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

Percentage Accurate: 97.4% → 98.4%

Time: 6.5s

Alternatives: 9

Speedup: 0.5×

• 24.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t_1 \leq 4 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z t)))))
   (if (<= t_1 4e+306) t_1 (+ x (/ (* (- y x) z) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= 4e+306) {
		tmp = t_1;
	} else {
		tmp = x + (((y - x) * 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 + ((y - x) * (z / t))
    if (t_1 <= 4d+306) then
        tmp = t_1
    else
        tmp = x + (((y - x) * 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 + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= 4e+306) {
		tmp = t_1;
	} else {
		tmp = x + (((y - x) * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - x) * (z / t))
	tmp = 0
	if t_1 <= 4e+306:
		tmp = t_1
	else:
		tmp = x + (((y - x) * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / t)))
	tmp = 0.0
	if (t_1 <= 4e+306)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - x) * (z / t));
	tmp = 0.0;
	if (t_1 <= 4e+306)
		tmp = t_1;
	else
		tmp = x + (((y - x) * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+306], t$95$1, N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < 4.00000000000000007e306

   1. Initial program 98.1%

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

   if 4.00000000000000007e306 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 84.7%

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

      1. associate-*r/ 100.0%

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

   3. Applied egg-rr 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 2: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := \frac{x}{\frac{-t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+272}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))) (t_2 (/ x (/ (- t) z))))
   (if (<= (/ z t) -2e+224)
     t_2
     (if (<= (/ z t) 5e+22)
       t_1
       (if (<= (/ z t) 5e+215)
         t_2
         (if (<= (/ z t) 1e+272) t_1 (* x (/ (- z) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double t_2 = x / (-t / z);
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = t_2;
	} else if ((z / t) <= 5e+22) {
		tmp = t_1;
	} else if ((z / t) <= 5e+215) {
		tmp = t_2;
	} else if ((z / t) <= 1e+272) {
		tmp = t_1;
	} else {
		tmp = x * (-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) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = x / (-t / z)
    if ((z / t) <= (-2d+224)) then
        tmp = t_2
    else if ((z / t) <= 5d+22) then
        tmp = t_1
    else if ((z / t) <= 5d+215) then
        tmp = t_2
    else if ((z / t) <= 1d+272) then
        tmp = t_1
    else
        tmp = x * (-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 + (y * (z / t));
	double t_2 = x / (-t / z);
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = t_2;
	} else if ((z / t) <= 5e+22) {
		tmp = t_1;
	} else if ((z / t) <= 5e+215) {
		tmp = t_2;
	} else if ((z / t) <= 1e+272) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	t_2 = x / (-t / z)
	tmp = 0
	if (z / t) <= -2e+224:
		tmp = t_2
	elif (z / t) <= 5e+22:
		tmp = t_1
	elif (z / t) <= 5e+215:
		tmp = t_2
	elif (z / t) <= 1e+272:
		tmp = t_1
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(x / Float64(Float64(-t) / z))
	tmp = 0.0
	if (Float64(z / t) <= -2e+224)
		tmp = t_2;
	elseif (Float64(z / t) <= 5e+22)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e+215)
		tmp = t_2;
	elseif (Float64(z / t) <= 1e+272)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	t_2 = x / (-t / z);
	tmp = 0.0;
	if ((z / t) <= -2e+224)
		tmp = t_2;
	elseif ((z / t) <= 5e+22)
		tmp = t_1;
	elseif ((z / t) <= 5e+215)
		tmp = t_2;
	elseif ((z / t) <= 1e+272)
		tmp = t_1;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+224], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 5e+22], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e+215], t$95$2, If[LessEqual[N[(z / t), $MachinePrecision], 1e+272], t$95$1, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1.99999999999999994e224 or 4.9999999999999996e22 < (/.f64 z t) < 5.0000000000000001e215

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

      3. distribute-lft-out-- 74.8%

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

      4. *-rgt-identity 74.8%

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

   4. Simplified 74.8%

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

      1. clear-num 74.7%

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

      2. un-div-inv 74.8%

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

   6. Applied egg-rr 74.8%

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

   7. Taylor expanded in t around 0 70.1%

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

      1. associate-*r/ 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*l/ 70.1%

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

      4. metadata-eval 70.1%

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

      5. distribute-neg-frac 70.1%

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

      6. associate-*r* 74.8%

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

      7. distribute-neg-frac 74.8%

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

      8. metadata-eval 74.8%

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

      9. metadata-eval 74.8%

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

      10. associate-/r* 74.8%

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

      11. neg-mul-1 74.8%

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

      12. associate-/r/ 74.7%

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

      13. *-commutative 74.7%

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

      14. associate-*r/ 74.8%

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

      15. *-rgt-identity 74.8%

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

   9. Simplified 74.8%

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

   if -1.99999999999999994e224 < (/.f64 z t) < 4.9999999999999996e22 or 5.0000000000000001e215 < (/.f64 z t) < 1.0000000000000001e272

   1. Initial program 98.2%

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

   2. Taylor expanded in y around inf 83.5%

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

      1. associate-*r/ 88.5%

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

   4. Simplified 88.5%

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

   if 1.0000000000000001e272 < (/.f64 z t)

   1. Initial program 82.5%

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

   2. Taylor expanded in x around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. unsub-neg 66.4%

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

      3. distribute-lft-out-- 66.4%

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

      4. *-rgt-identity 66.4%

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

   4. Simplified 66.4%

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

      1. clear-num 66.4%

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

      2. un-div-inv 66.4%

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

   6. Applied egg-rr 66.4%

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

   7. Taylor expanded in t around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-*r/ 66.4%

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

      3. distribute-rgt-neg-out 66.4%

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

      4. distribute-neg-frac 66.4%

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

   9. Simplified 66.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+272}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{-t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+272}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t) z))))
   (if (<= (/ z t) -2e+224)
     t_1
     (if (<= (/ z t) 5e+22)
       (+ x (* y (/ z t)))
       (if (<= (/ z t) 5e+215)
         t_1
         (if (<= (/ z t) 1e+272) (+ x (* z (/ y t))) (* x (/ (- z) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (-t / z);
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = t_1;
	} else if ((z / t) <= 5e+22) {
		tmp = x + (y * (z / t));
	} else if ((z / t) <= 5e+215) {
		tmp = t_1;
	} else if ((z / t) <= 1e+272) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (-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 / (-t / z)
    if ((z / t) <= (-2d+224)) then
        tmp = t_1
    else if ((z / t) <= 5d+22) then
        tmp = x + (y * (z / t))
    else if ((z / t) <= 5d+215) then
        tmp = t_1
    else if ((z / t) <= 1d+272) then
        tmp = x + (z * (y / t))
    else
        tmp = x * (-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 / (-t / z);
	double tmp;
	if ((z / t) <= -2e+224) {
		tmp = t_1;
	} else if ((z / t) <= 5e+22) {
		tmp = x + (y * (z / t));
	} else if ((z / t) <= 5e+215) {
		tmp = t_1;
	} else if ((z / t) <= 1e+272) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (-t / z)
	tmp = 0
	if (z / t) <= -2e+224:
		tmp = t_1
	elif (z / t) <= 5e+22:
		tmp = x + (y * (z / t))
	elif (z / t) <= 5e+215:
		tmp = t_1
	elif (z / t) <= 1e+272:
		tmp = x + (z * (y / t))
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(-t) / z))
	tmp = 0.0
	if (Float64(z / t) <= -2e+224)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e+22)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (Float64(z / t) <= 5e+215)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e+272)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (-t / z);
	tmp = 0.0;
	if ((z / t) <= -2e+224)
		tmp = t_1;
	elseif ((z / t) <= 5e+22)
		tmp = x + (y * (z / t));
	elseif ((z / t) <= 5e+215)
		tmp = t_1;
	elseif ((z / t) <= 1e+272)
		tmp = x + (z * (y / t));
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+224], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e+22], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e+215], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e+272], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -1.99999999999999994e224 or 4.9999999999999996e22 < (/.f64 z t) < 5.0000000000000001e215

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

      3. distribute-lft-out-- 74.8%

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

      4. *-rgt-identity 74.8%

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

   4. Simplified 74.8%

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

      1. clear-num 74.7%

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

      2. un-div-inv 74.8%

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

   6. Applied egg-rr 74.8%

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

   7. Taylor expanded in t around 0 70.1%

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

      1. associate-*r/ 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*l/ 70.1%

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

      4. metadata-eval 70.1%

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

      5. distribute-neg-frac 70.1%

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

      6. associate-*r* 74.8%

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

      7. distribute-neg-frac 74.8%

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

      8. metadata-eval 74.8%

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

      9. metadata-eval 74.8%

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

      10. associate-/r* 74.8%

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

      11. neg-mul-1 74.8%

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

      12. associate-/r/ 74.7%

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

      13. *-commutative 74.7%

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

      14. associate-*r/ 74.8%

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

      15. *-rgt-identity 74.8%

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

   9. Simplified 74.8%

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

   if -1.99999999999999994e224 < (/.f64 z t) < 4.9999999999999996e22

   1. Initial program 98.1%

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

   2. Taylor expanded in y around inf 83.0%

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

      1. associate-*r/ 88.1%

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

   4. Simplified 88.1%

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

   if 5.0000000000000001e215 < (/.f64 z t) < 1.0000000000000001e272

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. mul-1-neg 80.0%

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

      3. sub-neg 80.0%

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

      4. associate-/l* 80.0%

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

      5. associate-/l* 80.0%

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

      6. div-sub 100.0%

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

      7. associate-/r/ 100.0%

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

      8. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if 1.0000000000000001e272 < (/.f64 z t)

   1. Initial program 82.5%

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

   2. Taylor expanded in x around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. unsub-neg 66.4%

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

      3. distribute-lft-out-- 66.4%

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

      4. *-rgt-identity 66.4%

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

   4. Simplified 66.4%

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

      1. clear-num 66.4%

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

      2. un-div-inv 66.4%

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

   6. Applied egg-rr 66.4%

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

   7. Taylor expanded in t around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-*r/ 66.4%

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

      3. distribute-rgt-neg-out 66.4%

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

      4. distribute-neg-frac 66.4%

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

   9. Simplified 66.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+272}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 4: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t_1 \leq 10^{+291}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z t)))))
   (if (<= t_1 1e+291) t_1 (+ x (* z (/ (- y x) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= 1e+291) {
		tmp = t_1;
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / t))
    if (t_1 <= 1d+291) then
        tmp = t_1
    else
        tmp = x + (z * ((y - x) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= 1e+291) {
		tmp = t_1;
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - x) * (z / t))
	tmp = 0
	if t_1 <= 1e+291:
		tmp = t_1
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / t)))
	tmp = 0.0
	if (t_1 <= 1e+291)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - x) * (z / t));
	tmp = 0.0;
	if (t_1 <= 1e+291)
		tmp = t_1;
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+291], t$95$1, N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < 9.9999999999999996e290

   1. Initial program 98.1%

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

   if 9.9999999999999996e290 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 85.1%

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

   2. Taylor expanded in y around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. sub-neg 89.6%

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

      4. associate-/l* 68.8%

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

      5. associate-/l* 62.7%

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

      6. div-sub 85.1%

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

      7. associate-/r/ 100.0%

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

      8. *-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq 10^{+291}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 5: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-72}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-95}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e-72)
   (+ x (* z (/ y t)))
   (if (<= y 1.15e-95) (- x (* x (/ z t))) (+ x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-72) {
		tmp = x + (z * (y / t));
	} else if (y <= 1.15e-95) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.3d-72)) then
        tmp = x + (z * (y / t))
    else if (y <= 1.15d-95) then
        tmp = x - (x * (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-72) {
		tmp = x + (z * (y / t));
	} else if (y <= 1.15e-95) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e-72:
		tmp = x + (z * (y / t))
	elif y <= 1.15e-95:
		tmp = x - (x * (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e-72)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (y <= 1.15e-95)
		tmp = Float64(x - Float64(x * Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e-72)
		tmp = x + (z * (y / t));
	elseif (y <= 1.15e-95)
		tmp = x - (x * (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e-72], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-95], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3e-72

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 86.5%

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

      1. +-commutative 86.5%

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

      2. mul-1-neg 86.5%

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

      3. sub-neg 86.5%

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

      4. associate-/l* 88.8%

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

      5. associate-/l* 87.3%

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

      6. div-sub 96.2%

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

      7. associate-/r/ 93.9%

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

      8. *-commutative 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in y around inf 86.9%

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

   if -3.3e-72 < y < 1.15e-95

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. distribute-lft-out-- 84.9%

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

      4. *-rgt-identity 84.9%

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

   4. Simplified 84.9%

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

   if 1.15e-95 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 77.7%

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

      1. associate-*r/ 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-72}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-95}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00047 \lor \neg \left(z \leq 6.6 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00047) (not (<= z 6.6e-81))) (* x (/ (- z) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00047) || !(z <= 6.6e-81)) {
		tmp = x * (-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 <= (-0.00047d0)) .or. (.not. (z <= 6.6d-81))) then
        tmp = x * (-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 <= -0.00047) || !(z <= 6.6e-81)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00047) or not (z <= 6.6e-81):
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00047) || !(z <= 6.6e-81))
		tmp = Float64(x * Float64(Float64(-z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00047) || ~((z <= 6.6e-81)))
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00047], N[Not[LessEqual[z, 6.6e-81]], $MachinePrecision]], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.69999999999999986e-4 or 6.59999999999999975e-81 < z

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

      3. distribute-lft-out-- 61.2%

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

      4. *-rgt-identity 61.2%

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

   4. Simplified 61.2%

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

      1. clear-num 61.2%

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

      2. un-div-inv 61.2%

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

   6. Applied egg-rr 61.2%

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

   7. Taylor expanded in t around 0 45.6%

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

      1. mul-1-neg 45.6%

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

      2. associate-*r/ 49.5%

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

      3. distribute-rgt-neg-out 49.5%

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

      4. distribute-neg-frac 49.5%

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

   9. Simplified 49.5%

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

   if -4.69999999999999986e-4 < z < 6.59999999999999975e-81

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 66.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00047 \lor \neg \left(z \leq 6.6 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00041:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.00041)
   (* x (/ (- z) t))
   (if (<= z 6.5e-81) x (/ x (/ (- t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00041) {
		tmp = x * (-z / t);
	} else if (z <= 6.5e-81) {
		tmp = x;
	} else {
		tmp = x / (-t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-0.00041d0)) then
        tmp = x * (-z / t)
    else if (z <= 6.5d-81) then
        tmp = x
    else
        tmp = x / (-t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00041) {
		tmp = x * (-z / t);
	} else if (z <= 6.5e-81) {
		tmp = x;
	} else {
		tmp = x / (-t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.00041:
		tmp = x * (-z / t)
	elif z <= 6.5e-81:
		tmp = x
	else:
		tmp = x / (-t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.00041)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= 6.5e-81)
		tmp = x;
	else
		tmp = Float64(x / Float64(Float64(-t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.00041)
		tmp = x * (-z / t);
	elseif (z <= 6.5e-81)
		tmp = x;
	else
		tmp = x / (-t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.00041], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-81], x, N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999999e-4

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. unsub-neg 59.2%

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

      3. distribute-lft-out-- 59.2%

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

      4. *-rgt-identity 59.2%

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

   4. Simplified 59.2%

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

      1. clear-num 59.1%

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

      2. un-div-inv 59.1%

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

   6. Applied egg-rr 59.1%

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

   7. Taylor expanded in t around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. associate-*r/ 48.7%

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

      3. distribute-rgt-neg-out 48.7%

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

      4. distribute-neg-frac 48.7%

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

   9. Simplified 48.7%

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

   if -4.0999999999999999e-4 < z < 6.5000000000000002e-81

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 66.9%

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

   if 6.5000000000000002e-81 < z

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. unsub-neg 63.4%

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

      3. distribute-lft-out-- 63.4%

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

      4. *-rgt-identity 63.4%

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

   4. Simplified 63.4%

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

      1. clear-num 63.4%

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

      2. un-div-inv 63.4%

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

   6. Applied egg-rr 63.4%

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

   7. Taylor expanded in t around 0 44.9%

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

      1. associate-*r/ 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-*l/ 44.8%

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

      4. metadata-eval 44.8%

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

      5. distribute-neg-frac 44.8%

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

      6. associate-*r* 50.3%

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

      7. distribute-neg-frac 50.3%

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

      8. metadata-eval 50.3%

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

      9. metadata-eval 50.3%

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

      10. associate-/r* 50.3%

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

      11. neg-mul-1 50.3%

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

      12. associate-/r/ 50.3%

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

      13. *-commutative 50.3%

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

      14. associate-*r/ 50.3%

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

      15. *-rgt-identity 50.3%

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

   9. Simplified 50.3%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00041:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \end{array} \]

Alternative 8: 92.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

2. Taylor expanded in y around 0 89.5%

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

   1. +-commutative 89.5%

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

   2. mul-1-neg 89.5%

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

   3. sub-neg 89.5%

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

   4. associate-/l* 88.4%

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

   5. associate-/l* 90.3%

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

   6. div-sub 96.3%

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

   7. associate-/r/ 95.5%

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

   8. *-commutative 95.5%

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

4. Simplified 95.5%

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

5. Final simplification 95.5%

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

Alternative 9: 38.6% 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 96.2%

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

2. Taylor expanded in z around 0 36.5%

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

3. Final simplification 36.5%

   \[\leadsto x \]

Developer target: 97.3% accurate, 0.4× 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 2023279 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

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

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