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

Percentage Accurate: 97.7% → 97.7%

Time: 6.6s

Alternatives: 11

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. +-commutative 97.1%

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

   2. fma-def 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 2: 63.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 50000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+238}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y z) t)))
   (if (<= (/ z t) -5e+120)
     t_1
     (if (<= (/ z t) -4e+28)
       (/ (* x (- z)) t)
       (if (<= (/ z t) -1e-27)
         t_1
         (if (<= (/ z t) 1e-9)
           x
           (if (<= (/ z t) 50000000.0)
             t_1
             (if (<= (/ z t) 5e+238) (* (/ z t) (- x)) (* z (/ y t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double tmp;
	if ((z / t) <= -5e+120) {
		tmp = t_1;
	} else if ((z / t) <= -4e+28) {
		tmp = (x * -z) / t;
	} else if ((z / t) <= -1e-27) {
		tmp = t_1;
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else if ((z / t) <= 50000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e+238) {
		tmp = (z / t) * -x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) / t
    if ((z / t) <= (-5d+120)) then
        tmp = t_1
    else if ((z / t) <= (-4d+28)) then
        tmp = (x * -z) / t
    else if ((z / t) <= (-1d-27)) then
        tmp = t_1
    else if ((z / t) <= 1d-9) then
        tmp = x
    else if ((z / t) <= 50000000.0d0) then
        tmp = t_1
    else if ((z / t) <= 5d+238) then
        tmp = (z / t) * -x
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double tmp;
	if ((z / t) <= -5e+120) {
		tmp = t_1;
	} else if ((z / t) <= -4e+28) {
		tmp = (x * -z) / t;
	} else if ((z / t) <= -1e-27) {
		tmp = t_1;
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else if ((z / t) <= 50000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e+238) {
		tmp = (z / t) * -x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) / t
	tmp = 0
	if (z / t) <= -5e+120:
		tmp = t_1
	elif (z / t) <= -4e+28:
		tmp = (x * -z) / t
	elif (z / t) <= -1e-27:
		tmp = t_1
	elif (z / t) <= 1e-9:
		tmp = x
	elif (z / t) <= 50000000.0:
		tmp = t_1
	elif (z / t) <= 5e+238:
		tmp = (z / t) * -x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) / t)
	tmp = 0.0
	if (Float64(z / t) <= -5e+120)
		tmp = t_1;
	elseif (Float64(z / t) <= -4e+28)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (Float64(z / t) <= -1e-27)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-9)
		tmp = x;
	elseif (Float64(z / t) <= 50000000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e+238)
		tmp = Float64(Float64(z / t) * Float64(-x));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) / t;
	tmp = 0.0;
	if ((z / t) <= -5e+120)
		tmp = t_1;
	elseif ((z / t) <= -4e+28)
		tmp = (x * -z) / t;
	elseif ((z / t) <= -1e-27)
		tmp = t_1;
	elseif ((z / t) <= 1e-9)
		tmp = x;
	elseif ((z / t) <= 50000000.0)
		tmp = t_1;
	elseif ((z / t) <= 5e+238)
		tmp = (z / t) * -x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e+120], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -4e+28], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -1e-27], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-9], x, If[LessEqual[N[(z / t), $MachinePrecision], 50000000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e+238], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 z t) < -5.00000000000000019e120 or -3.99999999999999983e28 < (/.f64 z t) < -1e-27 or 1.00000000000000006e-9 < (/.f64 z t) < 5e7

   1. Initial program 93.6%

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

      1. clear-num 93.5%

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

      2. un-div-inv 93.6%

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

   3. Applied egg-rr 93.6%

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

   4. Taylor expanded in t around 0 98.2%

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

   5. Taylor expanded in t around 0 87.6%

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

   6. Taylor expanded in y around inf 63.2%

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

      1. *-commutative 63.2%

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

   8. Simplified 63.2%

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

   if -5.00000000000000019e120 < (/.f64 z t) < -3.99999999999999983e28

   1. Initial program 99.6%

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

      1. clear-num 99.4%

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

      2. un-div-inv 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in t around 0 99.8%

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

   5. Taylor expanded in t around 0 99.8%

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

   6. Taylor expanded in y around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. distribute-rgt-neg-in 66.0%

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

   8. Simplified 66.0%

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

   if -1e-27 < (/.f64 z t) < 1.00000000000000006e-9

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 79.6%

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

   if 5e7 < (/.f64 z t) < 4.99999999999999995e238

   1. Initial program 99.6%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in t around 0 92.5%

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

   5. Taylor expanded in t around 0 92.5%

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

   6. Taylor expanded in y around 0 55.2%

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

      1. associate-*l/ 59.7%

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

      2. associate-*r* 59.7%

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

      3. mul-1-neg 59.7%

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

   8. Simplified 59.7%

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

   if 4.99999999999999995e238 < (/.f64 z t)

   1. Initial program 92.1%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.2%

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

   3. Applied egg-rr 92.2%

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

   4. Taylor expanded in t around 0 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

   6. Taylor expanded in y around inf 70.4%

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

      1. associate-*l/ 70.6%

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

      2. *-commutative 70.6%

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

   8. Simplified 70.6%

      \[\leadsto \color{blue}{z \cdot \frac{y}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+120}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 50000000:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+238}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 50000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+238}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y z) t)))
   (if (<= (/ z t) -1e-27)
     t_1
     (if (<= (/ z t) 1e-9)
       x
       (if (<= (/ z t) 50000000.0)
         t_1
         (if (<= (/ z t) 5e+238) (* (/ z t) (- x)) (* z (/ y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double tmp;
	if ((z / t) <= -1e-27) {
		tmp = t_1;
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else if ((z / t) <= 50000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e+238) {
		tmp = (z / t) * -x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) / t
    if ((z / t) <= (-1d-27)) then
        tmp = t_1
    else if ((z / t) <= 1d-9) then
        tmp = x
    else if ((z / t) <= 50000000.0d0) then
        tmp = t_1
    else if ((z / t) <= 5d+238) then
        tmp = (z / t) * -x
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double tmp;
	if ((z / t) <= -1e-27) {
		tmp = t_1;
	} else if ((z / t) <= 1e-9) {
		tmp = x;
	} else if ((z / t) <= 50000000.0) {
		tmp = t_1;
	} else if ((z / t) <= 5e+238) {
		tmp = (z / t) * -x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) / t
	tmp = 0
	if (z / t) <= -1e-27:
		tmp = t_1
	elif (z / t) <= 1e-9:
		tmp = x
	elif (z / t) <= 50000000.0:
		tmp = t_1
	elif (z / t) <= 5e+238:
		tmp = (z / t) * -x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) / t)
	tmp = 0.0
	if (Float64(z / t) <= -1e-27)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-9)
		tmp = x;
	elseif (Float64(z / t) <= 50000000.0)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e+238)
		tmp = Float64(Float64(z / t) * Float64(-x));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) / t;
	tmp = 0.0;
	if ((z / t) <= -1e-27)
		tmp = t_1;
	elseif ((z / t) <= 1e-9)
		tmp = x;
	elseif ((z / t) <= 50000000.0)
		tmp = t_1;
	elseif ((z / t) <= 5e+238)
		tmp = (z / t) * -x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e-27], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-9], x, If[LessEqual[N[(z / t), $MachinePrecision], 50000000.0], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e+238], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -1e-27 or 1.00000000000000006e-9 < (/.f64 z t) < 5e7

   1. Initial program 94.9%

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

      1. clear-num 94.8%

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

      2. un-div-inv 94.9%

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

   3. Applied egg-rr 94.9%

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

   4. Taylor expanded in t around 0 98.6%

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

   5. Taylor expanded in t around 0 90.3%

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

   6. Taylor expanded in y around inf 57.3%

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

      1. *-commutative 57.3%

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

   8. Simplified 57.3%

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

   if -1e-27 < (/.f64 z t) < 1.00000000000000006e-9

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 79.6%

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

   if 5e7 < (/.f64 z t) < 4.99999999999999995e238

   1. Initial program 99.6%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in t around 0 92.5%

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

   5. Taylor expanded in t around 0 92.5%

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

   6. Taylor expanded in y around 0 55.2%

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

      1. associate-*l/ 59.7%

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

      2. associate-*r* 59.7%

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

      3. mul-1-neg 59.7%

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

   8. Simplified 59.7%

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

   if 4.99999999999999995e238 < (/.f64 z t)

   1. Initial program 92.1%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.2%

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

   3. Applied egg-rr 92.2%

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

   4. Taylor expanded in t around 0 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

   6. Taylor expanded in y around inf 70.4%

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

      1. associate-*l/ 70.6%

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

      2. *-commutative 70.6%

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

   8. Simplified 70.6%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 50000000:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+238}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 94.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+28} \lor \neg \left(\frac{z}{t} \leq 0.0005\right):\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -4e+28) (not (<= (/ z t) 0.0005)))
   (/ (* (- y x) z) t)
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e+28) || !((z / t) <= 0.0005)) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-4d+28)) .or. (.not. ((z / t) <= 0.0005d0))) then
        tmp = ((y - x) * z) / t
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e+28) || !((z / t) <= 0.0005)) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -4e+28) or not ((z / t) <= 0.0005):
		tmp = ((y - x) * z) / t
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -4e+28) || !(Float64(z / t) <= 0.0005))
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -4e+28) || ~(((z / t) <= 0.0005)))
		tmp = ((y - x) * z) / t;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -4e+28], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.0005]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -3.99999999999999983e28 or 5.0000000000000001e-4 < (/.f64 z t)

   1. Initial program 95.3%

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

      1. clear-num 95.1%

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

      2. un-div-inv 95.2%

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

   3. Applied egg-rr 95.2%

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

   4. Taylor expanded in t around 0 97.5%

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

   5. Taylor expanded in t around 0 97.2%

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

   if -3.99999999999999983e28 < (/.f64 z t) < 5.0000000000000001e-4

   1. Initial program 98.7%

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

   2. Taylor expanded in y around inf 91.7%

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

      1. associate-*r/ 95.5%

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

   4. Simplified 95.5%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+28} \lor \neg \left(\frac{z}{t} \leq 0.0005\right):\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 54.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+66} \lor \neg \left(z \leq 9 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+223)
   (* z (/ (- x) t))
   (if (or (<= z -2.8e+66) (not (<= z 9e-24))) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+223) {
		tmp = z * (-x / t);
	} else if ((z <= -2.8e+66) || !(z <= 9e-24)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.5d+223)) then
        tmp = z * (-x / t)
    else if ((z <= (-2.8d+66)) .or. (.not. (z <= 9d-24))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+223) {
		tmp = z * (-x / t);
	} else if ((z <= -2.8e+66) || !(z <= 9e-24)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+223:
		tmp = z * (-x / t)
	elif (z <= -2.8e+66) or not (z <= 9e-24):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+223)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif ((z <= -2.8e+66) || !(z <= 9e-24))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e+223)
		tmp = z * (-x / t);
	elseif ((z <= -2.8e+66) || ~((z <= 9e-24)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+223], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.8e+66], N[Not[LessEqual[z, 9e-24]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000001e223

   1. Initial program 99.9%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in t around 0 84.1%

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

   5. Taylor expanded in t around 0 84.1%

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

   6. Taylor expanded in y around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*r/ 82.4%

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

      3. distribute-rgt-neg-in 82.4%

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

      4. distribute-neg-frac 82.4%

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

   8. Simplified 82.4%

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

   if -1.50000000000000001e223 < z < -2.8000000000000001e66 or 8.9999999999999995e-24 < z

   1. Initial program 94.0%

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

      1. clear-num 93.9%

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

      2. un-div-inv 93.9%

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

   3. Applied egg-rr 93.9%

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

   4. Taylor expanded in t around 0 91.0%

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

   5. Taylor expanded in t around 0 84.5%

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

   6. Taylor expanded in y around inf 59.4%

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

      1. associate-*l/ 62.4%

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

      2. *-commutative 62.4%

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

   8. Simplified 62.4%

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

   if -2.8000000000000001e66 < z < 8.9999999999999995e-24

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 59.8%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+66} \lor \neg \left(z \leq 9 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-40} \lor \neg \left(x \leq 4.8 \cdot 10^{-57}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.1e-40) (not (<= x 4.8e-57)))
   (- x (* x (/ z t)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.1e-40) || !(x <= 4.8e-57)) {
		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 ((x <= (-4.1d-40)) .or. (.not. (x <= 4.8d-57))) 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 ((x <= -4.1e-40) || !(x <= 4.8e-57)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.1e-40) or not (x <= 4.8e-57):
		tmp = x - (x * (z / t))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.1e-40) || !(x <= 4.8e-57))
		tmp = Float64(x - Float64(x * Float64(z / t)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.1e-40) || ~((x <= 4.8e-57)))
		tmp = x - (x * (z / t));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.1e-40], N[Not[LessEqual[x, 4.8e-57]], $MachinePrecision]], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.09999999999999963e-40 or 4.80000000000000012e-57 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 87.5%

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

      1. *-commutative 87.5%

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

      2. mul-1-neg 87.5%

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

      3. unsub-neg 87.5%

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

      4. distribute-lft-out-- 87.5%

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

      5. *-rgt-identity 87.5%

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

   4. Simplified 87.5%

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

   if -4.09999999999999963e-40 < x < 4.80000000000000012e-57

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf 91.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-40} \lor \neg \left(x \leq 4.8 \cdot 10^{-57}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 7: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.8e-40)
   (- x (/ x (/ t z)))
   (if (<= x 2.2e-55) (+ x (/ (* y z) t)) (- x (* x (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e-40) {
		tmp = x - (x / (t / z));
	} else if (x <= 2.2e-55) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x - (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) :: tmp
    if (x <= (-4.8d-40)) then
        tmp = x - (x / (t / z))
    else if (x <= 2.2d-55) then
        tmp = x + ((y * z) / t)
    else
        tmp = x - (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e-40) {
		tmp = x - (x / (t / z));
	} else if (x <= 2.2e-55) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.8e-40:
		tmp = x - (x / (t / z))
	elif x <= 2.2e-55:
		tmp = x + ((y * z) / t)
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.8e-40)
		tmp = Float64(x - Float64(x / Float64(t / z)));
	elseif (x <= 2.2e-55)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.8e-40)
		tmp = x - (x / (t / z));
	elseif (x <= 2.2e-55)
		tmp = x + ((y * z) / t);
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.8e-40], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-55], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.79999999999999982e-40

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. unsub-neg 85.9%

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

      4. distribute-lft-out-- 85.9%

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

      5. *-rgt-identity 85.9%

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

   4. Simplified 85.9%

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

      1. clear-num 85.9%

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

      2. div-inv 85.9%

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

   6. Applied egg-rr 85.9%

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

   if -4.79999999999999982e-40 < x < 2.2e-55

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf 91.5%

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

   if 2.2e-55 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. mul-1-neg 89.5%

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

      3. unsub-neg 89.5%

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

      4. distribute-lft-out-- 89.5%

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

      5. *-rgt-identity 89.5%

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

   4. Simplified 89.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+65} \lor \neg \left(z \leq 4.5 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.75e+65) (not (<= z 4.5e-20))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e+65) || !(z <= 4.5e-20)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.75d+65)) .or. (.not. (z <= 4.5d-20))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e+65) || !(z <= 4.5e-20)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.75e+65) or not (z <= 4.5e-20):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.75e+65) || !(z <= 4.5e-20))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.75e+65) || ~((z <= 4.5e-20)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.75e+65], N[Not[LessEqual[z, 4.5e-20]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e65 or 4.5000000000000001e-20 < z

   1. Initial program 94.6%

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

      1. clear-num 94.5%

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

      2. un-div-inv 94.6%

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

   3. Applied egg-rr 94.6%

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

   4. Taylor expanded in t around 0 90.2%

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

   5. Taylor expanded in t around 0 84.5%

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

   6. Taylor expanded in y around inf 54.9%

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

      1. associate-*l/ 57.5%

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

      2. *-commutative 57.5%

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

   8. Simplified 57.5%

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

   if -1.75e65 < z < 4.5000000000000001e-20

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 59.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+65} \lor \neg \left(z \leq 4.5 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

2. Final simplification 97.1%

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

Alternative 10: 76.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

2. Taylor expanded in y around inf 74.9%

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

   1. associate-*r/ 76.3%

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

4. Simplified 76.3%

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

5. Final simplification 76.3%

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

Alternative 11: 38.2% 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 97.1%

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

2. Taylor expanded in z around 0 39.0%

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

3. Final simplification 39.0%

   \[\leadsto x \]

Developer target: 97.5% 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 2023268 
(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))))