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

Percentage Accurate: 97.7% → 97.7%

Time: 6.8s

Alternatives: 12

Speedup: 1.0×

• 25.6% 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: 97.7% 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: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. +-commutative 98.4%

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

   2. fma-define 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 63.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z) t))))
   (if (<= (/ z t) -2e+123)
     t_1
     (if (<= (/ z t) -5e+41)
       (* y (/ z t))
       (if (<= (/ z t) -1.0)
         t_1
         (if (<= (/ z t) 2e-23)
           x
           (if (<= (/ z t) 2e+167) t_1 (* z (/ y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-z / t);
	double tmp;
	if ((z / t) <= -2e+123) {
		tmp = t_1;
	} else if ((z / t) <= -5e+41) {
		tmp = y * (z / t);
	} else if ((z / t) <= -1.0) {
		tmp = t_1;
	} else if ((z / t) <= 2e-23) {
		tmp = x;
	} else if ((z / t) <= 2e+167) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (-z / t)
    if ((z / t) <= (-2d+123)) then
        tmp = t_1
    else if ((z / t) <= (-5d+41)) then
        tmp = y * (z / t)
    else if ((z / t) <= (-1.0d0)) then
        tmp = t_1
    else if ((z / t) <= 2d-23) then
        tmp = x
    else if ((z / t) <= 2d+167) then
        tmp = t_1
    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 t_1 = x * (-z / t);
	double tmp;
	if ((z / t) <= -2e+123) {
		tmp = t_1;
	} else if ((z / t) <= -5e+41) {
		tmp = y * (z / t);
	} else if ((z / t) <= -1.0) {
		tmp = t_1;
	} else if ((z / t) <= 2e-23) {
		tmp = x;
	} else if ((z / t) <= 2e+167) {
		tmp = t_1;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-z / t)
	tmp = 0
	if (z / t) <= -2e+123:
		tmp = t_1
	elif (z / t) <= -5e+41:
		tmp = y * (z / t)
	elif (z / t) <= -1.0:
		tmp = t_1
	elif (z / t) <= 2e-23:
		tmp = x
	elif (z / t) <= 2e+167:
		tmp = t_1
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-z) / t))
	tmp = 0.0
	if (Float64(z / t) <= -2e+123)
		tmp = t_1;
	elseif (Float64(z / t) <= -5e+41)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= -1.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 2e-23)
		tmp = x;
	elseif (Float64(z / t) <= 2e+167)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-z / t);
	tmp = 0.0;
	if ((z / t) <= -2e+123)
		tmp = t_1;
	elseif ((z / t) <= -5e+41)
		tmp = y * (z / t);
	elseif ((z / t) <= -1.0)
		tmp = t_1;
	elseif ((z / t) <= 2e-23)
		tmp = x;
	elseif ((z / t) <= 2e+167)
		tmp = t_1;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+123], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -5e+41], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -1.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 2e-23], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+167], t$95$1, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -1.99999999999999996e123 or -5.00000000000000022e41 < (/.f64 z t) < -1 or 1.99999999999999992e-23 < (/.f64 z t) < 2.0000000000000001e167

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in z around inf 64.6%

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

      1. neg-mul-1 64.6%

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

      2. distribute-neg-frac2 64.6%

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

   8. Simplified 64.6%

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

   if -1.99999999999999996e123 < (/.f64 z t) < -5.00000000000000022e41

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 79.1%

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

   4. Taylor expanded in y around inf 56.3%

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

      1. clear-num 56.2%

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

      2. un-div-inv 56.3%

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

   6. Applied egg-rr 56.3%

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

   7. Taylor expanded in z around 0 47.0%

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

      1. associate-*r/ 66.8%

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

      2. *-commutative 66.8%

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

   9. Simplified 66.8%

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

   if -1 < (/.f64 z t) < 1.99999999999999992e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.2%

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

   if 2.0000000000000001e167 < (/.f64 z t)

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf 92.1%

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

   4. Taylor expanded in y around inf 64.8%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-94}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-178} \lor \neg \left(x \leq 1.58 \cdot 10^{-174}\right) \land \left(x \leq 1.95 \cdot 10^{-113} \lor \neg \left(x \leq 166\right)\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z t)))))
   (if (<= x -3.2e-45)
     t_1
     (if (<= x -5.4e-94)
       (/ (* y z) t)
       (if (or (<= x -6e-178)
               (and (not (<= x 1.58e-174))
                    (or (<= x 1.95e-113) (not (<= x 166.0)))))
         t_1
         (* y (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -3.2e-45) {
		tmp = t_1;
	} else if (x <= -5.4e-94) {
		tmp = (y * z) / t;
	} else if ((x <= -6e-178) || (!(x <= 1.58e-174) && ((x <= 1.95e-113) || !(x <= 166.0)))) {
		tmp = t_1;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / t))
    if (x <= (-3.2d-45)) then
        tmp = t_1
    else if (x <= (-5.4d-94)) then
        tmp = (y * z) / t
    else if ((x <= (-6d-178)) .or. (.not. (x <= 1.58d-174)) .and. (x <= 1.95d-113) .or. (.not. (x <= 166.0d0))) then
        tmp = t_1
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -3.2e-45) {
		tmp = t_1;
	} else if (x <= -5.4e-94) {
		tmp = (y * z) / t;
	} else if ((x <= -6e-178) || (!(x <= 1.58e-174) && ((x <= 1.95e-113) || !(x <= 166.0)))) {
		tmp = t_1;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (z / t))
	tmp = 0
	if x <= -3.2e-45:
		tmp = t_1
	elif x <= -5.4e-94:
		tmp = (y * z) / t
	elif (x <= -6e-178) or (not (x <= 1.58e-174) and ((x <= 1.95e-113) or not (x <= 166.0))):
		tmp = t_1
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (x <= -3.2e-45)
		tmp = t_1;
	elseif (x <= -5.4e-94)
		tmp = Float64(Float64(y * z) / t);
	elseif ((x <= -6e-178) || (!(x <= 1.58e-174) && ((x <= 1.95e-113) || !(x <= 166.0))))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (z / t));
	tmp = 0.0;
	if (x <= -3.2e-45)
		tmp = t_1;
	elseif (x <= -5.4e-94)
		tmp = (y * z) / t;
	elseif ((x <= -6e-178) || (~((x <= 1.58e-174)) && ((x <= 1.95e-113) || ~((x <= 166.0)))))
		tmp = t_1;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e-45], t$95$1, If[LessEqual[x, -5.4e-94], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[x, -6e-178], And[N[Not[LessEqual[x, 1.58e-174]], $MachinePrecision], Or[LessEqual[x, 1.95e-113], N[Not[LessEqual[x, 166.0]], $MachinePrecision]]]], t$95$1, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.20000000000000007e-45 or -5.4000000000000002e-94 < x < -5.9999999999999997e-178 or 1.58000000000000011e-174 < x < 1.9499999999999999e-113 or 166 < 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 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

   5. Simplified 87.0%

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

   if -3.20000000000000007e-45 < x < -5.4000000000000002e-94

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. sub-div 75.7%

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

      3. associate-/r/ 87.6%

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

   5. Applied egg-rr 87.6%

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

   6. Taylor expanded in y around inf 76.9%

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

   if -5.9999999999999997e-178 < x < 1.58000000000000011e-174 or 1.9499999999999999e-113 < x < 166

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 76.1%

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

   4. Taylor expanded in y around inf 67.8%

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

      1. clear-num 67.6%

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

      2. un-div-inv 68.4%

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

   6. Applied egg-rr 68.4%

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

   7. Taylor expanded in z around 0 65.5%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

   9. Simplified 72.4%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-94}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-178} \lor \neg \left(x \leq 1.58 \cdot 10^{-174}\right) \land \left(x \leq 1.95 \cdot 10^{-113} \lor \neg \left(x \leq 166\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-174} \lor \neg \left(x \leq 1.95 \cdot 10^{-110}\right) \land x \leq 770:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z t)))))
   (if (<= x -4e-44)
     t_1
     (if (<= x -7.6e-94)
       (/ (* y z) t)
       (if (<= x -3.1e-178)
         (* x (/ (- t z) t))
         (if (or (<= x 1.6e-174) (and (not (<= x 1.95e-110)) (<= x 770.0)))
           (* y (/ z t))
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -4e-44) {
		tmp = t_1;
	} else if (x <= -7.6e-94) {
		tmp = (y * z) / t;
	} else if (x <= -3.1e-178) {
		tmp = x * ((t - z) / t);
	} else if ((x <= 1.6e-174) || (!(x <= 1.95e-110) && (x <= 770.0))) {
		tmp = y * (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 * (1.0d0 - (z / t))
    if (x <= (-4d-44)) then
        tmp = t_1
    else if (x <= (-7.6d-94)) then
        tmp = (y * z) / t
    else if (x <= (-3.1d-178)) then
        tmp = x * ((t - z) / t)
    else if ((x <= 1.6d-174) .or. (.not. (x <= 1.95d-110)) .and. (x <= 770.0d0)) then
        tmp = y * (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 * (1.0 - (z / t));
	double tmp;
	if (x <= -4e-44) {
		tmp = t_1;
	} else if (x <= -7.6e-94) {
		tmp = (y * z) / t;
	} else if (x <= -3.1e-178) {
		tmp = x * ((t - z) / t);
	} else if ((x <= 1.6e-174) || (!(x <= 1.95e-110) && (x <= 770.0))) {
		tmp = y * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (z / t))
	tmp = 0
	if x <= -4e-44:
		tmp = t_1
	elif x <= -7.6e-94:
		tmp = (y * z) / t
	elif x <= -3.1e-178:
		tmp = x * ((t - z) / t)
	elif (x <= 1.6e-174) or (not (x <= 1.95e-110) and (x <= 770.0)):
		tmp = y * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (x <= -4e-44)
		tmp = t_1;
	elseif (x <= -7.6e-94)
		tmp = Float64(Float64(y * z) / t);
	elseif (x <= -3.1e-178)
		tmp = Float64(x * Float64(Float64(t - z) / t));
	elseif ((x <= 1.6e-174) || (!(x <= 1.95e-110) && (x <= 770.0)))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (z / t));
	tmp = 0.0;
	if (x <= -4e-44)
		tmp = t_1;
	elseif (x <= -7.6e-94)
		tmp = (y * z) / t;
	elseif (x <= -3.1e-178)
		tmp = x * ((t - z) / t);
	elseif ((x <= 1.6e-174) || (~((x <= 1.95e-110)) && (x <= 770.0)))
		tmp = y * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e-44], t$95$1, If[LessEqual[x, -7.6e-94], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, -3.1e-178], N[(x * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.6e-174], And[N[Not[LessEqual[x, 1.95e-110]], $MachinePrecision], LessEqual[x, 770.0]]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.99999999999999981e-44 or 1.6e-174 < x < 1.95e-110 or 770 < 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 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

   5. Simplified 87.7%

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

   if -3.99999999999999981e-44 < x < -7.59999999999999999e-94

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. sub-div 75.7%

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

      3. associate-/r/ 87.6%

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

   5. Applied egg-rr 87.6%

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

   6. Taylor expanded in y around inf 76.9%

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

   if -7.59999999999999999e-94 < x < -3.1e-178

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. unsub-neg 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in t around 0 78.9%

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

   if -3.1e-178 < x < 1.6e-174 or 1.95e-110 < x < 770

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 76.1%

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

   4. Taylor expanded in y around inf 67.8%

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

      1. clear-num 67.6%

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

      2. un-div-inv 68.4%

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

   6. Applied egg-rr 68.4%

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

   7. Taylor expanded in z around 0 65.5%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

   9. Simplified 72.4%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-174} \lor \neg \left(x \leq 1.95 \cdot 10^{-110}\right) \land x \leq 770:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 10^{+21}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e+27) (not (<= (/ z t) 1e+21)))
   (* z (/ (- y x) t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+27) || !((z / t) <= 1e+21)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (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+27)) .or. (.not. ((z / t) <= 1d+21))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x * (1.0d0 - (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+27) || !((z / t) <= 1e+21)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1e+27) or not ((z / t) <= 1e+21):
		tmp = z * ((y - x) / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e+27) || !(Float64(z / t) <= 1e+21))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1e+27) || ~(((z / t) <= 1e+21)))
		tmp = z * ((y - x) / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e+27], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e+21]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e27 or 1e21 < (/.f64 z t)

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf 92.8%

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

   4. Taylor expanded in t around 0 95.2%

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

   if -1e27 < (/.f64 z t) < 1e21

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 10^{+21}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000000 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -10000000000.0) (not (<= (/ z t) 2e-14)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000000.0) || !((z / t) <= 2e-14)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-10000000000.0d0)) .or. (.not. ((z / t) <= 2d-14))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000000.0) || !((z / t) <= 2e-14)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -10000000000.0) or not ((z / t) <= 2e-14):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -10000000000.0) || !(Float64(z / t) <= 2e-14))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -10000000000.0) || ~(((z / t) <= 2e-14)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -10000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-14]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e10 or 2e-14 < (/.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 88.7%

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

   4. Taylor expanded in t around 0 90.9%

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

   if -1e10 < (/.f64 z t) < 2e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 91.8%

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

      1. associate-*r/ 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000000 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1.0) (not (<= (/ z t) 2e-14)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1.0) || !((z / t) <= 2e-14)) {
		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) <= (-1.0d0)) .or. (.not. ((z / t) <= 2d-14))) 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) <= -1.0) || !((z / t) <= 2e-14)) {
		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) <= -1.0) or not ((z / t) <= 2e-14):
		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) <= -1.0) || !(Float64(z / t) <= 2e-14))
		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) <= -1.0) || ~(((z / t) <= 2e-14)))
		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], -1.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-14]], $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) < -1 or 2e-14 < (/.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 88.1%

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

      1. *-commutative 88.1%

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

      2. sub-div 90.3%

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

      3. associate-/r/ 95.1%

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

   5. Applied egg-rr 95.1%

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

   if -1 < (/.f64 z t) < 2e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 92.4%

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

      1. associate-*r/ 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e-10)
   (* y (/ z t))
   (if (<= (/ z t) 2e-23) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-10) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-23) {
		tmp = x;
	} 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 ((z / t) <= (-5d-10)) then
        tmp = y * (z / t)
    else if ((z / t) <= 2d-23) then
        tmp = x
    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 ((z / t) <= -5e-10) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-23) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e-10:
		tmp = y * (z / t)
	elif (z / t) <= 2e-23:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e-10)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 2e-23)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e-10)
		tmp = y * (z / t);
	elseif ((z / t) <= 2e-23)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e-10], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-23], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -5.00000000000000031e-10

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 87.7%

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

   4. Taylor expanded in y around inf 50.7%

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

      1. clear-num 50.6%

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

      2. un-div-inv 50.6%

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

   6. Applied egg-rr 50.6%

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

   7. Taylor expanded in z around 0 45.8%

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

      1. associate-*r/ 54.1%

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

      2. *-commutative 54.1%

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

   9. Simplified 54.1%

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

   if -5.00000000000000031e-10 < (/.f64 z t) < 1.99999999999999992e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.0%

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

   if 1.99999999999999992e-23 < (/.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 86.0%

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

   4. Taylor expanded in y around inf 53.2%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+60} \lor \neg \left(z \leq 3.8 \cdot 10^{-139}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e+60) (not (<= z 3.8e-139))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+60) || !(z <= 3.8e-139)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.8d+60)) .or. (.not. (z <= 3.8d-139))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+60) || !(z <= 3.8e-139)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e+60) or not (z <= 3.8e-139):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e+60) || !(z <= 3.8e-139))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.8e+60) || ~((z <= 3.8e-139)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e+60], N[Not[LessEqual[z, 3.8e-139]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999999e60 or 3.80000000000000008e-139 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 80.2%

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

   4. Taylor expanded in y around inf 53.5%

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

   if -5.79999999999999999e60 < z < 3.80000000000000008e-139

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 62.6%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+60} \lor \neg \left(z \leq 3.8 \cdot 10^{-139}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 11: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. clear-num 98.3%

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

   2. un-div-inv 98.4%

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

4. Applied egg-rr 98.4%

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

5. Final simplification 98.4%

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

Alternative 12: 38.7% 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 98.4%

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

3. Taylor expanded in z around 0 37.0%

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

4. Final simplification 37.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 97.2% 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 2024095 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (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))))