Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.8% → 97.4%

Time: 9.3s

Alternatives: 11

Speedup: 1.1×

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

Specification

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]

Initial Program: 97.8% 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]

Alternative 1: 97.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4 \cdot 10^{-109}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 4e-109) (fma (/ z t) (- y x) x) (fma (/ (- y x) t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4e-109) {
		tmp = fma((z / t), (y - x), x);
	} else {
		tmp = fma(((y - x) / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4e-109)
		tmp = fma(Float64(z / t), Float64(y - x), x);
	else
		tmp = fma(Float64(Float64(y - x) / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 4e-109], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4e-109

   1. Initial program 98.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.9

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

   4. Applied rewrites 98.9%

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

   if 4e-109 < t

   1. Initial program 94.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*l/ N/A

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

      11. *-lft-identity N/A

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

      12. lower-/.f64 99.4

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

   4. Applied rewrites 99.4%

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

Alternative 2: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{if}\;\frac{z}{t} \leq -4000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 100000:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- y x))))
   (if (<= (/ z t) -4000.0)
     t_1
     (if (<= (/ z t) 100000.0) (+ x (/ (* z y) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (y - x);
	double tmp;
	if ((z / t) <= -4000.0) {
		tmp = t_1;
	} else if ((z / t) <= 100000.0) {
		tmp = x + ((z * y) / 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 / t) * (y - x)
    if ((z / t) <= (-4000.0d0)) then
        tmp = t_1
    else if ((z / t) <= 100000.0d0) then
        tmp = x + ((z * y) / 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 / t) * (y - x);
	double tmp;
	if ((z / t) <= -4000.0) {
		tmp = t_1;
	} else if ((z / t) <= 100000.0) {
		tmp = x + ((z * y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * (y - x)
	tmp = 0
	if (z / t) <= -4000.0:
		tmp = t_1
	elif (z / t) <= 100000.0:
		tmp = x + ((z * y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(y - x))
	tmp = 0.0
	if (Float64(z / t) <= -4000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 100000.0)
		tmp = Float64(x + Float64(Float64(z * y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * (y - x);
	tmp = 0.0;
	if ((z / t) <= -4000.0)
		tmp = t_1;
	elseif ((z / t) <= 100000.0)
		tmp = x + ((z * y) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -4000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 100000.0], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4e3 or 1e5 < (/.f64 z t)

   1. Initial program 98.4%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 92.0

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

   5. Applied rewrites 92.0%

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

   7. Applied rewrites 97.1%

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

   if -4e3 < (/.f64 z t) < 1e5

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 95.3

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

   5. Applied rewrites 95.3%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4000:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 100000:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-16}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- y x))))
   (if (<= (/ z t) -2e-26)
     t_1
     (if (<= (/ z t) 4e-16) (+ x (* z (/ y t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (y - x);
	double tmp;
	if ((z / t) <= -2e-26) {
		tmp = t_1;
	} else if ((z / t) <= 4e-16) {
		tmp = x + (z * (y / 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 / t) * (y - x)
    if ((z / t) <= (-2d-26)) then
        tmp = t_1
    else if ((z / t) <= 4d-16) then
        tmp = x + (z * (y / 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 / t) * (y - x);
	double tmp;
	if ((z / t) <= -2e-26) {
		tmp = t_1;
	} else if ((z / t) <= 4e-16) {
		tmp = x + (z * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * (y - x)
	tmp = 0
	if (z / t) <= -2e-26:
		tmp = t_1
	elif (z / t) <= 4e-16:
		tmp = x + (z * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(y - x))
	tmp = 0.0
	if (Float64(z / t) <= -2e-26)
		tmp = t_1;
	elseif (Float64(z / t) <= 4e-16)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * (y - x);
	tmp = 0.0;
	if ((z / t) <= -2e-26)
		tmp = t_1;
	elseif ((z / t) <= 4e-16)
		tmp = x + (z * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e-26], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 4e-16], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.0000000000000001e-26 or 3.9999999999999999e-16 < (/.f64 z t)

   1. Initial program 98.5%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 88.5

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

   5. Applied rewrites 88.5%

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

   7. Applied rewrites 95.2%

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

   if -2.0000000000000001e-26 < (/.f64 z t) < 3.9999999999999999e-16

   1. Initial program 96.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 96.8

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

   5. Applied rewrites 96.8%

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

   7. Applied rewrites 96.7%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-26}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-16}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{z \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- y x))))
   (if (<= (/ z t) -2e-26)
     t_1
     (if (<= (/ z t) 5e-83) (- x (/ (* z x) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * (y - x);
	double tmp;
	if ((z / t) <= -2e-26) {
		tmp = t_1;
	} else if ((z / t) <= 5e-83) {
		tmp = x - ((z * x) / 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 / t) * (y - x)
    if ((z / t) <= (-2d-26)) then
        tmp = t_1
    else if ((z / t) <= 5d-83) then
        tmp = x - ((z * x) / 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 / t) * (y - x);
	double tmp;
	if ((z / t) <= -2e-26) {
		tmp = t_1;
	} else if ((z / t) <= 5e-83) {
		tmp = x - ((z * x) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * (y - x)
	tmp = 0
	if (z / t) <= -2e-26:
		tmp = t_1
	elif (z / t) <= 5e-83:
		tmp = x - ((z * x) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(y - x))
	tmp = 0.0
	if (Float64(z / t) <= -2e-26)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-83)
		tmp = Float64(x - Float64(Float64(z * x) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * (y - x);
	tmp = 0.0;
	if ((z / t) <= -2e-26)
		tmp = t_1;
	elseif ((z / t) <= 5e-83)
		tmp = x - ((z * x) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e-26], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-83], N[(x - N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.0000000000000001e-26 or 5e-83 < (/.f64 z t)

   1. Initial program 98.6%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 85.9

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

   5. Applied rewrites 85.9%

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

   7. Applied rewrites 93.5%

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

   if -2.0000000000000001e-26 < (/.f64 z t) < 5e-83

   1. Initial program 95.8%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 80.2

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

   5. Applied rewrites 80.2%

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

Alternative 5: 48.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 120:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z t) (- x))))
   (if (<= x -2e+14) t_1 (if (<= x 120.0) (/ (* z y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / t) * -x;
	double tmp;
	if (x <= -2e+14) {
		tmp = t_1;
	} else if (x <= 120.0) {
		tmp = (z * y) / 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 / t) * -x
    if (x <= (-2d+14)) then
        tmp = t_1
    else if (x <= 120.0d0) then
        tmp = (z * y) / 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 / t) * -x;
	double tmp;
	if (x <= -2e+14) {
		tmp = t_1;
	} else if (x <= 120.0) {
		tmp = (z * y) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / t) * -x
	tmp = 0
	if x <= -2e+14:
		tmp = t_1
	elif x <= 120.0:
		tmp = (z * y) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / t) * Float64(-x))
	tmp = 0.0
	if (x <= -2e+14)
		tmp = t_1;
	elseif (x <= 120.0)
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / t) * -x;
	tmp = 0.0;
	if (x <= -2e+14)
		tmp = t_1;
	elseif (x <= 120.0)
		tmp = (z * y) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[x, -2e+14], t$95$1, If[LessEqual[x, 120.0], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2e14 or 120 < x

   1. Initial program 99.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 48.7

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

   5. Applied rewrites 48.7%

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

   7. Applied rewrites 53.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 39.8%

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

   if -2e14 < x < 120

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.5

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

   5. Applied rewrites 63.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 120:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(-x\right)}{t}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 120:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z (- x)) t)))
   (if (<= x -2.1e+14) t_1 (if (<= x 120.0) (/ (* z y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * -x) / t;
	double tmp;
	if (x <= -2.1e+14) {
		tmp = t_1;
	} else if (x <= 120.0) {
		tmp = (z * y) / 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 * -x) / t
    if (x <= (-2.1d+14)) then
        tmp = t_1
    else if (x <= 120.0d0) then
        tmp = (z * y) / 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 * -x) / t;
	double tmp;
	if (x <= -2.1e+14) {
		tmp = t_1;
	} else if (x <= 120.0) {
		tmp = (z * y) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * -x) / t
	tmp = 0
	if x <= -2.1e+14:
		tmp = t_1
	elif x <= 120.0:
		tmp = (z * y) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * Float64(-x)) / t)
	tmp = 0.0
	if (x <= -2.1e+14)
		tmp = t_1;
	elseif (x <= 120.0)
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * -x) / t;
	tmp = 0.0;
	if (x <= -2.1e+14)
		tmp = t_1;
	elseif (x <= 120.0)
		tmp = (z * y) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * (-x)), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[x, -2.1e+14], t$95$1, If[LessEqual[x, 120.0], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e14 or 120 < x

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot \frac{z}{t} \]
   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. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 81.6

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

   5. Applied rewrites 81.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 38.9%

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

   if -2.1e14 < x < 120

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.5

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

   5. Applied rewrites 63.5%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \mathbf{elif}\;x \leq 120:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.4e-109) (* (/ z t) (- y x)) (* z (/ (- y x) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e-109) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.4d-109) then
        tmp = (z / t) * (y - x)
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e-109) {
		tmp = (z / t) * (y - x);
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.4e-109:
		tmp = (z / t) * (y - x)
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.4e-109)
		tmp = Float64(Float64(z / t) * Float64(y - x));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.4e-109)
		tmp = (z / t) * (y - x);
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.4e-109], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.39999999999999989e-109

   1. Initial program 98.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.3

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

   5. Applied rewrites 57.3%

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

   7. Applied rewrites 64.4%

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

   if 1.39999999999999989e-109 < t

   1. Initial program 94.1%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 56.8

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

   5. Applied rewrites 56.8%

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

Alternative 8: 40.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.9 \cdot 10^{-138}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.9e-138) (* (/ z t) y) (* z (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.9e-138) {
		tmp = (z / t) * y;
	} else {
		tmp = z * (y / 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 (t <= 1.9d-138) then
        tmp = (z / t) * y
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.9e-138) {
		tmp = (z / t) * y;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.9e-138:
		tmp = (z / t) * y
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.9e-138)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.9e-138)
		tmp = (z / t) * y;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.9e-138], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.9000000000000001e-138

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.5

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

   5. Applied rewrites 41.5%

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

   7. Applied rewrites 44.9%

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

   if 1.9000000000000001e-138 < t

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 38.6

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

   5. Applied rewrites 38.6%

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

   7. Applied rewrites 39.2%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.9 \cdot 10^{-138}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 97.4

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

4. Applied rewrites 97.4%

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

Alternative 10: 58.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lower--.f64 57.1

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

5. Applied rewrites 57.1%

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

Alternative 11: 37.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ z \cdot \frac{y}{t} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return z * (y / 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 = z * (y / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

3. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 40.5

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

5. Applied rewrites 40.5%

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

7. Applied rewrites 38.1%

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

8. Final simplification 38.1%

   \[\leadsto z \cdot \frac{y}{t} \]
9. Add Preprocessing

Developer Target 1: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t\_1 < -1013646692435.8867:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024221 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* (- y x) (/ z t)) -10136466924358867/10000) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z))))))

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