Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.4% → 97.5%

Time: 9.4s

Alternatives: 11

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.4% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.0%

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

   3. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

   4. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

   5. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

   8. /-lowering-/.f64 98.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

4. Applied egg-rr 98.0%

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

5. Final simplification 98.0%

   \[\leadsto x + \frac{y - x}{\frac{t}{z}} \]
6. Add Preprocessing

Alternative 2: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-39}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 1.92 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t z)))))
   (if (<= y -8e+125)
     t_1
     (if (<= y -1.75e-39)
       (* (- y x) (/ z t))
       (if (<= y 1.92e-62) (* x (- 1.0 (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (y <= -8e+125) {
		tmp = t_1;
	} else if (y <= -1.75e-39) {
		tmp = (y - x) * (z / t);
	} else if (y <= 1.92e-62) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (t / z))
    if (y <= (-8d+125)) then
        tmp = t_1
    else if (y <= (-1.75d-39)) then
        tmp = (y - x) * (z / t)
    else if (y <= 1.92d-62) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (y <= -8e+125) {
		tmp = t_1;
	} else if (y <= -1.75e-39) {
		tmp = (y - x) * (z / t);
	} else if (y <= 1.92e-62) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y / (t / z))
	tmp = 0
	if y <= -8e+125:
		tmp = t_1
	elif y <= -1.75e-39:
		tmp = (y - x) * (z / t)
	elif y <= 1.92e-62:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (y <= -8e+125)
		tmp = t_1;
	elseif (y <= -1.75e-39)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	elseif (y <= 1.92e-62)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y / (t / z));
	tmp = 0.0;
	if (y <= -8e+125)
		tmp = t_1;
	elseif (y <= -1.75e-39)
		tmp = (y - x) * (z / t);
	elseif (y <= 1.92e-62)
		tmp = x * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+125], t$95$1, If[LessEqual[y, -1.75e-39], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.92e-62], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9999999999999994e125 or 1.92e-62 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 86.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   5. Simplified 86.5%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{z}\right)\right), x\right) \]

      7. /-lowering-/.f64 92.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 92.8%

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

   if -7.9999999999999994e125 < y < -1.75e-39

   1. Initial program 86.5%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \left(y - x\right)\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y - x\right)\right), t\right) \]

      3. --lowering--.f64 72.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, x\right)\right), t\right) \]

   7. Simplified 72.5%

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

      1. clear-num N/A

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

      2. associate-/l/ N/A

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

      3. clear-num N/A

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

      4. associate-/r/ N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{\left(y - x\right)}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \left(\color{blue}{y} - x\right)\right) \]

      7. --lowering--.f64 85.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 85.8%

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

   if -1.75e-39 < y < 1.92e-62

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 85.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 85.3%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-39}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 1.92 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-39}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= y -1.2e+150)
     t_1
     (if (<= y -2.05e-39)
       (* (- y x) (/ z t))
       (if (<= y 1.52e-58) (* x (- 1.0 (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (y <= -1.2e+150) {
		tmp = t_1;
	} else if (y <= -2.05e-39) {
		tmp = (y - x) * (z / t);
	} else if (y <= 1.52e-58) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (y <= (-1.2d+150)) then
        tmp = t_1
    else if (y <= (-2.05d-39)) then
        tmp = (y - x) * (z / t)
    else if (y <= 1.52d-58) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (y <= -1.2e+150) {
		tmp = t_1;
	} else if (y <= -2.05e-39) {
		tmp = (y - x) * (z / t);
	} else if (y <= 1.52e-58) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	tmp = 0
	if y <= -1.2e+150:
		tmp = t_1
	elif y <= -2.05e-39:
		tmp = (y - x) * (z / t)
	elif y <= 1.52e-58:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (y <= -1.2e+150)
		tmp = t_1;
	elseif (y <= -2.05e-39)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	elseif (y <= 1.52e-58)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (y <= -1.2e+150)
		tmp = t_1;
	elseif (y <= -2.05e-39)
		tmp = (y - x) * (z / t);
	elseif (y <= 1.52e-58)
		tmp = x * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+150], t$95$1, If[LessEqual[y, -2.05e-39], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e-58], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.20000000000000001e150 or 1.51999999999999993e-58 < y

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 86.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   5. Simplified 86.1%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z}{t} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{y}\right)\right) \]

      4. /-lowering-/.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), y\right)\right) \]

   7. Applied egg-rr 92.5%

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

   if -1.20000000000000001e150 < y < -2.05e-39

   1. Initial program 87.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \left(y - x\right)\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y - x\right)\right), t\right) \]

      3. --lowering--.f64 75.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, x\right)\right), t\right) \]

   7. Simplified 75.2%

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

      1. clear-num N/A

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

      2. associate-/l/ N/A

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

      3. clear-num N/A

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

      4. associate-/r/ N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{\left(y - x\right)}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \left(\color{blue}{y} - x\right)\right) \]

      7. --lowering--.f64 87.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 87.2%

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

   if -2.05e-39 < y < 1.51999999999999993e-58

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 85.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 85.3%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-39}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t z)))))
   (if (<= t -1.7e-32) t_1 (if (<= t 1.3e+51) (/ (* (- y x) z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (t <= -1.7e-32) {
		tmp = t_1;
	} else if (t <= 1.3e+51) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (t / z))
    if (t <= (-1.7d-32)) then
        tmp = t_1
    else if (t <= 1.3d+51) then
        tmp = ((y - x) * z) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (t <= -1.7e-32) {
		tmp = t_1;
	} else if (t <= 1.3e+51) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y / (t / z))
	tmp = 0
	if t <= -1.7e-32:
		tmp = t_1
	elif t <= 1.3e+51:
		tmp = ((y - x) * z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (t <= -1.7e-32)
		tmp = t_1;
	elseif (t <= 1.3e+51)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y / (t / z));
	tmp = 0.0;
	if (t <= -1.7e-32)
		tmp = t_1;
	elseif (t <= 1.3e+51)
		tmp = ((y - x) * z) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-32], t$95$1, If[LessEqual[t, 1.3e+51], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.69999999999999989e-32 or 1.3000000000000001e51 < t

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   5. Simplified 81.4%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{z}\right)\right), x\right) \]

      7. /-lowering-/.f64 89.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 89.3%

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

   if -1.69999999999999989e-32 < t < 1.3000000000000001e51

   1. Initial program 98.5%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 97.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \left(y - x\right)\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y - x\right)\right), t\right) \]

      3. --lowering--.f64 86.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, x\right)\right), t\right) \]

   7. Simplified 86.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) t))))
   (if (<= z -4.3e+24) t_1 (if (<= z 7.7e-115) (* x (- 1.0 (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if (z <= -4.3e+24) {
		tmp = t_1;
	} else if (z <= 7.7e-115) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / t)
    if (z <= (-4.3d+24)) then
        tmp = t_1
    else if (z <= 7.7d-115) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if (z <= -4.3e+24) {
		tmp = t_1;
	} else if (z <= 7.7e-115) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((y - x) / t)
	tmp = 0
	if z <= -4.3e+24:
		tmp = t_1
	elif z <= 7.7e-115:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (z <= -4.3e+24)
		tmp = t_1;
	elseif (z <= 7.7e-115)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((y - x) / t);
	tmp = 0.0;
	if (z <= -4.3e+24)
		tmp = t_1;
	elseif (z <= 7.7e-115)
		tmp = x * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+24], t$95$1, If[LessEqual[z, 7.7e-115], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.29999999999999987e24 or 7.7000000000000002e-115 < z

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y - x}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 85.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), t\right)\right) \]

   5. Simplified 85.8%

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

   if -4.29999999999999987e24 < z < 7.7000000000000002e-115

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 78.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 78.3%

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

Alternative 6: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ t z))))
   (if (<= y -5.5e+67) t_1 (if (<= y 7.2e+33) (* x (- 1.0 (/ z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if (y <= -5.5e+67) {
		tmp = t_1;
	} else if (y <= 7.2e+33) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (t / z)
    if (y <= (-5.5d+67)) then
        tmp = t_1
    else if (y <= 7.2d+33) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if (y <= -5.5e+67) {
		tmp = t_1;
	} else if (y <= 7.2e+33) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t / z)
	tmp = 0
	if y <= -5.5e+67:
		tmp = t_1
	elif y <= 7.2e+33:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (y <= -5.5e+67)
		tmp = t_1;
	elseif (y <= 7.2e+33)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t / z);
	tmp = 0.0;
	if (y <= -5.5e+67)
		tmp = t_1;
	elseif (y <= 7.2e+33)
		tmp = x * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+67], t$95$1, If[LessEqual[y, 7.2e+33], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999968e67 or 7.2000000000000005e33 < y

   1. Initial program 90.8%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 99.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot y\right), t\right) \]

      3. *-lowering-*.f64 65.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), t\right) \]

   7. Simplified 65.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. /-rgt-identity N/A

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

      4. associate-/r/ N/A

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

      5. associate-/l/ N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{1}{z} \cdot t\right)}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(t \cdot \color{blue}{\frac{1}{z}}\right)\right) \]

      8. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{t}{\color{blue}{z}}\right)\right) \]

      9. /-lowering-/.f64 72.0%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 72.0%

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

   if -5.49999999999999968e67 < y < 7.2000000000000005e33

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{z}{t}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{z}{t}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]

      5. /-lowering-/.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 80.1%

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

Alternative 7: 53.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e+24) (/ y (/ t z)) (if (<= z 2e-115) x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+24) {
		tmp = y / (t / z);
	} else if (z <= 2e-115) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	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 <= (-5.8d+24)) then
        tmp = y / (t / z)
    else if (z <= 2d-115) then
        tmp = x
    else
        tmp = z / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+24) {
		tmp = y / (t / z);
	} else if (z <= 2e-115) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e+24:
		tmp = y / (t / z)
	elif z <= 2e-115:
		tmp = x
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e+24)
		tmp = Float64(y / Float64(t / z));
	elseif (z <= 2e-115)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.8e+24)
		tmp = y / (t / z);
	elseif (z <= 2e-115)
		tmp = x;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e+24], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-115], x, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.79999999999999958e24

   1. Initial program 86.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 98.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot y\right), t\right) \]

      3. *-lowering-*.f64 53.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), t\right) \]

   7. Simplified 53.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. /-rgt-identity N/A

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

      4. associate-/r/ N/A

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

      5. associate-/l/ N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{1}{z} \cdot t\right)}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(t \cdot \color{blue}{\frac{1}{z}}\right)\right) \]

      8. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{t}{\color{blue}{z}}\right)\right) \]

      9. /-lowering-/.f64 61.2%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 61.2%

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

   if -5.79999999999999958e24 < z < 2.0000000000000001e-115

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.8%

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

   if 2.0000000000000001e-115 < z

   1. Initial program 91.6%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 96.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot y\right), t\right) \]

      3. *-lowering-*.f64 48.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), t\right) \]

   7. Simplified 48.6%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{t}{y}\right)}\right) \]

      5. /-lowering-/.f64 53.7%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 53.7%

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

Alternative 8: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ t z))))
   (if (<= z -2.2e+25) t_1 (if (<= z 1.15e-114) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if (z <= -2.2e+25) {
		tmp = t_1;
	} else if (z <= 1.15e-114) {
		tmp = x;
	} 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 = y / (t / z)
    if (z <= (-2.2d+25)) then
        tmp = t_1
    else if (z <= 1.15d-114) then
        tmp = x
    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 = y / (t / z);
	double tmp;
	if (z <= -2.2e+25) {
		tmp = t_1;
	} else if (z <= 1.15e-114) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t / z)
	tmp = 0
	if z <= -2.2e+25:
		tmp = t_1
	elif z <= 1.15e-114:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (z <= -2.2e+25)
		tmp = t_1;
	elseif (z <= 1.15e-114)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t / z);
	tmp = 0.0;
	if (z <= -2.2e+25)
		tmp = t_1;
	elseif (z <= 1.15e-114)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+25], t$95$1, If[LessEqual[z, 1.15e-114], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e25 or 1.15e-114 < z

   1. Initial program 89.3%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 97.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot y\right), t\right) \]

      3. *-lowering-*.f64 50.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), t\right) \]

   7. Simplified 50.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. /-rgt-identity N/A

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

      4. associate-/r/ N/A

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

      5. associate-/l/ N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{1}{z} \cdot t\right)}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(t \cdot \color{blue}{\frac{1}{z}}\right)\right) \]

      8. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{t}{\color{blue}{z}}\right)\right) \]

      9. /-lowering-/.f64 56.2%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 56.2%

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

   if -2.2000000000000001e25 < z < 1.15e-114

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.8%

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

Alternative 9: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= z -5.8e+24) t_1 (if (<= z 7.4e-115) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (z <= -5.8e+24) {
		tmp = t_1;
	} else if (z <= 7.4e-115) {
		tmp = x;
	} 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 = y * (z / t)
    if (z <= (-5.8d+24)) then
        tmp = t_1
    else if (z <= 7.4d-115) then
        tmp = x
    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 = y * (z / t);
	double tmp;
	if (z <= -5.8e+24) {
		tmp = t_1;
	} else if (z <= 7.4e-115) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if z <= -5.8e+24:
		tmp = t_1
	elif z <= 7.4e-115:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (z <= -5.8e+24)
		tmp = t_1;
	elseif (z <= 7.4e-115)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (z <= -5.8e+24)
		tmp = t_1;
	elseif (z <= 7.4e-115)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+24], t$95$1, If[LessEqual[z, 7.4e-115], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999958e24 or 7.4e-115 < z

   1. Initial program 89.3%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot z}{t}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{z}{t}\right), x\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \frac{1}{\frac{t}{z}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{\frac{t}{z}}\right), x\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{t}{z}\right)\right), x\right) \]

      8. /-lowering-/.f64 97.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot y\right), t\right) \]

      3. *-lowering-*.f64 50.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), t\right) \]

   7. Simplified 50.4%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{y}\right) \]

      3. /-lowering-/.f64 56.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), y\right) \]

   9. Applied egg-rr 56.2%

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

   if -5.79999999999999958e24 < z < 7.4e-115

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.8%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.5% 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 93.0%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\frac{z}{t}}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z}{t} \cdot \color{blue}{\left(y - x\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \color{blue}{\left(y - x\right)}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \left(\color{blue}{y} - x\right)\right)\right) \]

   5. --lowering--.f64 98.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

4. Applied egg-rr 98.0%

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

5. Final simplification 98.0%

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

Alternative 11: 39.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.0%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 34.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 97.3% accurate, 0.5× 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 2024158 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1805102239106601/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (* (/ z t) (- x y))) (if (< x 855006432740143/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z))))))

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