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

Percentage Accurate: 97.8% → 97.8%

Time: 6.0s

Alternatives: 9

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% 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: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. +-commutative 98.6%

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

   2. fma-def 98.6%

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

3. Simplified 98.6%

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

4. Final simplification 98.6%

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

Alternative 2: 54.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ t_2 := z \cdot \frac{-x}{t}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+220} \lor \neg \left(z \leq 2.8 \cdot 10^{+272}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ t z))) (t_2 (* z (/ (- x) t))))
   (if (<= z -2.9e+181)
     t_1
     (if (<= z -6.5e+149)
       t_2
       (if (<= z -1.5e+29)
         (* z (/ y t))
         (if (<= z 6.8e-20)
           x
           (if (<= z 4.8e+76)
             t_1
             (if (<= z 2.15e+99)
               x
               (if (or (<= z 6e+220) (not (<= z 2.8e+272))) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double t_2 = z * (-x / t);
	double tmp;
	if (z <= -2.9e+181) {
		tmp = t_1;
	} else if (z <= -6.5e+149) {
		tmp = t_2;
	} else if (z <= -1.5e+29) {
		tmp = z * (y / t);
	} else if (z <= 6.8e-20) {
		tmp = x;
	} else if (z <= 4.8e+76) {
		tmp = t_1;
	} else if (z <= 2.15e+99) {
		tmp = x;
	} else if ((z <= 6e+220) || !(z <= 2.8e+272)) {
		tmp = t_1;
	} 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 / (t / z)
    t_2 = z * (-x / t)
    if (z <= (-2.9d+181)) then
        tmp = t_1
    else if (z <= (-6.5d+149)) then
        tmp = t_2
    else if (z <= (-1.5d+29)) then
        tmp = z * (y / t)
    else if (z <= 6.8d-20) then
        tmp = x
    else if (z <= 4.8d+76) then
        tmp = t_1
    else if (z <= 2.15d+99) then
        tmp = x
    else if ((z <= 6d+220) .or. (.not. (z <= 2.8d+272))) then
        tmp = t_1
    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 / (t / z);
	double t_2 = z * (-x / t);
	double tmp;
	if (z <= -2.9e+181) {
		tmp = t_1;
	} else if (z <= -6.5e+149) {
		tmp = t_2;
	} else if (z <= -1.5e+29) {
		tmp = z * (y / t);
	} else if (z <= 6.8e-20) {
		tmp = x;
	} else if (z <= 4.8e+76) {
		tmp = t_1;
	} else if (z <= 2.15e+99) {
		tmp = x;
	} else if ((z <= 6e+220) || !(z <= 2.8e+272)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t / z)
	t_2 = z * (-x / t)
	tmp = 0
	if z <= -2.9e+181:
		tmp = t_1
	elif z <= -6.5e+149:
		tmp = t_2
	elif z <= -1.5e+29:
		tmp = z * (y / t)
	elif z <= 6.8e-20:
		tmp = x
	elif z <= 4.8e+76:
		tmp = t_1
	elif z <= 2.15e+99:
		tmp = x
	elif (z <= 6e+220) or not (z <= 2.8e+272):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t / z))
	t_2 = Float64(z * Float64(Float64(-x) / t))
	tmp = 0.0
	if (z <= -2.9e+181)
		tmp = t_1;
	elseif (z <= -6.5e+149)
		tmp = t_2;
	elseif (z <= -1.5e+29)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 6.8e-20)
		tmp = x;
	elseif (z <= 4.8e+76)
		tmp = t_1;
	elseif (z <= 2.15e+99)
		tmp = x;
	elseif ((z <= 6e+220) || !(z <= 2.8e+272))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t / z);
	t_2 = z * (-x / t);
	tmp = 0.0;
	if (z <= -2.9e+181)
		tmp = t_1;
	elseif (z <= -6.5e+149)
		tmp = t_2;
	elseif (z <= -1.5e+29)
		tmp = z * (y / t);
	elseif (z <= 6.8e-20)
		tmp = x;
	elseif (z <= 4.8e+76)
		tmp = t_1;
	elseif (z <= 2.15e+99)
		tmp = x;
	elseif ((z <= 6e+220) || ~((z <= 2.8e+272)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+181], t$95$1, If[LessEqual[z, -6.5e+149], t$95$2, If[LessEqual[z, -1.5e+29], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-20], x, If[LessEqual[z, 4.8e+76], t$95$1, If[LessEqual[z, 2.15e+99], x, If[Or[LessEqual[z, 6e+220], N[Not[LessEqual[z, 2.8e+272]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9e181 or 6.7999999999999994e-20 < z < 4.8e76 or 2.1500000000000001e99 < z < 6.00000000000000048e220 or 2.7999999999999999e272 < z

   1. Initial program 98.8%

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

      1. clear-num 98.8%

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

      2. un-div-inv 98.8%

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

   3. Applied egg-rr 98.8%

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

   4. Taylor expanded in t around 0 88.0%

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

   5. Taylor expanded in t around 0 79.1%

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

   6. Taylor expanded in y around inf 58.2%

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

      1. associate-/l* 68.8%

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

   8. Simplified 68.8%

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

   if -2.9e181 < z < -6.50000000000000015e149 or 6.00000000000000048e220 < z < 2.7999999999999999e272

   1. Initial program 95.0%

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

      1. clear-num 95.0%

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

      2. un-div-inv 95.1%

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

   3. Applied egg-rr 95.1%

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

   4. Taylor expanded in t around 0 90.1%

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

   5. Taylor expanded in t around 0 90.1%

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

   6. Taylor expanded in y around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. associate-*r/ 88.6%

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

      3. distribute-rgt-neg-out 88.6%

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

      4. distribute-neg-frac 88.6%

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

   8. Simplified 88.6%

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

   if -6.50000000000000015e149 < z < -1.5e29

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      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 86.1%

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

   5. Taylor expanded in t around 0 86.1%

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

   6. Taylor expanded in y around inf 72.0%

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

      1. associate-*l/ 85.8%

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

      2. *-commutative 85.8%

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

   8. Simplified 85.8%

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

   if -1.5e29 < z < 6.7999999999999994e-20 or 4.8e76 < z < 2.1500000000000001e99

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 64.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+181}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+220} \lor \neg \left(z \leq 2.8 \cdot 10^{+272}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \end{array} \]

Alternative 3: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+44} \lor \neg \left(x \leq -5 \cdot 10^{-6}\right) \land \left(x \leq -1.9 \cdot 10^{-95} \lor \neg \left(x \leq 4.6 \cdot 10^{-89}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.75e+44)
         (and (not (<= x -5e-6)) (or (<= x -1.9e-95) (not (<= x 4.6e-89)))))
   (* x (- 1.0 (/ z t)))
   (/ y (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e+44) || (!(x <= -5e-6) && ((x <= -1.9e-95) || !(x <= 4.6e-89)))) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.75d+44)) .or. (.not. (x <= (-5d-6))) .and. (x <= (-1.9d-95)) .or. (.not. (x <= 4.6d-89))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e+44) || (!(x <= -5e-6) && ((x <= -1.9e-95) || !(x <= 4.6e-89)))) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.75e+44) or (not (x <= -5e-6) and ((x <= -1.9e-95) or not (x <= 4.6e-89))):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.75e+44) || (!(x <= -5e-6) && ((x <= -1.9e-95) || !(x <= 4.6e-89))))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.75e+44) || (~((x <= -5e-6)) && ((x <= -1.9e-95) || ~((x <= 4.6e-89)))))
		tmp = x * (1.0 - (z / t));
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.75e+44], And[N[Not[LessEqual[x, -5e-6]], $MachinePrecision], Or[LessEqual[x, -1.9e-95], N[Not[LessEqual[x, 4.6e-89]], $MachinePrecision]]]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75e44 or -5.00000000000000041e-6 < x < -1.8999999999999999e-95 or 4.6e-89 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

      4. distribute-lft-out-- 86.7%

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

      5. *-rgt-identity 86.7%

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

   4. Simplified 86.7%

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

   5. Taylor expanded in x around 0 86.7%

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

   if -1.75e44 < x < -5.00000000000000041e-6 or -1.8999999999999999e-95 < x < 4.6e-89

   1. Initial program 96.2%

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

      1. clear-num 96.1%

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

      2. un-div-inv 96.2%

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

   3. Applied egg-rr 96.2%

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

   4. Taylor expanded in t around 0 92.8%

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

   5. Taylor expanded in t around 0 71.8%

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

   6. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 72.4%

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

   8. Simplified 72.4%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+44} \lor \neg \left(x \leq -5 \cdot 10^{-6}\right) \land \left(x \leq -1.9 \cdot 10^{-95} \lor \neg \left(x \leq 4.6 \cdot 10^{-89}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 4: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+28} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-19}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e+28) (not (<= (/ z t) 2e-19)))
   (* (- y x) (/ z t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e+28) || !((z / t) <= 2e-19)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-5d+28)) .or. (.not. ((z / t) <= 2d-19))) then
        tmp = (y - x) * (z / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e+28) || !((z / t) <= 2e-19)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e+28) or not ((z / t) <= 2e-19):
		tmp = (y - x) * (z / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e+28) || !(Float64(z / t) <= 2e-19))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -5e+28) || ~(((z / t) <= 2e-19)))
		tmp = (y - x) * (z / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e+28], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-19]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.99999999999999957e28 or 2e-19 < (/.f64 z t)

   1. Initial program 98.4%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in t around 0 94.0%

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

   5. Taylor expanded in t around 0 93.4%

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

   6. Taylor expanded in y around 0 83.4%

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

      1. associate-*l/ 81.2%

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

      2. *-commutative 81.2%

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

      3. neg-mul-1 81.2%

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

      4. distribute-lft-neg-in 81.2%

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

      5. associate-*r/ 82.7%

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

      6. distribute-rgt-out 97.4%

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

      7. +-commutative 97.4%

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

      8. sub-neg 97.4%

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

      9. *-commutative 97.4%

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

   8. Simplified 97.4%

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

   if -4.99999999999999957e28 < (/.f64 z t) < 2e-19

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 80.5%

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

      1. *-commutative 80.5%

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

      2. mul-1-neg 80.5%

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

      3. unsub-neg 80.5%

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

      4. distribute-lft-out-- 80.5%

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

      5. *-rgt-identity 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in x around 0 80.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+28} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-19}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 5: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -20 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -20.0) (not (<= (/ z t) 5e-8)))
   (* (- y x) (/ z t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -20.0) || !((z / t) <= 5e-8)) {
		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) <= (-20.0d0)) .or. (.not. ((z / t) <= 5d-8))) 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) <= -20.0) || !((z / t) <= 5e-8)) {
		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) <= -20.0) or not ((z / t) <= 5e-8):
		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) <= -20.0) || !(Float64(z / t) <= 5e-8))
		tmp = Float64(Float64(y - 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 (((z / t) <= -20.0) || ~(((z / t) <= 5e-8)))
		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], -20.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-8]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -20 or 4.9999999999999998e-8 < (/.f64 z t)

   1. Initial program 98.4%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in t around 0 93.4%

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

   5. Taylor expanded in t around 0 91.8%

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

   6. Taylor expanded in y around 0 81.9%

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

      1. associate-*l/ 79.9%

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

      2. *-commutative 79.9%

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

      3. neg-mul-1 79.9%

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

      4. distribute-lft-neg-in 79.9%

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

      5. associate-*r/ 81.4%

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

      6. distribute-rgt-out 95.9%

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

      7. +-commutative 95.9%

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

      8. sub-neg 95.9%

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

      9. *-commutative 95.9%

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

   8. Simplified 95.9%

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

   if -20 < (/.f64 z t) < 4.9999999999999998e-8

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 95.7%

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

      1. associate-*r/ 97.5%

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

   4. Simplified 97.5%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -20 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 53.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+28} \lor \neg \left(z \leq 4.7 \cdot 10^{-20}\right) \land \left(z \leq 1.75 \cdot 10^{+76} \lor \neg \left(z \leq 1.95 \cdot 10^{+99}\right)\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e+28)
         (and (not (<= z 4.7e-20)) (or (<= z 1.75e+76) (not (<= z 1.95e+99)))))
   (* z (/ y t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+28) || (!(z <= 4.7e-20) && ((z <= 1.75e+76) || !(z <= 1.95e+99)))) {
		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 <= (-6d+28)) .or. (.not. (z <= 4.7d-20)) .and. (z <= 1.75d+76) .or. (.not. (z <= 1.95d+99))) 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 <= -6e+28) || (!(z <= 4.7e-20) && ((z <= 1.75e+76) || !(z <= 1.95e+99)))) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e+28) or (not (z <= 4.7e-20) and ((z <= 1.75e+76) or not (z <= 1.95e+99))):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e+28) || (!(z <= 4.7e-20) && ((z <= 1.75e+76) || !(z <= 1.95e+99))))
		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 <= -6e+28) || (~((z <= 4.7e-20)) && ((z <= 1.75e+76) || ~((z <= 1.95e+99)))))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e+28], And[N[Not[LessEqual[z, 4.7e-20]], $MachinePrecision], Or[LessEqual[z, 1.75e+76], N[Not[LessEqual[z, 1.95e+99]], $MachinePrecision]]]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000002e28 or 4.70000000000000015e-20 < z < 1.75e76 or 1.94999999999999997e99 < z

   1. Initial program 98.4%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.3%

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

   3. Applied egg-rr 98.3%

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

   4. Taylor expanded in t around 0 88.1%

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

   5. Taylor expanded in t around 0 81.6%

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

   6. Taylor expanded in y around inf 56.7%

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

      1. associate-*l/ 61.5%

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

      2. *-commutative 61.5%

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

   8. Simplified 61.5%

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

   if -6.0000000000000002e28 < z < 4.70000000000000015e-20 or 1.75e76 < z < 1.94999999999999997e99

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 64.4%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+28} \lor \neg \left(z \leq 4.7 \cdot 10^{-20}\right) \land \left(z \leq 1.75 \cdot 10^{+76} \lor \neg \left(z \leq 1.95 \cdot 10^{+99}\right)\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 54.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+28} \lor \neg \left(z \leq 2.3 \cdot 10^{-19}\right) \land \left(z \leq 4.8 \cdot 10^{+76} \lor \neg \left(z \leq 2.15 \cdot 10^{+99}\right)\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e+28)
         (and (not (<= z 2.3e-19)) (or (<= z 4.8e+76) (not (<= z 2.15e+99)))))
   (/ y (/ t z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+28) || (!(z <= 2.3e-19) && ((z <= 4.8e+76) || !(z <= 2.15e+99)))) {
		tmp = y / (t / z);
	} 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 <= (-4.8d+28)) .or. (.not. (z <= 2.3d-19)) .and. (z <= 4.8d+76) .or. (.not. (z <= 2.15d+99))) then
        tmp = y / (t / z)
    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 <= -4.8e+28) || (!(z <= 2.3e-19) && ((z <= 4.8e+76) || !(z <= 2.15e+99)))) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e+28) or (not (z <= 2.3e-19) and ((z <= 4.8e+76) or not (z <= 2.15e+99))):
		tmp = y / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e+28) || (!(z <= 2.3e-19) && ((z <= 4.8e+76) || !(z <= 2.15e+99))))
		tmp = Float64(y / Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e+28) || (~((z <= 2.3e-19)) && ((z <= 4.8e+76) || ~((z <= 2.15e+99)))))
		tmp = y / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e+28], And[N[Not[LessEqual[z, 2.3e-19]], $MachinePrecision], Or[LessEqual[z, 4.8e+76], N[Not[LessEqual[z, 2.15e+99]], $MachinePrecision]]]], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999962e28 or 2.2999999999999998e-19 < z < 4.8e76 or 2.1500000000000001e99 < z

   1. Initial program 98.4%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.3%

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

   3. Applied egg-rr 98.3%

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

   4. Taylor expanded in t around 0 88.1%

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

   5. Taylor expanded in t around 0 81.6%

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

   6. Taylor expanded in y around inf 56.7%

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

      1. associate-/l* 66.0%

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

   8. Simplified 66.0%

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

   if -4.79999999999999962e28 < z < 2.2999999999999998e-19 or 4.8e76 < z < 2.1500000000000001e99

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 64.4%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+28} \lor \neg \left(z \leq 2.3 \cdot 10^{-19}\right) \land \left(z \leq 4.8 \cdot 10^{+76} \lor \neg \left(z \leq 2.15 \cdot 10^{+99}\right)\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

2. Final simplification 98.6%

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

Alternative 9: 38.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 98.6%

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

2. Taylor expanded in z around 0 39.2%

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

3. Final simplification 39.2%

   \[\leadsto x \]

Developer target: 97.6% 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 2023240 
(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))))