Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.1s

Alternatives: 13

Speedup: 1.0×

• 34.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 37.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := -y \cdot x\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+159}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{+52}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-283}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (- (* y x))))
   (if (<= y -3.6e+159)
     t_2
     (if (<= y -9.4e+52)
       (* y t)
       (if (<= y -7e-65)
         t_1
         (if (<= y -1.4e-283) x (if (<= y 1.05e+136) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = -(y * x);
	double tmp;
	if (y <= -3.6e+159) {
		tmp = t_2;
	} else if (y <= -9.4e+52) {
		tmp = y * t;
	} else if (y <= -7e-65) {
		tmp = t_1;
	} else if (y <= -1.4e-283) {
		tmp = x;
	} else if (y <= 1.05e+136) {
		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 = z * -t
    t_2 = -(y * x)
    if (y <= (-3.6d+159)) then
        tmp = t_2
    else if (y <= (-9.4d+52)) then
        tmp = y * t
    else if (y <= (-7d-65)) then
        tmp = t_1
    else if (y <= (-1.4d-283)) then
        tmp = x
    else if (y <= 1.05d+136) 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 = z * -t;
	double t_2 = -(y * x);
	double tmp;
	if (y <= -3.6e+159) {
		tmp = t_2;
	} else if (y <= -9.4e+52) {
		tmp = y * t;
	} else if (y <= -7e-65) {
		tmp = t_1;
	} else if (y <= -1.4e-283) {
		tmp = x;
	} else if (y <= 1.05e+136) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = -(y * x)
	tmp = 0
	if y <= -3.6e+159:
		tmp = t_2
	elif y <= -9.4e+52:
		tmp = y * t
	elif y <= -7e-65:
		tmp = t_1
	elif y <= -1.4e-283:
		tmp = x
	elif y <= 1.05e+136:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(-Float64(y * x))
	tmp = 0.0
	if (y <= -3.6e+159)
		tmp = t_2;
	elseif (y <= -9.4e+52)
		tmp = Float64(y * t);
	elseif (y <= -7e-65)
		tmp = t_1;
	elseif (y <= -1.4e-283)
		tmp = x;
	elseif (y <= 1.05e+136)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = -(y * x);
	tmp = 0.0;
	if (y <= -3.6e+159)
		tmp = t_2;
	elseif (y <= -9.4e+52)
		tmp = y * t;
	elseif (y <= -7e-65)
		tmp = t_1;
	elseif (y <= -1.4e-283)
		tmp = x;
	elseif (y <= 1.05e+136)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = (-N[(y * x), $MachinePrecision])}, If[LessEqual[y, -3.6e+159], t$95$2, If[LessEqual[y, -9.4e+52], N[(y * t), $MachinePrecision], If[LessEqual[y, -7e-65], t$95$1, If[LessEqual[y, -1.4e-283], x, If[LessEqual[y, 1.05e+136], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.60000000000000037e159 or 1.05e136 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.0%

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

      1. mul-1-neg 67.0%

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

      2. unsub-neg 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around inf 62.4%

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

      1. neg-mul-1 62.4%

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

   8. Simplified 62.4%

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

   if -3.60000000000000037e159 < y < -9.3999999999999999e52

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 61.7%

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

   4. Taylor expanded in z around inf 51.7%

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

   5. Taylor expanded in z around 0 61.7%

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

      1. associate-+r+ 61.7%

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

      2. mul-1-neg 61.7%

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

      3. sub-neg 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in y around inf 56.1%

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

   if -9.3999999999999999e52 < y < -7.00000000000000009e-65 or -1.3999999999999999e-283 < y < 1.05e136

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 69.5%

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

   4. Taylor expanded in z around inf 69.5%

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

   5. Taylor expanded in z around 0 68.6%

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

      1. associate-+r+ 68.6%

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

      2. mul-1-neg 68.6%

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

      3. sub-neg 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in z around inf 39.7%

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

      1. mul-1-neg 39.7%

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

      2. distribute-rgt-neg-out 39.7%

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

   10. Simplified 39.7%

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

   if -7.00000000000000009e-65 < y < -1.3999999999999999e-283

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in y around 0 49.3%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+159}:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{+52}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-65}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-283}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+72}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+55}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+191}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -9e+72)
     (* z x)
     (if (<= z -4.6e-39)
       t_1
       (if (<= z 1.85e-45)
         x
         (if (<= z 2.1e+55) (* y t) (if (<= z 1.16e+191) (* z x) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -9e+72) {
		tmp = z * x;
	} else if (z <= -4.6e-39) {
		tmp = t_1;
	} else if (z <= 1.85e-45) {
		tmp = x;
	} else if (z <= 2.1e+55) {
		tmp = y * t;
	} else if (z <= 1.16e+191) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-9d+72)) then
        tmp = z * x
    else if (z <= (-4.6d-39)) then
        tmp = t_1
    else if (z <= 1.85d-45) then
        tmp = x
    else if (z <= 2.1d+55) then
        tmp = y * t
    else if (z <= 1.16d+191) then
        tmp = z * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -9e+72) {
		tmp = z * x;
	} else if (z <= -4.6e-39) {
		tmp = t_1;
	} else if (z <= 1.85e-45) {
		tmp = x;
	} else if (z <= 2.1e+55) {
		tmp = y * t;
	} else if (z <= 1.16e+191) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -9e+72:
		tmp = z * x
	elif z <= -4.6e-39:
		tmp = t_1
	elif z <= 1.85e-45:
		tmp = x
	elif z <= 2.1e+55:
		tmp = y * t
	elif z <= 1.16e+191:
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -9e+72)
		tmp = Float64(z * x);
	elseif (z <= -4.6e-39)
		tmp = t_1;
	elseif (z <= 1.85e-45)
		tmp = x;
	elseif (z <= 2.1e+55)
		tmp = Float64(y * t);
	elseif (z <= 1.16e+191)
		tmp = Float64(z * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -9e+72)
		tmp = z * x;
	elseif (z <= -4.6e-39)
		tmp = t_1;
	elseif (z <= 1.85e-45)
		tmp = x;
	elseif (z <= 2.1e+55)
		tmp = y * t;
	elseif (z <= 1.16e+191)
		tmp = z * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -9e+72], N[(z * x), $MachinePrecision], If[LessEqual[z, -4.6e-39], t$95$1, If[LessEqual[z, 1.85e-45], x, If[LessEqual[z, 2.1e+55], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.16e+191], N[(z * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999997e72 or 2.1000000000000001e55 < z < 1.15999999999999996e191

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around inf 51.1%

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

   if -8.9999999999999997e72 < z < -4.60000000000000016e-39 or 1.15999999999999996e191 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 71.4%

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

   4. Taylor expanded in z around inf 71.4%

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

   5. Taylor expanded in z around 0 64.7%

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

      1. associate-+r+ 64.7%

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

      2. mul-1-neg 64.7%

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

      3. sub-neg 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in z around inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. distribute-rgt-neg-out 57.2%

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

   10. Simplified 57.2%

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

   if -4.60000000000000016e-39 < z < 1.85e-45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.2%

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

      1. *-commutative 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in y around 0 39.4%

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

   if 1.85e-45 < z < 2.1000000000000001e55

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 62.6%

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

   4. Taylor expanded in z around inf 62.5%

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

   5. Taylor expanded in z around 0 62.6%

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

      1. associate-+r+ 62.6%

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

      2. mul-1-neg 62.6%

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

      3. sub-neg 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in y around inf 48.4%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+72}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+55}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+191}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+51} \lor \neg \left(y \leq 52000\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.15e+51) (not (<= y 52000.0)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.15e+51) || !(y <= 52000.0)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (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) :: tmp
    if ((y <= (-2.15d+51)) .or. (.not. (y <= 52000.0d0))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.15e+51) || !(y <= 52000.0)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.15e+51) or not (y <= 52000.0):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.15e+51) || !(y <= 52000.0))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.15e+51) || ~((y <= 52000.0)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.15e+51], N[Not[LessEqual[y, 52000.0]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e51 or 52000 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.3%

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

      1. *-commutative 84.3%

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

   5. Simplified 84.3%

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

   if -2.1499999999999999e51 < y < 52000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.1%

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

      1. mul-1-neg 92.1%

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

      2. unsub-neg 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+51} \lor \neg \left(y \leq 52000\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-97} \lor \neg \left(x \leq 8000000000000\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.5e-97) (not (<= x 8000000000000.0)))
   (* x (+ (- z y) 1.0))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e-97) || !(x <= 8000000000000.0)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (t * (z - y));
	}
	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 <= (-1.5d-97)) .or. (.not. (x <= 8000000000000.0d0))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e-97) || !(x <= 8000000000000.0)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.5e-97) or not (x <= 8000000000000.0):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.5e-97) || !(x <= 8000000000000.0))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.5e-97) || ~((x <= 8000000000000.0)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.5e-97], N[Not[LessEqual[x, 8000000000000.0]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000012e-97 or 8e12 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   5. Simplified 86.3%

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

   if -1.50000000000000012e-97 < x < 8e12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 86.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-97} \lor \neg \left(x \leq 8000000000000\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-97} \lor \neg \left(x \leq 5900000000000\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.4e-97) (not (<= x 5900000000000.0)))
   (* x (+ (- z y) 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e-97) || !(x <= 5900000000000.0)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.4d-97)) .or. (.not. (x <= 5900000000000.0d0))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e-97) || !(x <= 5900000000000.0)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.4e-97) or not (x <= 5900000000000.0):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.4e-97) || !(x <= 5900000000000.0))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.4e-97) || ~((x <= 5900000000000.0)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.4e-97], N[Not[LessEqual[x, 5900000000000.0]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4000000000000001e-97 or 5.9e12 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   5. Simplified 86.3%

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

   if -1.4000000000000001e-97 < x < 5.9e12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 86.3%

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

   4. Taylor expanded in z around inf 83.0%

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

   5. Taylor expanded in z around 0 81.8%

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

      1. associate-+r+ 81.8%

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

      2. mul-1-neg 81.8%

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

      3. sub-neg 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in x around 0 72.5%

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

      1. distribute-lft-out-- 77.0%

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

   10. Simplified 77.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-97} \lor \neg \left(x \leq 5900000000000\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-70} \lor \neg \left(x \leq 9 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.3e-70) (not (<= x 9e+37))) (* x (- 1.0 y)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.3e-70) || !(x <= 9e+37)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.3d-70)) .or. (.not. (x <= 9d+37))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.3e-70) || !(x <= 9e+37)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.3e-70) or not (x <= 9e+37):
		tmp = x * (1.0 - y)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.3e-70) || !(x <= 9e+37))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.3e-70) || ~((x <= 9e+37)))
		tmp = x * (1.0 - y);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.3e-70], N[Not[LessEqual[x, 9e+37]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.30000000000000016e-70 or 8.99999999999999923e37 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in z around 0 65.1%

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

   if -3.30000000000000016e-70 < x < 8.99999999999999923e37

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.5%

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

   4. Taylor expanded in z around inf 78.7%

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

   5. Taylor expanded in z around 0 78.4%

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

      1. associate-+r+ 78.4%

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

      2. mul-1-neg 78.4%

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

      3. sub-neg 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in x around 0 69.5%

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

      1. distribute-lft-out-- 73.6%

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

   10. Simplified 73.6%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-70} \lor \neg \left(x \leq 9 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -470000 \lor \neg \left(x \leq 650000000000\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -470000.0) (not (<= x 650000000000.0)))
   (* x (+ z 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -470000.0) || !(x <= 650000000000.0)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-470000.0d0)) .or. (.not. (x <= 650000000000.0d0))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -470000.0) || !(x <= 650000000000.0)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -470000.0) or not (x <= 650000000000.0):
		tmp = x * (z + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -470000.0) || !(x <= 650000000000.0))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -470000.0) || ~((x <= 650000000000.0)))
		tmp = x * (z + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -470000.0], N[Not[LessEqual[x, 650000000000.0]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7e5 or 6.5e11 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in y around 0 57.1%

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

      1. +-commutative 57.1%

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

   8. Simplified 57.1%

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

   if -4.7e5 < x < 6.5e11

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.0%

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

   4. Taylor expanded in z around inf 78.2%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. associate-+r+ 77.3%

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

      2. mul-1-neg 77.3%

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

      3. sub-neg 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in x around 0 66.9%

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

      1. distribute-lft-out-- 70.7%

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

   10. Simplified 70.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -470000 \lor \neg \left(x \leq 650000000000\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+16} \lor \neg \left(x \leq 3.2 \cdot 10^{+63}\right):\\ \;\;\;\;-y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.9e+16) (not (<= x 3.2e+63))) (- (* y x)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.9e+16) || !(x <= 3.2e+63)) {
		tmp = -(y * x);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.9d+16)) .or. (.not. (x <= 3.2d+63))) then
        tmp = -(y * x)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.9e+16) || !(x <= 3.2e+63)) {
		tmp = -(y * x);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.9e+16) or not (x <= 3.2e+63):
		tmp = -(y * x)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.9e+16) || !(x <= 3.2e+63))
		tmp = Float64(-Float64(y * x));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.9e+16) || ~((x <= 3.2e+63)))
		tmp = -(y * x);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.9e+16], N[Not[LessEqual[x, 3.2e+63]], $MachinePrecision]], (-N[(y * x), $MachinePrecision]), N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9e16 or 3.20000000000000011e63 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.4%

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

      1. mul-1-neg 91.4%

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

      2. unsub-neg 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in y around inf 44.5%

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

      1. neg-mul-1 44.5%

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

   8. Simplified 44.5%

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

   if -5.9e16 < x < 3.20000000000000011e63

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 78.6%

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

   4. Taylor expanded in z around inf 75.3%

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

   5. Taylor expanded in z around 0 75.1%

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

      1. associate-+r+ 75.1%

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

      2. mul-1-neg 75.1%

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

      3. sub-neg 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in x around 0 64.3%

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

      1. distribute-lft-out-- 67.8%

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

   10. Simplified 67.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+16} \lor \neg \left(x \leq 3.2 \cdot 10^{+63}\right):\\ \;\;\;\;-y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-70}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+39}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.8e-70)
   (- x (* y x))
   (if (<= x 2.65e+39) (* (- y z) t) (* x (- 1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e-70) {
		tmp = x - (y * x);
	} else if (x <= 2.65e+39) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	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-70)) then
        tmp = x - (y * x)
    else if (x <= 2.65d+39) then
        tmp = (y - z) * t
    else
        tmp = x * (1.0d0 - y)
    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-70) {
		tmp = x - (y * x);
	} else if (x <= 2.65e+39) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.8e-70:
		tmp = x - (y * x)
	elif x <= 2.65e+39:
		tmp = (y - z) * t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.8e-70)
		tmp = Float64(x - Float64(y * x));
	elseif (x <= 2.65e+39)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.8e-70)
		tmp = x - (y * x);
	elseif (x <= 2.65e+39)
		tmp = (y - z) * t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.8e-70], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.65e+39], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8000000000000002e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around 0 62.3%

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

      1. neg-mul-1 62.3%

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

   8. Simplified 62.3%

      \[\leadsto x + \color{blue}{\left(-x\right)} \cdot y \]
   9. Step-by-step derivation

      1. distribute-lft-neg-out 62.3%

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

      2. unsub-neg 62.3%

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

      3. *-commutative 62.3%

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

   10. Applied egg-rr 62.3%

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

   if -4.8000000000000002e-70 < x < 2.64999999999999989e39

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.5%

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

   4. Taylor expanded in z around inf 78.7%

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

   5. Taylor expanded in z around 0 78.4%

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

      1. associate-+r+ 78.4%

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

      2. mul-1-neg 78.4%

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

      3. sub-neg 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in x around 0 69.5%

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

      1. distribute-lft-out-- 73.6%

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

   10. Simplified 73.6%

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

   if 2.64999999999999989e39 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in z around 0 69.5%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-70}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+39}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-17} \lor \neg \left(y \leq 6.6 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e-17) (not (<= y 6.6e-8))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e-17) || !(y <= 6.6e-8)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.6d-17)) .or. (.not. (y <= 6.6d-8))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e-17) || !(y <= 6.6e-8)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e-17) or not (y <= 6.6e-8):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e-17) || !(y <= 6.6e-8))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.6e-17) || ~((y <= 6.6e-8)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.6e-17], N[Not[LessEqual[y, 6.6e-8]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000003e-17 or 6.59999999999999954e-8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 49.8%

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

   4. Taylor expanded in z around inf 50.0%

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

   5. Taylor expanded in z around 0 45.3%

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

      1. associate-+r+ 45.3%

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

      2. mul-1-neg 45.3%

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

      3. sub-neg 45.3%

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

   7. Simplified 45.3%

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

   8. Taylor expanded in y around inf 38.7%

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

   if -2.60000000000000003e-17 < y < 6.59999999999999954e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 43.7%

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

      1. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in y around 0 37.1%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-17} \lor \neg \left(y \leq 6.6 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 13: 18.1% 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 100.0%

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

3. Taylor expanded in y around inf 62.3%

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

   1. *-commutative 62.3%

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

5. Simplified 62.3%

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

6. Taylor expanded in y around 0 19.3%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Developer Target 1: 96.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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