2e-95], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.2e-95

   1. Initial program 96.7%

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

   if 4.2e-95 < z

   1. Initial program 88.2%

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

      1. associate-*l/ 99.0%

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

   3. Applied egg-rr 99.0%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.2 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

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 94.0%

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

   1. +-commutative 94.0%

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

   2. remove-double-neg 94.0%

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

   3. unsub-neg 94.0%

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

   4. associate-*r/ 97.2%

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

   5. fma-neg 97.2%

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

   6. remove-double-neg 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 3: 70.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+101}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.2e+193)
   x
   (if (<= t -8.5e+137)
     (* z (/ (- y x) t))
     (if (<= t -2.95e+16) x (if (<= t 2e+101) (* (- y x) (/ z t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e+193) {
		tmp = x;
	} else if (t <= -8.5e+137) {
		tmp = z * ((y - x) / t);
	} else if (t <= -2.95e+16) {
		tmp = x;
	} else if (t <= 2e+101) {
		tmp = (y - x) * (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 (t <= (-1.2d+193)) then
        tmp = x
    else if (t <= (-8.5d+137)) then
        tmp = z * ((y - x) / t)
    else if (t <= (-2.95d+16)) then
        tmp = x
    else if (t <= 2d+101) then
        tmp = (y - x) * (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 (t <= -1.2e+193) {
		tmp = x;
	} else if (t <= -8.5e+137) {
		tmp = z * ((y - x) / t);
	} else if (t <= -2.95e+16) {
		tmp = x;
	} else if (t <= 2e+101) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.2e+193:
		tmp = x
	elif t <= -8.5e+137:
		tmp = z * ((y - x) / t)
	elif t <= -2.95e+16:
		tmp = x
	elif t <= 2e+101:
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.2e+193)
		tmp = x;
	elseif (t <= -8.5e+137)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	elseif (t <= -2.95e+16)
		tmp = x;
	elseif (t <= 2e+101)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.2e+193)
		tmp = x;
	elseif (t <= -8.5e+137)
		tmp = z * ((y - x) / t);
	elseif (t <= -2.95e+16)
		tmp = x;
	elseif (t <= 2e+101)
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.2e+193], x, If[LessEqual[t, -8.5e+137], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.95e+16], x, If[LessEqual[t, 2e+101], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e193 or -8.50000000000000028e137 < t < -2.95e16 or 2e101 < t

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. remove-double-neg 89.4%

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

      3. unsub-neg 89.4%

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

      4. associate-*r/ 98.4%

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

      5. fma-neg 98.4%

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

      6. remove-double-neg 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 77.1%

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

   if -1.2e193 < t < -8.50000000000000028e137

   1. Initial program 74.1%

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

      1. +-commutative 74.1%

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

      2. remove-double-neg 74.1%

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

      3. unsub-neg 74.1%

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

      4. associate-*r/ 99.7%

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

      5. fma-neg 99.9%

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

      6. remove-double-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 70.3%

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

   5. Taylor expanded in y around 0 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. sub-neg 70.3%

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

      4. div-sub 70.3%

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

   7. Simplified 70.3%

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

   if -2.95e16 < t < 2e101

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. remove-double-neg 98.1%

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

      3. unsub-neg 98.1%

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

      4. associate-*r/ 96.3%

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

      5. fma-neg 96.3%

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

      6. remove-double-neg 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around inf 69.0%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. sub-neg 69.0%

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

      4. div-sub 71.7%

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

   7. Simplified 71.7%

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

      1. clear-num 71.5%

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

      2. un-div-inv 72.1%

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

   9. Applied egg-rr 72.1%

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

       1. associate-/r/ 78.4%

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

   11. Applied egg-rr 78.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+101}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 55.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{t}\\ \mathbf{if}\;t \leq -1200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-264}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y z) t)))
   (if (<= t -1200000000000.0)
     x
     (if (<= t -1.8e-249)
       t_1
       (if (<= t -2.8e-264) (* (/ x t) (- z)) (if (<= t 2.3e-33) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double tmp;
	if (t <= -1200000000000.0) {
		tmp = x;
	} else if (t <= -1.8e-249) {
		tmp = t_1;
	} else if (t <= -2.8e-264) {
		tmp = (x / t) * -z;
	} else if (t <= 2.3e-33) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y * z) / t
    if (t <= (-1200000000000.0d0)) then
        tmp = x
    else if (t <= (-1.8d-249)) then
        tmp = t_1
    else if (t <= (-2.8d-264)) then
        tmp = (x / t) * -z
    else if (t <= 2.3d-33) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double tmp;
	if (t <= -1200000000000.0) {
		tmp = x;
	} else if (t <= -1.8e-249) {
		tmp = t_1;
	} else if (t <= -2.8e-264) {
		tmp = (x / t) * -z;
	} else if (t <= 2.3e-33) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) / t
	tmp = 0
	if t <= -1200000000000.0:
		tmp = x
	elif t <= -1.8e-249:
		tmp = t_1
	elif t <= -2.8e-264:
		tmp = (x / t) * -z
	elif t <= 2.3e-33:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) / t)
	tmp = 0.0
	if (t <= -1200000000000.0)
		tmp = x;
	elseif (t <= -1.8e-249)
		tmp = t_1;
	elseif (t <= -2.8e-264)
		tmp = Float64(Float64(x / t) * Float64(-z));
	elseif (t <= 2.3e-33)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) / t;
	tmp = 0.0;
	if (t <= -1200000000000.0)
		tmp = x;
	elseif (t <= -1.8e-249)
		tmp = t_1;
	elseif (t <= -2.8e-264)
		tmp = (x / t) * -z;
	elseif (t <= 2.3e-33)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -1200000000000.0], x, If[LessEqual[t, -1.8e-249], t$95$1, If[LessEqual[t, -2.8e-264], N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[t, 2.3e-33], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e12 or 2.29999999999999986e-33 < t

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. remove-double-neg 90.0%

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

      3. unsub-neg 90.0%

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

      4. associate-*r/ 98.8%

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

      5. fma-neg 98.8%

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

      6. remove-double-neg 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 65.8%

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

   if -1.2e12 < t < -1.79999999999999997e-249 or -2.80000000000000012e-264 < t < 2.29999999999999986e-33

   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/ 96.2%

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

      5. fma-neg 96.2%

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

      6. remove-double-neg 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around inf 69.4%

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

   5. Taylor expanded in y around 0 69.4%

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

      1. +-commutative 69.4%

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

      2. mul-1-neg 69.4%

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

      3. sub-neg 69.4%

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

      4. div-sub 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in z around 0 83.1%

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

   9. Taylor expanded in y around inf 61.6%

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

   if -1.79999999999999997e-249 < t < -2.80000000000000012e-264

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. remove-double-neg 99.7%

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

      3. unsub-neg 99.7%

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

      4. associate-*r/ 84.6%

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

      5. fma-neg 84.6%

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

      6. remove-double-neg 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-249}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-264}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-33}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 94.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-131} \lor \neg \left(z \leq 5.5 \cdot 10^{-97}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.75e-131) (not (<= z 5.5e-97)))
   (+ x (* z (/ (- y x) t)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e-131) || !(z <= 5.5e-97)) {
		tmp = x + (z * ((y - x) / 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 ((z <= (-1.75d-131)) .or. (.not. (z <= 5.5d-97))) then
        tmp = x + (z * ((y - x) / 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 ((z <= -1.75e-131) || !(z <= 5.5e-97)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.75e-131) or not (z <= 5.5e-97):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.75e-131) || !(z <= 5.5e-97))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.75e-131) || ~((z <= 5.5e-97)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.75e-131], N[Not[LessEqual[z, 5.5e-97]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e-131 or 5.49999999999999948e-97 < z

   1. Initial program 91.8%

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

      1. associate-*l/ 98.9%

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

   3. Applied egg-rr 98.9%

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

   if -1.7500000000000001e-131 < z < 5.49999999999999948e-97

   1. Initial program 97.9%

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

   2. Taylor expanded in y around inf 91.5%

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

      1. *-commutative 91.5%

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

   4. Simplified 91.5%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-131} \lor \neg \left(z \leq 5.5 \cdot 10^{-97}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 6: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+118} \lor \neg \left(x \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.42e+118) (not (<= x 5.2e+42)))
   (* x (- (- -1.0) (/ z t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.42e+118) || !(x <= 5.2e+42)) {
		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 <= (-1.42d+118)) .or. (.not. (x <= 5.2d+42))) 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 <= -1.42e+118) || !(x <= 5.2e+42)) {
		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 <= -1.42e+118) or not (x <= 5.2e+42):
		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 <= -1.42e+118) || !(x <= 5.2e+42))
		tmp = Float64(x * Float64(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 <= -1.42e+118) || ~((x <= 5.2e+42)))
		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, -1.42e+118], N[Not[LessEqual[x, 5.2e+42]], $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 < -1.41999999999999999e118 or 5.1999999999999998e42 < x

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. remove-double-neg 92.5%

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

      3. unsub-neg 92.5%

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

      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 x around -inf 91.5%

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

      1. associate-*r* 91.5%

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

      2. neg-mul-1 91.5%

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

      3. *-commutative 91.5%

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

      4. sub-neg 91.5%

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

      5. metadata-eval 91.5%

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

      6. +-commutative 91.5%

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

   6. Simplified 91.5%

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

   if -1.41999999999999999e118 < x < 5.1999999999999998e42

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 85.9%

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

      1. associate-/l* 88.3%

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

   4. Simplified 88.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+118} \lor \neg \left(x \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 7: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-85} \lor \neg \left(z \leq 3.8 \cdot 10^{-77}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-85) (not (<= z 3.8e-77))) (* z (/ (- y x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-85) || !(z <= 3.8e-77)) {
		tmp = z * ((y - x) / 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 <= (-7.2d-85)) .or. (.not. (z <= 3.8d-77))) then
        tmp = z * ((y - x) / 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 <= -7.2e-85) || !(z <= 3.8e-77)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-85) or not (z <= 3.8e-77):
		tmp = z * ((y - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-85) || !(z <= 3.8e-77))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.2e-85) || ~((z <= 3.8e-77)))
		tmp = z * ((y - x) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-85], N[Not[LessEqual[z, 3.8e-77]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999996e-85 or 3.7999999999999999e-77 < z

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. remove-double-neg 91.7%

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

      3. unsub-neg 91.7%

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

      4. associate-*r/ 96.2%

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

      5. fma-neg 96.2%

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

      6. remove-double-neg 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around inf 76.2%

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

   5. Taylor expanded in y around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. mul-1-neg 76.2%

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

      3. sub-neg 76.2%

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

      4. div-sub 77.5%

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

   7. Simplified 77.5%

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

   if -7.1999999999999996e-85 < z < 3.7999999999999999e-77

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. remove-double-neg 97.3%

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

      3. unsub-neg 97.3%

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

      4. associate-*r/ 98.6%

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

      5. fma-neg 98.6%

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

      6. remove-double-neg 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 64.1%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-85} \lor \neg \left(z \leq 3.8 \cdot 10^{-77}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+145} \lor \neg \left(z \leq 6.4 \cdot 10^{+68}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e+145) (not (<= z 6.4e+68)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e+145) || !(z <= 6.4e+68)) {
		tmp = z * ((y - x) / 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 ((z <= (-1.25d+145)) .or. (.not. (z <= 6.4d+68))) then
        tmp = z * ((y - x) / 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 ((z <= -1.25e+145) || !(z <= 6.4e+68)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e+145) or not (z <= 6.4e+68):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e+145) || !(z <= 6.4e+68))
		tmp = Float64(z * Float64(Float64(y - x) / 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 ((z <= -1.25e+145) || ~((z <= 6.4e+68)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.25e+145], N[Not[LessEqual[z, 6.4e+68]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999992e145 or 6.39999999999999989e68 < z

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. remove-double-neg 90.3%

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

      3. unsub-neg 90.3%

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

      4. associate-*r/ 92.9%

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

      5. fma-neg 92.9%

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

      6. remove-double-neg 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around inf 85.9%

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

   5. Taylor expanded in y around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. sub-neg 85.9%

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

      4. div-sub 88.3%

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

   7. Simplified 88.3%

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

   if -1.24999999999999992e145 < z < 6.39999999999999989e68

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 86.6%

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

      1. associate-/l* 88.8%

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

   4. Simplified 88.8%

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

      1. div-inv 88.7%

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

      2. clear-num 88.8%

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

      3. *-commutative 88.8%

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

   6. Applied egg-rr 88.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+145} \lor \neg \left(z \leq 6.4 \cdot 10^{+68}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+144}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e+144)
   (/ z (/ t (- y x)))
   (if (<= z 1.3e+65) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+144) {
		tmp = z / (t / (y - x));
	} else if (z <= 1.3e+65) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / 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 <= (-1.9d+144)) then
        tmp = z / (t / (y - x))
    else if (z <= 1.3d+65) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+144) {
		tmp = z / (t / (y - x));
	} else if (z <= 1.3e+65) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.9e+144:
		tmp = z / (t / (y - x))
	elif z <= 1.3e+65:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e+144)
		tmp = Float64(z / Float64(t / Float64(y - x)));
	elseif (z <= 1.3e+65)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.9e+144)
		tmp = z / (t / (y - x));
	elseif (z <= 1.3e+65)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e+144], N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+65], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000013e144

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. remove-double-neg 93.3%

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

      3. unsub-neg 93.3%

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

      4. associate-*r/ 90.3%

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

      5. fma-neg 90.3%

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

      6. remove-double-neg 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around inf 96.3%

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

   5. Taylor expanded in y around 0 96.3%

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

      1. +-commutative 96.3%

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

      2. mul-1-neg 96.3%

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

      3. sub-neg 96.3%

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

      4. div-sub 99.8%

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

   7. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -1.90000000000000013e144 < z < 1.30000000000000001e65

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 86.6%

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

      1. associate-/l* 88.8%

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

   4. Simplified 88.8%

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

      1. div-inv 88.7%

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

      2. clear-num 88.8%

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

      3. *-commutative 88.8%

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

   6. Applied egg-rr 88.8%

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

   if 1.30000000000000001e65 < z

   1. Initial program 88.6%

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

      1. +-commutative 88.6%

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

      2. remove-double-neg 88.6%

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

      3. unsub-neg 88.6%

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

      4. associate-*r/ 94.4%

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

      5. fma-neg 94.4%

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

      6. remove-double-neg 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around inf 79.9%

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

   5. Taylor expanded in y around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. sub-neg 79.9%

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

      4. div-sub 81.8%

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

   7. Simplified 81.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+144}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 10: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -650000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -650000000000.0) x (if (<= t 1.65e-34) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -650000000000.0) {
		tmp = x;
	} else if (t <= 1.65e-34) {
		tmp = z * (y / 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 (t <= (-650000000000.0d0)) then
        tmp = x
    else if (t <= 1.65d-34) then
        tmp = z * (y / 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 (t <= -650000000000.0) {
		tmp = x;
	} else if (t <= 1.65e-34) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -650000000000.0:
		tmp = x
	elif t <= 1.65e-34:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -650000000000.0)
		tmp = x;
	elseif (t <= 1.65e-34)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -650000000000.0)
		tmp = x;
	elseif (t <= 1.65e-34)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -650000000000.0], x, If[LessEqual[t, 1.65e-34], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5e11 or 1.64999999999999991e-34 < t

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. remove-double-neg 90.0%

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

      3. unsub-neg 90.0%

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

      4. associate-*r/ 98.8%

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

      5. fma-neg 98.8%

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

      6. remove-double-neg 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 65.8%

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

   if -6.5e11 < t < 1.64999999999999991e-34

   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/ 95.7%

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

      5. fma-neg 95.7%

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

      6. remove-double-neg 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around inf 70.8%

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

   5. Taylor expanded in y around inf 53.7%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -650000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 55.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4400000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-35}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4400000000000.0) x (if (<= t 1.02e-35) (/ (* y z) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4400000000000.0) {
		tmp = x;
	} else if (t <= 1.02e-35) {
		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 (t <= (-4400000000000.0d0)) then
        tmp = x
    else if (t <= 1.02d-35) 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 (t <= -4400000000000.0) {
		tmp = x;
	} else if (t <= 1.02e-35) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4400000000000.0:
		tmp = x
	elif t <= 1.02e-35:
		tmp = (y * z) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4400000000000.0)
		tmp = x;
	elseif (t <= 1.02e-35)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4400000000000.0)
		tmp = x;
	elseif (t <= 1.02e-35)
		tmp = (y * z) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4400000000000.0], x, If[LessEqual[t, 1.02e-35], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e12 or 1.01999999999999995e-35 < t

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. remove-double-neg 90.0%

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

      3. unsub-neg 90.0%

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

      4. associate-*r/ 98.8%

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

      5. fma-neg 98.8%

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

      6. remove-double-neg 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 65.8%

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

   if -4.4e12 < t < 1.01999999999999995e-35

   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/ 95.7%

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

      5. fma-neg 95.7%

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

      6. remove-double-neg 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around inf 70.8%

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

   5. Taylor expanded in y around 0 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. sub-neg 70.8%

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

      4. div-sub 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in z around 0 83.9%

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

   9. Taylor expanded in y around inf 59.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4400000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-35}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 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 94.0%

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

   1. +-commutative 94.0%

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

   2. remove-double-neg 94.0%

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

   3. unsub-neg 94.0%

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

   4. associate-*r/ 97.2%

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

   5. fma-neg 97.2%

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

   6. remove-double-neg 97.2%

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

3. Simplified 97.2%

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

   1. fma-udef 97.2%

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

5. Applied egg-rr 97.2%

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

6. Final simplification 97.2%

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

Alternative 13: 38.3% 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 94.0%

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

   1. +-commutative 94.0%

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

   2. remove-double-neg 94.0%

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

   3. unsub-neg 94.0%

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

   4. associate-*r/ 97.2%

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

   5. fma-neg 97.2%

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

   6. remove-double-neg 97.2%

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

3. Simplified 97.2%

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

4. Taylor expanded in z around 0 39.8%

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

5. Final simplification 39.8%

   \[\leadsto x \]

Developer target: 97.4% 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 2023297 
(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)))