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

Percentage Accurate: 97.4% → 97.5%

Time: 7.0s

Alternatives: 11

Speedup: 1.0×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 97.4% 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: 97.5% 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 98.6%

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

3. Taylor expanded in y around 0 86.3%

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

   1. +-commutative 86.3%

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

   2. mul-1-neg 86.3%

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

   3. sub-neg 86.3%

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

   4. associate-/l* 85.6%

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

   5. associate-/l* 91.1%

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

   6. div-sub 98.6%

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

5. Simplified 98.6%

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

6. Final simplification 98.6%

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

Alternative 2: 64.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t} \cdot \left(-z\right)\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+183}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x t) (- z))) (t_2 (* y (/ z t))))
   (if (<= (/ z t) -1e+278)
     t_1
     (if (<= (/ z t) -1e+183)
       (/ (* y z) t)
       (if (<= (/ z t) -1e+104)
         t_1
         (if (<= (/ z t) -1e-22)
           t_2
           (if (<= (/ z t) 4e-9) x (if (<= (/ z t) 2e+55) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) * -z;
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+278) {
		tmp = t_1;
	} else if ((z / t) <= -1e+183) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -1e+104) {
		tmp = t_1;
	} else if ((z / t) <= -1e-22) {
		tmp = t_2;
	} else if ((z / t) <= 4e-9) {
		tmp = x;
	} else if ((z / t) <= 2e+55) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / t) * -z
    t_2 = y * (z / t)
    if ((z / t) <= (-1d+278)) then
        tmp = t_1
    else if ((z / t) <= (-1d+183)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-1d+104)) then
        tmp = t_1
    else if ((z / t) <= (-1d-22)) then
        tmp = t_2
    else if ((z / t) <= 4d-9) then
        tmp = x
    else if ((z / t) <= 2d+55) then
        tmp = t_2
    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 / t) * -z;
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+278) {
		tmp = t_1;
	} else if ((z / t) <= -1e+183) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -1e+104) {
		tmp = t_1;
	} else if ((z / t) <= -1e-22) {
		tmp = t_2;
	} else if ((z / t) <= 4e-9) {
		tmp = x;
	} else if ((z / t) <= 2e+55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) * -z
	t_2 = y * (z / t)
	tmp = 0
	if (z / t) <= -1e+278:
		tmp = t_1
	elif (z / t) <= -1e+183:
		tmp = (y * z) / t
	elif (z / t) <= -1e+104:
		tmp = t_1
	elif (z / t) <= -1e-22:
		tmp = t_2
	elif (z / t) <= 4e-9:
		tmp = x
	elif (z / t) <= 2e+55:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) * Float64(-z))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e+278)
		tmp = t_1;
	elseif (Float64(z / t) <= -1e+183)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -1e+104)
		tmp = t_1;
	elseif (Float64(z / t) <= -1e-22)
		tmp = t_2;
	elseif (Float64(z / t) <= 4e-9)
		tmp = x;
	elseif (Float64(z / t) <= 2e+55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) * -z;
	t_2 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1e+278)
		tmp = t_1;
	elseif ((z / t) <= -1e+183)
		tmp = (y * z) / t;
	elseif ((z / t) <= -1e+104)
		tmp = t_1;
	elseif ((z / t) <= -1e-22)
		tmp = t_2;
	elseif ((z / t) <= 4e-9)
		tmp = x;
	elseif ((z / t) <= 2e+55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+278], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -1e+183], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -1e+104], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -1e-22], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 4e-9], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+55], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -9.99999999999999964e277 or -9.99999999999999947e182 < (/.f64 z t) < -1e104 or 2.00000000000000002e55 < (/.f64 z t)

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 92.2%

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

   4. Taylor expanded in y around 0 75.3%

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

      1. neg-mul-1 75.3%

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

      2. distribute-neg-frac 75.3%

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

   6. Simplified 75.3%

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

   if -9.99999999999999964e277 < (/.f64 z t) < -9.99999999999999947e182

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around inf 77.4%

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

      1. associate-*r/ 77.6%

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

   6. Applied egg-rr 77.6%

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

   if -1e104 < (/.f64 z t) < -1e-22 or 4.00000000000000025e-9 < (/.f64 z t) < 2.00000000000000002e55

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 68.6%

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

   4. Taylor expanded in y around inf 53.7%

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

   5. Taylor expanded in z around 0 56.6%

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

      1. associate-*r/ 68.3%

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

   7. Simplified 68.3%

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

   if -1e-22 < (/.f64 z t) < 4.00000000000000025e-9

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 81.6%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+183}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t} \cdot \left(-z\right)\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+183}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+104}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x t) (- z))) (t_2 (* y (/ z t))))
   (if (<= (/ z t) -1e+278)
     t_1
     (if (<= (/ z t) -1e+183)
       (/ (* y z) t)
       (if (<= (/ z t) -1e+104)
         (/ (* x (- z)) t)
         (if (<= (/ z t) -1e-22)
           t_2
           (if (<= (/ z t) 4e-9) x (if (<= (/ z t) 2e+55) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) * -z;
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+278) {
		tmp = t_1;
	} else if ((z / t) <= -1e+183) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -1e+104) {
		tmp = (x * -z) / t;
	} else if ((z / t) <= -1e-22) {
		tmp = t_2;
	} else if ((z / t) <= 4e-9) {
		tmp = x;
	} else if ((z / t) <= 2e+55) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / t) * -z
    t_2 = y * (z / t)
    if ((z / t) <= (-1d+278)) then
        tmp = t_1
    else if ((z / t) <= (-1d+183)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-1d+104)) then
        tmp = (x * -z) / t
    else if ((z / t) <= (-1d-22)) then
        tmp = t_2
    else if ((z / t) <= 4d-9) then
        tmp = x
    else if ((z / t) <= 2d+55) then
        tmp = t_2
    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 / t) * -z;
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -1e+278) {
		tmp = t_1;
	} else if ((z / t) <= -1e+183) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -1e+104) {
		tmp = (x * -z) / t;
	} else if ((z / t) <= -1e-22) {
		tmp = t_2;
	} else if ((z / t) <= 4e-9) {
		tmp = x;
	} else if ((z / t) <= 2e+55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) * -z
	t_2 = y * (z / t)
	tmp = 0
	if (z / t) <= -1e+278:
		tmp = t_1
	elif (z / t) <= -1e+183:
		tmp = (y * z) / t
	elif (z / t) <= -1e+104:
		tmp = (x * -z) / t
	elif (z / t) <= -1e-22:
		tmp = t_2
	elif (z / t) <= 4e-9:
		tmp = x
	elif (z / t) <= 2e+55:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) * Float64(-z))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1e+278)
		tmp = t_1;
	elseif (Float64(z / t) <= -1e+183)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -1e+104)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (Float64(z / t) <= -1e-22)
		tmp = t_2;
	elseif (Float64(z / t) <= 4e-9)
		tmp = x;
	elseif (Float64(z / t) <= 2e+55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) * -z;
	t_2 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1e+278)
		tmp = t_1;
	elseif ((z / t) <= -1e+183)
		tmp = (y * z) / t;
	elseif ((z / t) <= -1e+104)
		tmp = (x * -z) / t;
	elseif ((z / t) <= -1e-22)
		tmp = t_2;
	elseif ((z / t) <= 4e-9)
		tmp = x;
	elseif ((z / t) <= 2e+55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+278], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -1e+183], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -1e+104], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -1e-22], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 4e-9], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+55], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -9.99999999999999964e277 or 2.00000000000000002e55 < (/.f64 z t)

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 92.7%

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

   4. Taylor expanded in y around 0 75.2%

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

      1. neg-mul-1 75.2%

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

      2. distribute-neg-frac 75.2%

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

   6. Simplified 75.2%

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

   if -9.99999999999999964e277 < (/.f64 z t) < -9.99999999999999947e182

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around inf 77.4%

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

      1. associate-*r/ 77.6%

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

   6. Applied egg-rr 77.6%

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

   if -9.99999999999999947e182 < (/.f64 z t) < -1e104

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 87.9%

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

      1. sub-div 87.9%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. distribute-lft-neg-out 88.1%

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

      3. *-commutative 88.1%

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

   8. Simplified 88.1%

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

   if -1e104 < (/.f64 z t) < -1e-22 or 4.00000000000000025e-9 < (/.f64 z t) < 2.00000000000000002e55

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 68.6%

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

   4. Taylor expanded in y around inf 53.7%

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

   5. Taylor expanded in z around 0 56.6%

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

      1. associate-*r/ 68.3%

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

   7. Simplified 68.3%

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

   if -1e-22 < (/.f64 z t) < 4.00000000000000025e-9

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 81.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+183}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+104}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+69} \lor \neg \left(\frac{z}{t} \leq 40000000\right):\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e+69) (not (<= (/ z t) 40000000.0)))
   (/ (* (- y x) z) t)
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+69) || !((z / t) <= 40000000.0)) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1d+69)) .or. (.not. ((z / t) <= 40000000.0d0))) then
        tmp = ((y - x) * z) / t
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+69) || !((z / t) <= 40000000.0)) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1e+69) or not ((z / t) <= 40000000.0):
		tmp = ((y - x) * z) / t
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e+69) || !(Float64(z / t) <= 40000000.0))
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1e+69) || ~(((z / t) <= 40000000.0)))
		tmp = ((y - x) * z) / t;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e+69], N[Not[LessEqual[N[(z / t), $MachinePrecision], 40000000.0]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1.0000000000000001e69 or 4e7 < (/.f64 z t)

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 89.5%

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

      1. sub-div 92.5%

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

      2. associate-*r/ 94.3%

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

      3. *-commutative 94.3%

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

   5. Applied egg-rr 94.3%

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

   if -1.0000000000000001e69 < (/.f64 z t) < 4e7

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 92.1%

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

      1. associate-*r/ 96.6%

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

   5. Simplified 96.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+69} \lor \neg \left(\frac{z}{t} \leq 40000000\right):\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+46} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -4e+46) (not (<= (/ z t) 4e-9)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e+46) || !((z / t) <= 4e-9)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-4d+46)) .or. (.not. ((z / t) <= 4d-9))) then
        tmp = (y - x) / (t / z)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e+46) || !((z / t) <= 4e-9)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -4e+46) or not ((z / t) <= 4e-9):
		tmp = (y - x) / (t / z)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -4e+46) || !(Float64(z / t) <= 4e-9))
		tmp = Float64(Float64(y - x) / Float64(t / z));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -4e+46) || ~(((z / t) <= 4e-9)))
		tmp = (y - x) / (t / z);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -4e+46], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e-9]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4e46 or 4.00000000000000025e-9 < (/.f64 z t)

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. sub-div 92.4%

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

      3. associate-/r/ 97.5%

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

   5. Applied egg-rr 97.5%

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

   if -4e46 < (/.f64 z t) < 4.00000000000000025e-9

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 93.7%

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

      1. associate-*r/ 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+46} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-22} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e-22) (not (<= (/ z t) 4e-9))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e-22) || !((z / t) <= 4e-9)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1d-22)) .or. (.not. ((z / t) <= 4d-9))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e-22) || !((z / t) <= 4e-9)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1e-22) or not ((z / t) <= 4e-9):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e-22) || !(Float64(z / t) <= 4e-9))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1e-22) || ~(((z / t) <= 4e-9)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e-22], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e-9]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e-22 or 4.00000000000000025e-9 < (/.f64 z t)

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 86.5%

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

   4. Taylor expanded in y around inf 41.5%

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

   5. Taylor expanded in z around 0 41.5%

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

      1. associate-*r/ 49.4%

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

   7. Simplified 49.4%

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

   if -1e-22 < (/.f64 z t) < 4.00000000000000025e-9

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 81.6%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-22} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1e-22) (/ y (/ t z)) (if (<= (/ z t) 4e-9) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e-22) {
		tmp = y / (t / z);
	} else if ((z / t) <= 4e-9) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-1d-22)) then
        tmp = y / (t / z)
    else if ((z / t) <= 4d-9) then
        tmp = x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e-22) {
		tmp = y / (t / z);
	} else if ((z / t) <= 4e-9) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1e-22:
		tmp = y / (t / z)
	elif (z / t) <= 4e-9:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1e-22)
		tmp = Float64(y / Float64(t / z));
	elseif (Float64(z / t) <= 4e-9)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1e-22)
		tmp = y / (t / z);
	elseif ((z / t) <= 4e-9)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1e-22], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-9], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e-22

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 84.5%

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

   4. Taylor expanded in y around inf 45.2%

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

      1. associate-*r/ 46.7%

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

      2. *-commutative 46.7%

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

      3. associate-/l* 54.3%

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

   6. Applied egg-rr 54.3%

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

   if -1e-22 < (/.f64 z t) < 4.00000000000000025e-9

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 81.6%

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

   if 4.00000000000000025e-9 < (/.f64 z t)

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 88.7%

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

   4. Taylor expanded in y around inf 37.4%

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

   5. Taylor expanded in z around 0 35.6%

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

      1. associate-*r/ 44.0%

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

   7. Simplified 44.0%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+61} \lor \neg \left(x \leq 3.15 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e+61) (not (<= x 3.15e+41)))
   (* x (- 1.0 (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e+61) || !(x <= 3.15e+41)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-9d+61)) .or. (.not. (x <= 3.15d+41))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9e+61) || !(x <= 3.15e+41)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9e+61) or not (x <= 3.15e+41):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9e+61) || !(x <= 3.15e+41))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9e+61) || ~((x <= 3.15e+41)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9e+61], N[Not[LessEqual[x, 3.15e+41]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9e61 or 3.1499999999999999e41 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

   5. Simplified 96.4%

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

   if -9e61 < x < 3.1499999999999999e41

   1. Initial program 97.4%

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

   3. Taylor expanded in y around inf 82.7%

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

      1. associate-*r/ 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+61} \lor \neg \left(x \leq 3.15 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e+179)
   (* y (/ z t))
   (if (<= y 1.8e+178) (* x (- 1.0 (/ z t))) (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+179) {
		tmp = y * (z / t);
	} else if (y <= 1.8e+178) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.6d+179)) then
        tmp = y * (z / t)
    else if (y <= 1.8d+178) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+179) {
		tmp = y * (z / t);
	} else if (y <= 1.8e+178) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e+179:
		tmp = y * (z / t)
	elif y <= 1.8e+178:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e+179)
		tmp = Float64(y * Float64(z / t));
	elseif (y <= 1.8e+178)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e+179)
		tmp = y * (z / t);
	elseif (y <= 1.8e+178)
		tmp = x * (1.0 - (z / t));
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e+179], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+178], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999988e179

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 55.2%

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

   4. Taylor expanded in y around inf 55.7%

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

   5. Taylor expanded in z around 0 55.7%

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

      1. associate-*r/ 66.3%

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

   7. Simplified 66.3%

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

   if -4.59999999999999988e179 < y < 1.7999999999999999e178

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   5. Simplified 81.3%

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

   if 1.7999999999999999e178 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 56.6%

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

   4. Taylor expanded in y around inf 56.8%

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

      1. associate-*r/ 66.2%

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

      2. *-commutative 66.2%

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

      3. associate-/l* 75.8%

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

   6. Applied egg-rr 75.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.4% 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 98.6%

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

3. Final simplification 98.6%

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

Alternative 11: 37.9% 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 98.6%

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

3. Taylor expanded in z around 0 45.8%

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

4. Final simplification 45.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 97.3% 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 2024021 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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