Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.0% → 97.7%

Time: 7.6s

Alternatives: 11

Speedup: 1.0×

• 25.2% 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: 93.0% 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: 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 91.1%

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

   1. associate-/l* 97.9%

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

3. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 2: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+301} \lor \neg \left(t_1 \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (or (<= t_1 -2e+301) (not (<= t_1 2e+307))) (/ (- y x) (/ t z)) t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -2e+301) || !(t_1 <= 2e+307)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * z) / t)
    if ((t_1 <= (-2d+301)) .or. (.not. (t_1 <= 2d+307))) then
        tmp = (y - x) / (t / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -2e+301) || !(t_1 <= 2e+307)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if (t_1 <= -2e+301) or not (t_1 <= 2e+307):
		tmp = (y - x) / (t / z)
	else:
		tmp = t_1
	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 <= -2e+301) || !(t_1 <= 2e+307))
		tmp = Float64(Float64(y - x) / Float64(t / z));
	else
		tmp = t_1;
	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 <= -2e+301) || ~((t_1 <= 2e+307)))
		tmp = (y - x) / (t / z);
	else
		tmp = t_1;
	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[Or[LessEqual[t$95$1, -2e+301], N[Not[LessEqual[t$95$1, 2e+307]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -2.00000000000000011e301 or 1.99999999999999997e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 75.6%

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

   2. Taylor expanded in z around inf 85.0%

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

   3. Taylor expanded in y around 0 60.4%

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

      1. associate-*r/ 68.5%

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

      2. +-commutative 68.5%

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

      3. mul-1-neg 68.5%

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

      4. associate-*r/ 75.3%

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

      5. unsub-neg 75.3%

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

      6. associate-*r/ 64.2%

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

      7. associate-/l* 77.5%

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

      8. *-commutative 77.5%

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

      9. associate-/r/ 74.2%

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

      10. div-sub 91.6%

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

   5. Simplified 91.6%

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

   if -2.00000000000000011e301 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 1.99999999999999997e307

   1. Initial program 99.8%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -2 \cdot 10^{+301} \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 3: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -1.92 \cdot 10^{-295}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ t z)))))
   (if (<= x -1.65e-12)
     t_1
     (if (<= x -2.2e-87)
       (/ (- y x) (/ t z))
       (if (<= x -1.92e-295)
         (+ x (* z (/ y t)))
         (if (<= x 4.6e+64) (+ x (/ y (/ t z))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x / (t / z));
	double tmp;
	if (x <= -1.65e-12) {
		tmp = t_1;
	} else if (x <= -2.2e-87) {
		tmp = (y - x) / (t / z);
	} else if (x <= -1.92e-295) {
		tmp = x + (z * (y / t));
	} else if (x <= 4.6e+64) {
		tmp = x + (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x / (t / z))
    if (x <= (-1.65d-12)) then
        tmp = t_1
    else if (x <= (-2.2d-87)) then
        tmp = (y - x) / (t / z)
    else if (x <= (-1.92d-295)) then
        tmp = x + (z * (y / t))
    else if (x <= 4.6d+64) then
        tmp = x + (y / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (x / (t / z));
	double tmp;
	if (x <= -1.65e-12) {
		tmp = t_1;
	} else if (x <= -2.2e-87) {
		tmp = (y - x) / (t / z);
	} else if (x <= -1.92e-295) {
		tmp = x + (z * (y / t));
	} else if (x <= 4.6e+64) {
		tmp = x + (y / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x / (t / z))
	tmp = 0
	if x <= -1.65e-12:
		tmp = t_1
	elif x <= -2.2e-87:
		tmp = (y - x) / (t / z)
	elif x <= -1.92e-295:
		tmp = x + (z * (y / t))
	elif x <= 4.6e+64:
		tmp = x + (y / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x / Float64(t / z)))
	tmp = 0.0
	if (x <= -1.65e-12)
		tmp = t_1;
	elseif (x <= -2.2e-87)
		tmp = Float64(Float64(y - x) / Float64(t / z));
	elseif (x <= -1.92e-295)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (x <= 4.6e+64)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x / (t / z));
	tmp = 0.0;
	if (x <= -1.65e-12)
		tmp = t_1;
	elseif (x <= -2.2e-87)
		tmp = (y - x) / (t / z);
	elseif (x <= -1.92e-295)
		tmp = x + (z * (y / t));
	elseif (x <= 4.6e+64)
		tmp = x + (y / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e-12], t$95$1, If[LessEqual[x, -2.2e-87], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.92e-295], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+64], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.65e-12 or 4.6e64 < x

   1. Initial program 88.1%

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

   2. Taylor expanded in x around inf 91.8%

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

      1. *-commutative 91.8%

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

      2. distribute-rgt-in 91.7%

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

      3. *-lft-identity 91.7%

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

      4. mul-1-neg 91.7%

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

      5. cancel-sign-sub-inv 91.7%

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

      6. *-commutative 91.7%

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

   4. Simplified 91.7%

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

      1. clear-num 91.7%

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

      2. un-div-inv 91.8%

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

   6. Applied egg-rr 91.8%

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

   if -1.65e-12 < x < -2.19999999999999988e-87

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 83.0%

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

   3. Taylor expanded in y around 0 82.7%

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

      1. associate-*r/ 94.1%

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

      2. +-commutative 94.1%

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

      3. mul-1-neg 94.1%

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

      4. associate-*r/ 94.1%

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

      5. unsub-neg 94.1%

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

      6. associate-*r/ 82.7%

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

      7. associate-/l* 94.0%

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

      8. *-commutative 94.0%

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

      9. associate-/r/ 94.0%

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

      10. div-sub 94.0%

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

   5. Simplified 94.0%

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

   if -2.19999999999999988e-87 < x < -1.91999999999999997e-295

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 80.3%

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

      1. associate-*l/ 88.0%

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

      2. *-commutative 88.0%

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

   4. Simplified 88.0%

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

   if -1.91999999999999997e-295 < x < 4.6e64

   1. Initial program 97.1%

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

   2. Taylor expanded in y around inf 82.6%

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

      1. associate-*r/ 54.8%

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

   4. Simplified 85.3%

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

      1. clear-num 54.8%

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

      2. un-div-inv 55.6%

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

   6. Applied egg-rr 86.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -1.92 \cdot 10^{-295}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \]

Alternative 4: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- x))))
   (if (<= z -6e-16)
     t_1
     (if (<= z 6e-13) x (if (<= z 1.3e+287) t_1 (* y (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * -x;
	double tmp;
	if (z <= -6e-16) {
		tmp = t_1;
	} else if (z <= 6e-13) {
		tmp = x;
	} else if (z <= 1.3e+287) {
		tmp = t_1;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / t) * -x
    if (z <= (-6d-16)) then
        tmp = t_1
    else if (z <= 6d-13) then
        tmp = x
    else if (z <= 1.3d+287) then
        tmp = t_1
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * -x;
	double tmp;
	if (z <= -6e-16) {
		tmp = t_1;
	} else if (z <= 6e-13) {
		tmp = x;
	} else if (z <= 1.3e+287) {
		tmp = t_1;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * -x
	tmp = 0
	if z <= -6e-16:
		tmp = t_1
	elif z <= 6e-13:
		tmp = x
	elif z <= 1.3e+287:
		tmp = t_1
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(-x))
	tmp = 0.0
	if (z <= -6e-16)
		tmp = t_1;
	elseif (z <= 6e-13)
		tmp = x;
	elseif (z <= 1.3e+287)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * -x;
	tmp = 0.0;
	if (z <= -6e-16)
		tmp = t_1;
	elseif (z <= 6e-13)
		tmp = x;
	elseif (z <= 1.3e+287)
		tmp = t_1;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[z, -6e-16], t$95$1, If[LessEqual[z, 6e-13], x, If[LessEqual[z, 1.3e+287], t$95$1, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999987e-16 or 5.99999999999999968e-13 < z < 1.3000000000000001e287

   1. Initial program 86.0%

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

   2. Taylor expanded in t around 0 74.0%

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

   3. Taylor expanded in y around 0 46.1%

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

      1. associate-*r/ 46.1%

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

      2. mul-1-neg 46.1%

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

      3. distribute-rgt-neg-out 46.1%

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

      4. associate-*l/ 49.9%

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

   5. Simplified 49.9%

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

   if -5.99999999999999987e-16 < z < 5.99999999999999968e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 67.0%

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

   if 1.3000000000000001e287 < z

   1. Initial program 76.5%

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

   2. Taylor expanded in t around 0 76.5%

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

   3. Taylor expanded in y around inf 76.5%

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

      1. associate-*r/ 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-16}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+287}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{-\frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+292}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e-19)
   (/ x (- (/ t z)))
   (if (<= z 4.2e-13) x (if (<= z 8e+292) (* (/ z t) (- x)) (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e-19) {
		tmp = x / -(t / z);
	} else if (z <= 4.2e-13) {
		tmp = x;
	} else if (z <= 8e+292) {
		tmp = (z / t) * -x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.2d-19)) then
        tmp = x / -(t / z)
    else if (z <= 4.2d-13) then
        tmp = x
    else if (z <= 8d+292) then
        tmp = (z / t) * -x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e-19) {
		tmp = x / -(t / z);
	} else if (z <= 4.2e-13) {
		tmp = x;
	} else if (z <= 8e+292) {
		tmp = (z / t) * -x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e-19:
		tmp = x / -(t / z)
	elif z <= 4.2e-13:
		tmp = x
	elif z <= 8e+292:
		tmp = (z / t) * -x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e-19)
		tmp = Float64(x / Float64(-Float64(t / z)));
	elseif (z <= 4.2e-13)
		tmp = x;
	elseif (z <= 8e+292)
		tmp = Float64(Float64(z / t) * Float64(-x));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.2e-19)
		tmp = x / -(t / z);
	elseif (z <= 4.2e-13)
		tmp = x;
	elseif (z <= 8e+292)
		tmp = (z / t) * -x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e-19], N[(x / (-N[(t / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 4.2e-13], x, If[LessEqual[z, 8e+292], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.2000000000000002e-19

   1. Initial program 83.0%

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

   2. Taylor expanded in z around inf 77.5%

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

   3. Taylor expanded in y around 0 45.7%

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

      1. mul-1-neg 45.7%

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

      2. distribute-frac-neg 45.7%

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

   5. Simplified 45.7%

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

      1. associate-*l/ 44.1%

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

      2. associate-/l* 48.7%

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

      3. add-sqr-sqrt 26.8%

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

      4. sqrt-unprod 25.2%

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

      5. sqr-neg 25.2%

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

      6. sqrt-unprod 2.6%

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

      7. add-sqr-sqrt 4.6%

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

      8. frac-2neg 4.6%

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

      9. add-sqr-sqrt 2.1%

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

      10. sqrt-unprod 16.5%

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

      11. sqr-neg 16.5%

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

      12. sqrt-unprod 21.8%

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

      13. add-sqr-sqrt 48.7%

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

      14. distribute-neg-frac 48.7%

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

   7. Applied egg-rr 48.7%

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

   if -7.2000000000000002e-19 < z < 4.19999999999999977e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 67.0%

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

   if 4.19999999999999977e-13 < z < 8.0000000000000001e292

   1. Initial program 88.4%

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

   2. Taylor expanded in t around 0 77.2%

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

   3. Taylor expanded in y around 0 47.7%

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

      1. associate-*r/ 47.7%

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

      2. mul-1-neg 47.7%

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

      3. distribute-rgt-neg-out 47.7%

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

      4. associate-*l/ 50.8%

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

   5. Simplified 50.8%

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

   if 8.0000000000000001e292 < z

   1. Initial program 76.5%

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

   2. Taylor expanded in t around 0 76.5%

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

   3. Taylor expanded in y around inf 76.5%

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

      1. associate-*r/ 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{-\frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+292}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.3 \cdot 10^{+238} \lor \neg \left(z \leq 3.4 \cdot 10^{+293}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z 2.3e+238) (not (<= z 3.4e+293)))
   (+ x (* y (/ z t)))
   (/ x (- (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= 2.3e+238) || !(z <= 3.4e+293)) {
		tmp = x + (y * (z / t));
	} 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+238) .or. (.not. (z <= 3.4d+293))) then
        tmp = x + (y * (z / t))
    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+238) || !(z <= 3.4e+293)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x / -(t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= 2.3e+238) or not (z <= 3.4e+293):
		tmp = x + (y * (z / t))
	else:
		tmp = x / -(t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= 2.3e+238) || !(z <= 3.4e+293))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x / Float64(-Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= 2.3e+238) || ~((z <= 3.4e+293)))
		tmp = x + (y * (z / t));
	else
		tmp = x / -(t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, 2.3e+238], N[Not[LessEqual[z, 3.4e+293]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / (-N[(t / z), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.30000000000000003e238 or 3.4000000000000003e293 < z

   1. Initial program 91.0%

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

   2. Taylor expanded in y around inf 71.0%

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

      1. associate-*r/ 38.7%

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

   4. Simplified 76.2%

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

   if 2.30000000000000003e238 < z < 3.4000000000000003e293

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 91.4%

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

   3. Taylor expanded in y around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-frac-neg 65.1%

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

   5. Simplified 65.1%

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

      1. associate-*l/ 66.1%

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

      2. associate-/l* 72.0%

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

      3. add-sqr-sqrt 30.6%

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

      4. sqrt-unprod 31.2%

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

      5. sqr-neg 31.2%

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

      6. sqrt-unprod 0.3%

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

      7. add-sqr-sqrt 0.7%

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

      8. frac-2neg 0.7%

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

      9. add-sqr-sqrt 0.4%

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

      10. sqrt-unprod 35.1%

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

      11. sqr-neg 35.1%

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

      12. sqrt-unprod 41.1%

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

      13. add-sqr-sqrt 72.0%

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

      14. distribute-neg-frac 72.0%

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

   7. Applied egg-rr 72.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.3 \cdot 10^{+238} \lor \neg \left(z \leq 3.4 \cdot 10^{+293}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-\frac{t}{z}}\\ \end{array} \]

Alternative 7: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-26} \lor \neg \left(x \leq 9.5 \cdot 10^{+59}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.2e-26) (not (<= x 9.5e+59)))
   (- x (* x (/ z t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.2e-26) || !(x <= 9.5e+59)) {
		tmp = x - (x * (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-26)) .or. (.not. (x <= 9.5d+59))) then
        tmp = x - (x * (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-26) || !(x <= 9.5e+59)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.2e-26) or not (x <= 9.5e+59):
		tmp = x - (x * (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.2e-26) || !(x <= 9.5e+59))
		tmp = Float64(x - Float64(x * 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-26) || ~((x <= 9.5e+59)))
		tmp = x - (x * (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-26], N[Not[LessEqual[x, 9.5e+59]], $MachinePrecision]], N[(x - N[(x * 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 < -3.2000000000000001e-26 or 9.50000000000000023e59 < x

   1. Initial program 88.4%

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

   2. Taylor expanded in x around inf 91.7%

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

      1. *-commutative 91.7%

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

      2. distribute-rgt-in 91.6%

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

      3. *-lft-identity 91.6%

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

      4. mul-1-neg 91.6%

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

      5. cancel-sign-sub-inv 91.6%

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

      6. *-commutative 91.6%

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

   4. Simplified 91.6%

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

   if -3.2000000000000001e-26 < x < 9.50000000000000023e59

   1. Initial program 93.9%

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

   2. Taylor expanded in y around inf 79.2%

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

      1. associate-*r/ 57.7%

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

   4. Simplified 83.6%

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

      1. clear-num 57.7%

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

      2. un-div-inv 58.1%

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

   6. Applied egg-rr 84.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-26} \lor \neg \left(x \leq 9.5 \cdot 10^{+59}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 8: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-27} \lor \neg \left(x \leq 1.2 \cdot 10^{+66}\right):\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-27) (not (<= x 1.2e+66)))
   (- x (/ x (/ t z)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-27) || !(x <= 1.2e+66)) {
		tmp = x - (x / (t / z));
	} 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 <= (-3.1d-27)) .or. (.not. (x <= 1.2d+66))) then
        tmp = x - (x / (t / z))
    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 <= -3.1e-27) || !(x <= 1.2e+66)) {
		tmp = x - (x / (t / z));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e-27) or not (x <= 1.2e+66):
		tmp = x - (x / (t / z))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-27) || !(x <= 1.2e+66))
		tmp = Float64(x - Float64(x / Float64(t / z)));
	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 <= -3.1e-27) || ~((x <= 1.2e+66)))
		tmp = x - (x / (t / z));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-27], N[Not[LessEqual[x, 1.2e+66]], $MachinePrecision]], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999998e-27 or 1.2000000000000001e66 < x

   1. Initial program 88.4%

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

   2. Taylor expanded in x around inf 91.7%

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

      1. *-commutative 91.7%

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

      2. distribute-rgt-in 91.6%

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

      3. *-lft-identity 91.6%

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

      4. mul-1-neg 91.6%

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

      5. cancel-sign-sub-inv 91.6%

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

      6. *-commutative 91.6%

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

   4. Simplified 91.6%

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

      1. clear-num 91.6%

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

      2. un-div-inv 91.7%

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

   6. Applied egg-rr 91.7%

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

   if -3.0999999999999998e-27 < x < 1.2000000000000001e66

   1. Initial program 93.9%

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

   2. Taylor expanded in y around inf 79.2%

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

      1. associate-*r/ 57.7%

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

   4. Simplified 83.6%

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

      1. clear-num 57.7%

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

      2. un-div-inv 58.1%

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

   6. Applied egg-rr 84.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-27} \lor \neg \left(x \leq 1.2 \cdot 10^{+66}\right):\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-131} \lor \neg \left(z \leq 5.5 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.4e-131) (not (<= z 5.5e-13))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4e-131) || !(z <= 5.5e-13)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.4d-131)) .or. (.not. (z <= 5.5d-13))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4e-131) || !(z <= 5.5e-13)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.4e-131) or not (z <= 5.5e-13):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.4e-131) || !(z <= 5.5e-13))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.4e-131) || ~((z <= 5.5e-13)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.4e-131], N[Not[LessEqual[z, 5.5e-13]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.3999999999999999e-131 or 5.49999999999999979e-13 < z

   1. Initial program 86.6%

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

   2. Taylor expanded in t around 0 73.4%

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

   3. Taylor expanded in y around inf 40.1%

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

      1. associate-*r/ 45.2%

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

   5. Simplified 45.2%

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

   if -4.3999999999999999e-131 < z < 5.49999999999999979e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 72.6%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-131} \lor \neg \left(z \leq 5.5 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.4e-131) (* y (/ z t)) (if (<= z 1.2e-13) x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e-131) {
		tmp = y * (z / t);
	} else if (z <= 1.2e-13) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-4.4d-131)) then
        tmp = y * (z / t)
    else if (z <= 1.2d-13) then
        tmp = x
    else
        tmp = 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 (z <= -4.4e-131) {
		tmp = y * (z / t);
	} else if (z <= 1.2e-13) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.4e-131:
		tmp = y * (z / t)
	elif z <= 1.2e-13:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.4e-131)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 1.2e-13)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.4e-131)
		tmp = y * (z / t);
	elseif (z <= 1.2e-13)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.4e-131], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-13], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3999999999999999e-131

   1. Initial program 85.9%

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

   2. Taylor expanded in t around 0 69.3%

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

   3. Taylor expanded in y around inf 35.1%

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

      1. associate-*r/ 44.0%

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

   5. Simplified 44.0%

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

   if -4.3999999999999999e-131 < z < 1.1999999999999999e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 72.6%

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

   if 1.1999999999999999e-13 < z

   1. Initial program 87.3%

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

   2. Taylor expanded in t around 0 77.2%

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

   3. Taylor expanded in y around inf 44.6%

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

      1. associate-*r/ 46.3%

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

   5. Simplified 46.3%

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

      1. clear-num 46.3%

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

      2. un-div-inv 46.9%

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

   7. Applied egg-rr 46.9%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 11: 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 91.1%

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

2. Taylor expanded in z around 0 36.6%

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

3. Final simplification 36.6%

   \[\leadsto x \]

Developer target: 97.8% 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 2023196 
(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)))