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

Percentage Accurate: 97.5% → 97.5%

Time: 12.4s

Alternatives: 11

Speedup: 1.0×

• 24.8% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 2: 65.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{-t}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- t)))) (t_2 (* y (/ z t))))
   (if (<= (/ z t) -5e+213)
     t_1
     (if (<= (/ z t) -5e+89)
       (/ (* y z) t)
       (if (<= (/ z t) -2e+44)
         t_1
         (if (<= (/ z t) -5e-30)
           t_2
           (if (<= (/ z t) 1e-18) x (if (<= (/ z t) 2e+82) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+213) {
		tmp = t_1;
	} else if ((z / t) <= -5e+89) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -2e+44) {
		tmp = t_1;
	} else if ((z / t) <= -5e-30) {
		tmp = t_2;
	} else if ((z / t) <= 1e-18) {
		tmp = x;
	} else if ((z / t) <= 2e+82) {
		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 * (z / -t)
    t_2 = y * (z / t)
    if ((z / t) <= (-5d+213)) then
        tmp = t_1
    else if ((z / t) <= (-5d+89)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-2d+44)) then
        tmp = t_1
    else if ((z / t) <= (-5d-30)) then
        tmp = t_2
    else if ((z / t) <= 1d-18) then
        tmp = x
    else if ((z / t) <= 2d+82) 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 * (z / -t);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+213) {
		tmp = t_1;
	} else if ((z / t) <= -5e+89) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -2e+44) {
		tmp = t_1;
	} else if ((z / t) <= -5e-30) {
		tmp = t_2;
	} else if ((z / t) <= 1e-18) {
		tmp = x;
	} else if ((z / t) <= 2e+82) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / -t)
	t_2 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e+213:
		tmp = t_1
	elif (z / t) <= -5e+89:
		tmp = (y * z) / t
	elif (z / t) <= -2e+44:
		tmp = t_1
	elif (z / t) <= -5e-30:
		tmp = t_2
	elif (z / t) <= 1e-18:
		tmp = x
	elif (z / t) <= 2e+82:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(-t)))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+213)
		tmp = t_1;
	elseif (Float64(z / t) <= -5e+89)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -2e+44)
		tmp = t_1;
	elseif (Float64(z / t) <= -5e-30)
		tmp = t_2;
	elseif (Float64(z / t) <= 1e-18)
		tmp = x;
	elseif (Float64(z / t) <= 2e+82)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / -t);
	t_2 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e+213)
		tmp = t_1;
	elseif ((z / t) <= -5e+89)
		tmp = (y * z) / t;
	elseif ((z / t) <= -2e+44)
		tmp = t_1;
	elseif ((z / t) <= -5e-30)
		tmp = t_2;
	elseif ((z / t) <= 1e-18)
		tmp = x;
	elseif ((z / t) <= 2e+82)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+213], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -5e+89], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -2e+44], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -5e-30], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 1e-18], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+82], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -4.9999999999999998e213 or -4.99999999999999983e89 < (/.f64 z t) < -2.0000000000000002e44 or 1.9999999999999999e82 < (/.f64 z t)

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. fma-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. unsub-neg 69.6%

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

      3. associate-/l* 70.7%

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

      4. *-rgt-identity 70.7%

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

      5. distribute-lft-out-- 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in z around inf 70.7%

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

      1. associate-*r/ 70.7%

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

      2. neg-mul-1 70.7%

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

   10. Simplified 70.7%

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

   if -4.9999999999999998e213 < (/.f64 z t) < -4.99999999999999983e89

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 95.0%

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

   6. Taylor expanded in y around inf 65.1%

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

      1. associate-*r/ 75.0%

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

   8. Applied egg-rr 75.0%

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

   if -2.0000000000000002e44 < (/.f64 z t) < -4.99999999999999972e-30 or 1.0000000000000001e-18 < (/.f64 z t) < 1.9999999999999999e82

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 74.9%

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

   6. Taylor expanded in y around inf 49.6%

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

      1. clear-num 49.5%

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

      2. un-div-inv 51.1%

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

   8. Applied egg-rr 51.1%

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

      1. associate-/r/ 63.2%

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

   10. Applied egg-rr 63.2%

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

   if -4.99999999999999972e-30 < (/.f64 z t) < 1.0000000000000001e-18

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-define 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 74.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{-t}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- t)))) (t_2 (* y (/ z t))))
   (if (<= (/ z t) -5e+213)
     (* z (/ x (- t)))
     (if (<= (/ z t) -5e+89)
       (/ (* y z) t)
       (if (<= (/ z t) -2e+44)
         t_1
         (if (<= (/ z t) -5e-30)
           t_2
           (if (<= (/ z t) 1e-18) x (if (<= (/ z t) 2e+82) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+213) {
		tmp = z * (x / -t);
	} else if ((z / t) <= -5e+89) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -2e+44) {
		tmp = t_1;
	} else if ((z / t) <= -5e-30) {
		tmp = t_2;
	} else if ((z / t) <= 1e-18) {
		tmp = x;
	} else if ((z / t) <= 2e+82) {
		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 * (z / -t)
    t_2 = y * (z / t)
    if ((z / t) <= (-5d+213)) then
        tmp = z * (x / -t)
    else if ((z / t) <= (-5d+89)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-2d+44)) then
        tmp = t_1
    else if ((z / t) <= (-5d-30)) then
        tmp = t_2
    else if ((z / t) <= 1d-18) then
        tmp = x
    else if ((z / t) <= 2d+82) 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 * (z / -t);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+213) {
		tmp = z * (x / -t);
	} else if ((z / t) <= -5e+89) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -2e+44) {
		tmp = t_1;
	} else if ((z / t) <= -5e-30) {
		tmp = t_2;
	} else if ((z / t) <= 1e-18) {
		tmp = x;
	} else if ((z / t) <= 2e+82) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / -t)
	t_2 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e+213:
		tmp = z * (x / -t)
	elif (z / t) <= -5e+89:
		tmp = (y * z) / t
	elif (z / t) <= -2e+44:
		tmp = t_1
	elif (z / t) <= -5e-30:
		tmp = t_2
	elif (z / t) <= 1e-18:
		tmp = x
	elif (z / t) <= 2e+82:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(-t)))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+213)
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif (Float64(z / t) <= -5e+89)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -2e+44)
		tmp = t_1;
	elseif (Float64(z / t) <= -5e-30)
		tmp = t_2;
	elseif (Float64(z / t) <= 1e-18)
		tmp = x;
	elseif (Float64(z / t) <= 2e+82)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / -t);
	t_2 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e+213)
		tmp = z * (x / -t);
	elseif ((z / t) <= -5e+89)
		tmp = (y * z) / t;
	elseif ((z / t) <= -2e+44)
		tmp = t_1;
	elseif ((z / t) <= -5e-30)
		tmp = t_2;
	elseif ((z / t) <= 1e-18)
		tmp = x;
	elseif ((z / t) <= 2e+82)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+213], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e+89], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -2e+44], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -5e-30], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 1e-18], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+82], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -4.9999999999999998e213

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. fma-define 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around inf 90.8%

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

   6. Taylor expanded in y around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-frac-neg2 73.1%

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

   8. Simplified 73.1%

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

   if -4.9999999999999998e213 < (/.f64 z t) < -4.99999999999999983e89

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 95.0%

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

   6. Taylor expanded in y around inf 65.1%

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

      1. associate-*r/ 75.0%

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

   8. Applied egg-rr 75.0%

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

   if -4.99999999999999983e89 < (/.f64 z t) < -2.0000000000000002e44 or 1.9999999999999999e82 < (/.f64 z t)

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

      3. associate-/l* 72.6%

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

      4. *-rgt-identity 72.6%

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

      5. distribute-lft-out-- 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in z around inf 72.6%

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

      1. associate-*r/ 72.6%

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

      2. neg-mul-1 72.6%

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

   10. Simplified 72.6%

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

   if -2.0000000000000002e44 < (/.f64 z t) < -4.99999999999999972e-30 or 1.0000000000000001e-18 < (/.f64 z t) < 1.9999999999999999e82

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 74.9%

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

   6. Taylor expanded in y around inf 49.6%

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

      1. clear-num 49.5%

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

      2. un-div-inv 51.1%

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

   8. Applied egg-rr 51.1%

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

      1. associate-/r/ 63.2%

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

   10. Applied egg-rr 63.2%

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

   if -4.99999999999999972e-30 < (/.f64 z t) < 1.0000000000000001e-18

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-define 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 74.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{-t}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+213}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- t)))) (t_2 (* y (/ z t))))
   (if (<= (/ z t) -5e+213)
     (/ (* x z) (- t))
     (if (<= (/ z t) -5e+89)
       (/ (* y z) t)
       (if (<= (/ z t) -2e+44)
         t_1
         (if (<= (/ z t) -5e-30)
           t_2
           (if (<= (/ z t) 1e-18) x (if (<= (/ z t) 2e+82) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+213) {
		tmp = (x * z) / -t;
	} else if ((z / t) <= -5e+89) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -2e+44) {
		tmp = t_1;
	} else if ((z / t) <= -5e-30) {
		tmp = t_2;
	} else if ((z / t) <= 1e-18) {
		tmp = x;
	} else if ((z / t) <= 2e+82) {
		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 * (z / -t)
    t_2 = y * (z / t)
    if ((z / t) <= (-5d+213)) then
        tmp = (x * z) / -t
    else if ((z / t) <= (-5d+89)) then
        tmp = (y * z) / t
    else if ((z / t) <= (-2d+44)) then
        tmp = t_1
    else if ((z / t) <= (-5d-30)) then
        tmp = t_2
    else if ((z / t) <= 1d-18) then
        tmp = x
    else if ((z / t) <= 2d+82) 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 * (z / -t);
	double t_2 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e+213) {
		tmp = (x * z) / -t;
	} else if ((z / t) <= -5e+89) {
		tmp = (y * z) / t;
	} else if ((z / t) <= -2e+44) {
		tmp = t_1;
	} else if ((z / t) <= -5e-30) {
		tmp = t_2;
	} else if ((z / t) <= 1e-18) {
		tmp = x;
	} else if ((z / t) <= 2e+82) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / -t)
	t_2 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e+213:
		tmp = (x * z) / -t
	elif (z / t) <= -5e+89:
		tmp = (y * z) / t
	elif (z / t) <= -2e+44:
		tmp = t_1
	elif (z / t) <= -5e-30:
		tmp = t_2
	elif (z / t) <= 1e-18:
		tmp = x
	elif (z / t) <= 2e+82:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(-t)))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e+213)
		tmp = Float64(Float64(x * z) / Float64(-t));
	elseif (Float64(z / t) <= -5e+89)
		tmp = Float64(Float64(y * z) / t);
	elseif (Float64(z / t) <= -2e+44)
		tmp = t_1;
	elseif (Float64(z / t) <= -5e-30)
		tmp = t_2;
	elseif (Float64(z / t) <= 1e-18)
		tmp = x;
	elseif (Float64(z / t) <= 2e+82)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / -t);
	t_2 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e+213)
		tmp = (x * z) / -t;
	elseif ((z / t) <= -5e+89)
		tmp = (y * z) / t;
	elseif ((z / t) <= -2e+44)
		tmp = t_1;
	elseif ((z / t) <= -5e-30)
		tmp = t_2;
	elseif ((z / t) <= 1e-18)
		tmp = x;
	elseif ((z / t) <= 2e+82)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+213], N[(N[(x * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -5e+89], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -2e+44], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -5e-30], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 1e-18], x, If[LessEqual[N[(z / t), $MachinePrecision], 2e+82], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -4.9999999999999998e213

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. fma-define 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around inf 90.8%

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

   6. Taylor expanded in y around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-frac-neg2 73.1%

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

   8. Simplified 73.1%

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

      1. *-commutative 73.1%

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

      2. distribute-frac-neg2 73.1%

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

      3. distribute-frac-neg 73.1%

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

      4. associate-*l/ 73.2%

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

   10. Applied egg-rr 73.2%

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

   if -4.9999999999999998e213 < (/.f64 z t) < -4.99999999999999983e89

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 95.0%

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

   6. Taylor expanded in y around inf 65.1%

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

      1. associate-*r/ 75.0%

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

   8. Applied egg-rr 75.0%

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

   if -4.99999999999999983e89 < (/.f64 z t) < -2.0000000000000002e44 or 1.9999999999999999e82 < (/.f64 z t)

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

      3. associate-/l* 72.6%

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

      4. *-rgt-identity 72.6%

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

      5. distribute-lft-out-- 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in z around inf 72.6%

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

      1. associate-*r/ 72.6%

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

      2. neg-mul-1 72.6%

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

   10. Simplified 72.6%

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

   if -2.0000000000000002e44 < (/.f64 z t) < -4.99999999999999972e-30 or 1.0000000000000001e-18 < (/.f64 z t) < 1.9999999999999999e82

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 74.9%

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

   6. Taylor expanded in y around inf 49.6%

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

      1. clear-num 49.5%

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

      2. un-div-inv 51.1%

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

   8. Applied egg-rr 51.1%

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

      1. associate-/r/ 63.2%

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

   10. Applied egg-rr 63.2%

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

   if -4.99999999999999972e-30 < (/.f64 z t) < 1.0000000000000001e-18

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-define 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 74.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+213}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500000 \lor \neg \left(\frac{z}{t} \leq 10^{-18}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -500000.0) (not (<= (/ z t) 1e-18)))
   (* 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) <= -500000.0) || !((z / t) <= 1e-18)) {
		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) <= (-500000.0d0)) .or. (.not. ((z / t) <= 1d-18))) 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) <= -500000.0) || !((z / t) <= 1e-18)) {
		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) <= -500000.0) or not ((z / t) <= 1e-18):
		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) <= -500000.0) || !(Float64(z / t) <= 1e-18))
		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) <= -500000.0) || ~(((z / t) <= 1e-18)))
		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], -500000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-18]], $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) < -5e5 or 1.0000000000000001e-18 < (/.f64 z t)

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 90.9%

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

   6. Taylor expanded in t around 0 93.0%

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

   if -5e5 < (/.f64 z t) < 1.0000000000000001e-18

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. fma-define 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

      3. associate-/l* 73.7%

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

      4. *-rgt-identity 73.7%

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

      5. distribute-lft-out-- 73.7%

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

   7. Simplified 73.7%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -500000 \lor \neg \left(\frac{z}{t} \leq 10^{-18}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000 \lor \neg \left(\frac{z}{t} \leq 1000000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5000.0) (not (<= (/ z t) 1000000.0)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5000.0) || !((z / t) <= 1000000.0)) {
		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) <= (-5000.0d0)) .or. (.not. ((z / t) <= 1000000.0d0))) 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) <= -5000.0) || !((z / t) <= 1000000.0)) {
		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) <= -5000.0) or not ((z / t) <= 1000000.0):
		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) <= -5000.0) || !(Float64(z / t) <= 1000000.0))
		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) <= -5000.0) || ~(((z / t) <= 1000000.0)))
		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], -5000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1000000.0]], $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) < -5e3 or 1e6 < (/.f64 z t)

   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. Taylor expanded in z around inf 91.5%

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

   6. Taylor expanded in t around 0 93.7%

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

   if -5e3 < (/.f64 z t) < 1e6

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf 93.5%

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

      1. associate-*r/ 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5000 \lor \neg \left(\frac{z}{t} \leq 1000000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -40 \lor \neg \left(\frac{z}{t} \leq 1000000\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -40.0) (not (<= (/ z t) 1000000.0)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -40.0) || !((z / t) <= 1000000.0)) {
		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) <= (-40.0d0)) .or. (.not. ((z / t) <= 1000000.0d0))) 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) <= -40.0) || !((z / t) <= 1000000.0)) {
		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) <= -40.0) or not ((z / t) <= 1000000.0):
		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) <= -40.0) || !(Float64(z / t) <= 1000000.0))
		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) <= -40.0) || ~(((z / t) <= 1000000.0)))
		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], -40.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1000000.0]], $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) < -40 or 1e6 < (/.f64 z t)

   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. Taylor expanded in z around inf 90.9%

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

      1. sub-div 93.1%

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

      2. associate-*r/ 91.0%

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

      3. *-commutative 91.0%

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

      4. associate-/l* 97.3%

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

      5. clear-num 97.2%

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

      6. un-div-inv 97.3%

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

   7. Applied egg-rr 97.3%

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

   if -40 < (/.f64 z t) < 1e6

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf 94.2%

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

      1. associate-*r/ 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -40 \lor \neg \left(\frac{z}{t} \leq 1000000\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-30} \lor \neg \left(\frac{z}{t} \leq 10^{-18}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-30) (not (<= (/ z t) 1e-18))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-30) || !((z / t) <= 1e-18)) {
		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) <= (-5d-30)) .or. (.not. ((z / t) <= 1d-18))) 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) <= -5e-30) || !((z / t) <= 1e-18)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-30) or not ((z / t) <= 1e-18):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-30) || !(Float64(z / t) <= 1e-18))
		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) <= -5e-30) || ~(((z / t) <= 1e-18)))
		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], -5e-30], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-18]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.99999999999999972e-30 or 1.0000000000000001e-18 < (/.f64 z t)

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. fma-define 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around inf 88.5%

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

   6. Taylor expanded in y around inf 49.1%

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

      1. clear-num 49.1%

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

      2. un-div-inv 50.0%

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

   8. Applied egg-rr 50.0%

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

      1. associate-/r/ 55.4%

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

   10. Applied egg-rr 55.4%

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

   if -4.99999999999999972e-30 < (/.f64 z t) < 1.0000000000000001e-18

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-define 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 74.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-30} \lor \neg \left(\frac{z}{t} \leq 10^{-18}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+127}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e+127)
   (/ (* y z) t)
   (if (<= y 2.4e+93) (* x (- 1.0 (/ z t))) (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e+127) {
		tmp = (y * z) / t;
	} else if (y <= 2.4e+93) {
		tmp = x * (1.0 - (z / t));
	} 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 (y <= (-3.7d+127)) then
        tmp = (y * z) / t
    else if (y <= 2.4d+93) then
        tmp = x * (1.0d0 - (z / t))
    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 (y <= -3.7e+127) {
		tmp = (y * z) / t;
	} else if (y <= 2.4e+93) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e+127:
		tmp = (y * z) / t
	elif y <= 2.4e+93:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e+127)
		tmp = Float64(Float64(y * z) / t);
	elseif (y <= 2.4e+93)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.7e+127)
		tmp = (y * z) / t;
	elseif (y <= 2.4e+93)
		tmp = x * (1.0 - (z / t));
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e+127], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 2.4e+93], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6999999999999998e127

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. fma-define 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around inf 71.5%

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

   6. Taylor expanded in y around inf 69.2%

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

      1. associate-*r/ 78.2%

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

   8. Applied egg-rr 78.2%

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

   if -3.6999999999999998e127 < y < 2.4000000000000001e93

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. fma-define 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around 0 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

      3. associate-/l* 80.1%

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

      4. *-rgt-identity 80.1%

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

      5. distribute-lft-out-- 80.1%

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

   7. Simplified 80.1%

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

   if 2.4000000000000001e93 < y

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. fma-define 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around inf 60.8%

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

   6. Taylor expanded in y around inf 58.1%

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

      1. clear-num 58.0%

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

      2. un-div-inv 60.3%

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

   8. Applied egg-rr 60.3%

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

      1. associate-/r/ 65.8%

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

   10. Applied egg-rr 65.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+127}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-71} \lor \neg \left(y \leq 3.6 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.9e-71) (not (<= y 3.6e+28))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.9e-71) || !(y <= 3.6e+28)) {
		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 ((y <= (-6.9d-71)) .or. (.not. (y <= 3.6d+28))) 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 ((y <= -6.9e-71) || !(y <= 3.6e+28)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.9e-71) or not (y <= 3.6e+28):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.9e-71) || !(y <= 3.6e+28))
		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 ((y <= -6.9e-71) || ~((y <= 3.6e+28)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.9e-71], N[Not[LessEqual[y, 3.6e+28]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.9000000000000003e-71 or 3.5999999999999999e28 < y

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 66.6%

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

   6. Taylor expanded in y around inf 56.9%

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

   if -6.9000000000000003e-71 < y < 3.5999999999999999e28

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. fma-define 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around 0 45.2%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-71} \lor \neg \left(y \leq 3.6 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.4% 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 98.3%

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

   1. +-commutative 98.3%

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

   2. fma-define 98.3%

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

3. Simplified 98.3%

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

5. Taylor expanded in z around 0 33.8%

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

6. Final simplification 33.8%

   \[\leadsto x \]
7. 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 2024076 
(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))))