Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.4s

Alternatives: 15

Speedup: 1.0×

• 35.2% 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: 37.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -7600000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+44}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+210}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -7600000000000.0)
     t_1
     (if (<= z -2.45e-114)
       (* y (- x))
       (if (<= z 5e-48)
         x
         (if (<= z 5e+44) (* y t) (if (<= z 3.7e+210) (* z x) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -7600000000000.0) {
		tmp = t_1;
	} else if (z <= -2.45e-114) {
		tmp = y * -x;
	} else if (z <= 5e-48) {
		tmp = x;
	} else if (z <= 5e+44) {
		tmp = y * t;
	} else if (z <= 3.7e+210) {
		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 <= (-7600000000000.0d0)) then
        tmp = t_1
    else if (z <= (-2.45d-114)) then
        tmp = y * -x
    else if (z <= 5d-48) then
        tmp = x
    else if (z <= 5d+44) then
        tmp = y * t
    else if (z <= 3.7d+210) 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 <= -7600000000000.0) {
		tmp = t_1;
	} else if (z <= -2.45e-114) {
		tmp = y * -x;
	} else if (z <= 5e-48) {
		tmp = x;
	} else if (z <= 5e+44) {
		tmp = y * t;
	} else if (z <= 3.7e+210) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -7600000000000.0:
		tmp = t_1
	elif z <= -2.45e-114:
		tmp = y * -x
	elif z <= 5e-48:
		tmp = x
	elif z <= 5e+44:
		tmp = y * t
	elif z <= 3.7e+210:
		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 <= -7600000000000.0)
		tmp = t_1;
	elseif (z <= -2.45e-114)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 5e-48)
		tmp = x;
	elseif (z <= 5e+44)
		tmp = Float64(y * t);
	elseif (z <= 3.7e+210)
		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 <= -7600000000000.0)
		tmp = t_1;
	elseif (z <= -2.45e-114)
		tmp = y * -x;
	elseif (z <= 5e-48)
		tmp = x;
	elseif (z <= 5e+44)
		tmp = y * t;
	elseif (z <= 3.7e+210)
		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, -7600000000000.0], t$95$1, If[LessEqual[z, -2.45e-114], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 5e-48], x, If[LessEqual[z, 5e+44], N[(y * t), $MachinePrecision], If[LessEqual[z, 3.7e+210], N[(z * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.6e12 or 3.69999999999999998e210 < 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 60.8%

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

   4. Taylor expanded in y around 0 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

      3. *-commutative 53.5%

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

   6. Simplified 53.5%

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

   7. Taylor expanded in x around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. *-commutative 53.6%

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

      3. distribute-rgt-neg-out 53.6%

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

   9. Simplified 53.6%

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

   if -7.6e12 < z < -2.4499999999999999e-114

   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 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in y around inf 48.3%

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

      1. neg-mul-1 48.3%

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

   8. Simplified 48.3%

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

   if -2.4499999999999999e-114 < z < 4.9999999999999999e-48

   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 83.3%

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

   4. Taylor expanded in x around inf 47.7%

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

   if 4.9999999999999999e-48 < z < 4.9999999999999996e44

   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 66.1%

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

   4. Taylor expanded in t around inf 64.6%

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

   5. Taylor expanded in y around inf 45.7%

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

   if 4.9999999999999996e44 < z < 3.69999999999999998e210

   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 69.1%

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

      1. mul-1-neg 69.1%

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

      2. unsub-neg 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in z around inf 52.5%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7600000000000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+44}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+210}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -8200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* y (- t x))))
   (if (<= z -8200000000000.0)
     t_1
     (if (<= z -5.2e-278)
       t_2
       (if (<= z 3.8e-49) (* x (- 1.0 y)) (if (<= z 1e-6) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -8200000000000.0) {
		tmp = t_1;
	} else if (z <= -5.2e-278) {
		tmp = t_2;
	} else if (z <= 3.8e-49) {
		tmp = x * (1.0 - y);
	} else if (z <= 1e-6) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = y * (t - x)
    if (z <= (-8200000000000.0d0)) then
        tmp = t_1
    else if (z <= (-5.2d-278)) then
        tmp = t_2
    else if (z <= 3.8d-49) then
        tmp = x * (1.0d0 - y)
    else if (z <= 1d-6) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -8200000000000.0) {
		tmp = t_1;
	} else if (z <= -5.2e-278) {
		tmp = t_2;
	} else if (z <= 3.8e-49) {
		tmp = x * (1.0 - y);
	} else if (z <= 1e-6) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = y * (t - x)
	tmp = 0
	if z <= -8200000000000.0:
		tmp = t_1
	elif z <= -5.2e-278:
		tmp = t_2
	elif z <= 3.8e-49:
		tmp = x * (1.0 - y)
	elif z <= 1e-6:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (z <= -8200000000000.0)
		tmp = t_1;
	elseif (z <= -5.2e-278)
		tmp = t_2;
	elseif (z <= 3.8e-49)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 1e-6)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = y * (t - x);
	tmp = 0.0;
	if (z <= -8200000000000.0)
		tmp = t_1;
	elseif (z <= -5.2e-278)
		tmp = t_2;
	elseif (z <= 3.8e-49)
		tmp = x * (1.0 - y);
	elseif (z <= 1e-6)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8200000000000.0], t$95$1, If[LessEqual[z, -5.2e-278], t$95$2, If[LessEqual[z, 3.8e-49], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-6], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e12 or 9.99999999999999955e-7 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in t around 0 96.3%

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

      1. associate-+r+ 96.3%

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

      2. *-rgt-identity 96.3%

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

      3. mul-1-neg 96.3%

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

      4. distribute-rgt-neg-in 96.3%

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

      5. distribute-lft-in 96.3%

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

      6. sub-neg 96.3%

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

      7. +-commutative 96.3%

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

      8. mul-1-neg 96.3%

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

      9. sub-neg 96.3%

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

      10. fma-define 98.5%

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

   7. Simplified 98.5%

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

   8. Taylor expanded in z around inf 81.2%

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

      1. neg-mul-1 81.2%

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

      2. unsub-neg 81.2%

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

   10. Simplified 81.2%

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

   if -8.2e12 < z < -5.1999999999999997e-278 or 3.7999999999999997e-49 < z < 9.99999999999999955e-7

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in t around 0 96.9%

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

      1. associate-+r+ 96.9%

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

      2. *-rgt-identity 96.9%

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

      3. mul-1-neg 96.9%

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

      4. distribute-rgt-neg-in 96.9%

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

      5. distribute-lft-in 96.9%

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

      6. sub-neg 96.9%

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

      7. +-commutative 96.9%

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

      8. mul-1-neg 96.9%

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

      9. sub-neg 96.9%

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

      10. fma-define 96.9%

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

   7. Simplified 96.9%

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

   8. Taylor expanded in y around inf 68.1%

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

      1. neg-mul-1 68.1%

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

      2. unsub-neg 68.1%

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

   10. Simplified 68.1%

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

   if -5.1999999999999997e-278 < z < 3.7999999999999997e-49

   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 69.9%

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

      1. mul-1-neg 69.9%

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

      2. unsub-neg 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in z around 0 69.9%

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

Alternative 4: 38.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+23}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+44}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+23)
   (* z x)
   (if (<= z -7.4e-115)
     (* y (- x))
     (if (<= z 2.35e-49) x (if (<= z 6.2e+44) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+23) {
		tmp = z * x;
	} else if (z <= -7.4e-115) {
		tmp = y * -x;
	} else if (z <= 2.35e-49) {
		tmp = x;
	} else if (z <= 6.2e+44) {
		tmp = y * t;
	} else {
		tmp = z * 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 <= (-4d+23)) then
        tmp = z * x
    else if (z <= (-7.4d-115)) then
        tmp = y * -x
    else if (z <= 2.35d-49) then
        tmp = x
    else if (z <= 6.2d+44) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+23) {
		tmp = z * x;
	} else if (z <= -7.4e-115) {
		tmp = y * -x;
	} else if (z <= 2.35e-49) {
		tmp = x;
	} else if (z <= 6.2e+44) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e+23:
		tmp = z * x
	elif z <= -7.4e-115:
		tmp = y * -x
	elif z <= 2.35e-49:
		tmp = x
	elif z <= 6.2e+44:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e+23)
		tmp = Float64(z * x);
	elseif (z <= -7.4e-115)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 2.35e-49)
		tmp = x;
	elseif (z <= 6.2e+44)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e+23)
		tmp = z * x;
	elseif (z <= -7.4e-115)
		tmp = y * -x;
	elseif (z <= 2.35e-49)
		tmp = x;
	elseif (z <= 6.2e+44)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e+23], N[(z * x), $MachinePrecision], If[LessEqual[z, -7.4e-115], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 2.35e-49], x, If[LessEqual[z, 6.2e+44], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.9999999999999997e23 or 6.19999999999999991e44 < z

   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 51.6%

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

      1. mul-1-neg 51.6%

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

      2. unsub-neg 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in z around inf 44.5%

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

   if -3.9999999999999997e23 < z < -7.4e-115

   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 51.7%

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

      1. mul-1-neg 51.7%

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

      2. unsub-neg 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in y around inf 46.3%

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

      1. neg-mul-1 46.3%

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

   8. Simplified 46.3%

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

   if -7.4e-115 < z < 2.35000000000000011e-49

   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 83.3%

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

   4. Taylor expanded in x around inf 47.7%

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

   if 2.35000000000000011e-49 < z < 6.19999999999999991e44

   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 66.1%

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

   4. Taylor expanded in t around inf 64.6%

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

   5. Taylor expanded in y around inf 45.7%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+23}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+44}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-278}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+45}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.6e+67)
   (* z x)
   (if (<= z -4.2e-278)
     (* y t)
     (if (<= z 5e-48) x (if (<= z 3.6e+45) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e+67) {
		tmp = z * x;
	} else if (z <= -4.2e-278) {
		tmp = y * t;
	} else if (z <= 5e-48) {
		tmp = x;
	} else if (z <= 3.6e+45) {
		tmp = y * t;
	} else {
		tmp = z * 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 <= (-2.6d+67)) then
        tmp = z * x
    else if (z <= (-4.2d-278)) then
        tmp = y * t
    else if (z <= 5d-48) then
        tmp = x
    else if (z <= 3.6d+45) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e+67) {
		tmp = z * x;
	} else if (z <= -4.2e-278) {
		tmp = y * t;
	} else if (z <= 5e-48) {
		tmp = x;
	} else if (z <= 3.6e+45) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.6e+67:
		tmp = z * x
	elif z <= -4.2e-278:
		tmp = y * t
	elif z <= 5e-48:
		tmp = x
	elif z <= 3.6e+45:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.6e+67)
		tmp = Float64(z * x);
	elseif (z <= -4.2e-278)
		tmp = Float64(y * t);
	elseif (z <= 5e-48)
		tmp = x;
	elseif (z <= 3.6e+45)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.6e+67)
		tmp = z * x;
	elseif (z <= -4.2e-278)
		tmp = y * t;
	elseif (z <= 5e-48)
		tmp = x;
	elseif (z <= 3.6e+45)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.6e+67], N[(z * x), $MachinePrecision], If[LessEqual[z, -4.2e-278], N[(y * t), $MachinePrecision], If[LessEqual[z, 5e-48], x, If[LessEqual[z, 3.6e+45], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e67 or 3.6e45 < z

   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 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in z around inf 46.5%

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

   if -2.6e67 < z < -4.20000000000000027e-278 or 4.9999999999999999e-48 < z < 3.6e45

   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 70.0%

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

   4. Taylor expanded in t around inf 70.5%

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

   5. Taylor expanded in y around inf 37.1%

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

   if -4.20000000000000027e-278 < z < 4.9999999999999999e-48

   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 87.1%

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

   4. Taylor expanded in x around inf 57.1%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-278}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+45}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.015:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.05e+14)
     t_1
     (if (<= z -3.7e-114) (* y (- t x)) (if (<= z 0.015) (+ x (* y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -3.7e-114) {
		tmp = y * (t - x);
	} else if (z <= 0.015) {
		tmp = x + (y * t);
	} 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 * (x - t)
    if (z <= (-1.05d+14)) then
        tmp = t_1
    else if (z <= (-3.7d-114)) then
        tmp = y * (t - x)
    else if (z <= 0.015d0) then
        tmp = x + (y * t)
    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 * (x - t);
	double tmp;
	if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -3.7e-114) {
		tmp = y * (t - x);
	} else if (z <= 0.015) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.05e+14:
		tmp = t_1
	elif z <= -3.7e-114:
		tmp = y * (t - x)
	elif z <= 0.015:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -3.7e-114)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 0.015)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -3.7e-114)
		tmp = y * (t - x);
	elseif (z <= 0.015)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+14], t$95$1, If[LessEqual[z, -3.7e-114], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.015], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e14 or 0.014999999999999999 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in t around 0 96.2%

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

      1. associate-+r+ 96.2%

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

      2. *-rgt-identity 96.2%

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

      3. mul-1-neg 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

      5. distribute-lft-in 96.2%

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

      6. sub-neg 96.2%

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

      7. +-commutative 96.2%

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

      8. mul-1-neg 96.2%

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

      9. sub-neg 96.2%

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

      10. fma-define 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in z around inf 82.2%

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

      1. neg-mul-1 82.2%

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

      2. unsub-neg 82.2%

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

   10. Simplified 82.2%

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

   if -1.05e14 < z < -3.69999999999999965e-114

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 94.1%

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

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in t around 0 88.2%

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

      1. associate-+r+ 88.2%

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

      2. *-rgt-identity 88.2%

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

      3. mul-1-neg 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

      5. distribute-lft-in 88.1%

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

      6. sub-neg 88.1%

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

      7. +-commutative 88.1%

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

      8. mul-1-neg 88.1%

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

      9. sub-neg 88.1%

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

      10. fma-define 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in y around inf 83.2%

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

      1. neg-mul-1 83.2%

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

      2. unsub-neg 83.2%

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

   10. Simplified 83.2%

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

   if -3.69999999999999965e-114 < z < 0.014999999999999999

   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 81.8%

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

   4. Taylor expanded in z around 0 74.7%

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

      1. *-commutative 74.7%

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

   6. Simplified 74.7%

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

Alternative 7: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-81} \lor \neg \left(t \leq 2.1 \cdot 10^{-97}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.8e-81) (not (<= t 2.1e-97)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.8e-81) || !(t <= 2.1e-97)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 ((t <= (-8.8d-81)) .or. (.not. (t <= 2.1d-97))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.8e-81) || !(t <= 2.1e-97)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.8e-81) or not (t <= 2.1e-97):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.8e-81) || !(t <= 2.1e-97))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.8e-81) || ~((t <= 2.1e-97)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.8e-81], N[Not[LessEqual[t, 2.1e-97]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.7999999999999997e-81 or 2.1000000000000001e-97 < t

   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 86.0%

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

   if -8.7999999999999997e-81 < t < 2.1000000000000001e-97

   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 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   5. Simplified 89.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-81} \lor \neg \left(t \leq 2.1 \cdot 10^{-97}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7600000000000 \lor \neg \left(z \leq 0.112\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7600000000000.0) (not (<= z 0.112)))
   (* z (- x t))
   (- x (* y (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7600000000000.0) || !(z <= 0.112)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7600000000000.0d0)) .or. (.not. (z <= 0.112d0))) then
        tmp = z * (x - t)
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7600000000000.0) || !(z <= 0.112)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7600000000000.0) or not (z <= 0.112):
		tmp = z * (x - t)
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7600000000000.0) || !(z <= 0.112))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7600000000000.0) || ~((z <= 0.112)))
		tmp = z * (x - t);
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7600000000000.0], N[Not[LessEqual[z, 0.112]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6e12 or 0.112000000000000002 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in t around 0 96.2%

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

      1. associate-+r+ 96.2%

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

      2. *-rgt-identity 96.2%

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

      3. mul-1-neg 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

      5. distribute-lft-in 96.2%

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

      6. sub-neg 96.2%

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

      7. +-commutative 96.2%

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

      8. mul-1-neg 96.2%

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

      9. sub-neg 96.2%

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

      10. fma-define 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in z around inf 82.2%

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

      1. neg-mul-1 82.2%

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

      2. unsub-neg 82.2%

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

   10. Simplified 82.2%

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

   if -7.6e12 < z < 0.112000000000000002

   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 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7600000000000 \lor \neg \left(z \leq 0.112\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+56} \lor \neg \left(t \leq 10^{+87}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.4e+56) (not (<= t 1e+87)))
   (* (- y z) t)
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.4e+56) || !(t <= 1e+87)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 ((t <= (-4.4d+56)) .or. (.not. (t <= 1d+87))) then
        tmp = (y - z) * t
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.4e+56) || !(t <= 1e+87)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.4e+56) or not (t <= 1e+87):
		tmp = (y - z) * t
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.4e+56) || !(t <= 1e+87))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.4e+56) || ~((t <= 1e+87)))
		tmp = (y - z) * t;
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.4e+56], N[Not[LessEqual[t, 1e+87]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.40000000000000032e56 or 9.9999999999999996e86 < t

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in t around 0 93.6%

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

      1. associate-+r+ 93.6%

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

      2. *-rgt-identity 93.6%

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

      3. mul-1-neg 93.6%

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

      4. distribute-rgt-neg-in 93.6%

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

      5. distribute-lft-in 93.6%

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

      6. sub-neg 93.6%

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

      7. +-commutative 93.6%

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

      8. mul-1-neg 93.6%

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

      9. sub-neg 93.6%

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

      10. fma-define 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in x around 0 88.6%

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

   if -4.40000000000000032e56 < t < 9.9999999999999996e86

   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 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

   5. Simplified 77.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+56} \lor \neg \left(t \leq 10^{+87}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \left(\left(y + \frac{x}{t}\right) - z\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.15e-85)
   (* t (- (+ y (/ x t)) z))
   (if (<= t 4.4e-99) (* x (+ (- z y) 1.0)) (+ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e-85) {
		tmp = t * ((y + (x / t)) - z);
	} else if (t <= 4.4e-99) {
		tmp = x * ((z - y) + 1.0);
	} 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 (t <= (-1.15d-85)) then
        tmp = t * ((y + (x / t)) - z)
    else if (t <= 4.4d-99) then
        tmp = x * ((z - y) + 1.0d0)
    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 (t <= -1.15e-85) {
		tmp = t * ((y + (x / t)) - z);
	} else if (t <= 4.4e-99) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.15e-85:
		tmp = t * ((y + (x / t)) - z)
	elif t <= 4.4e-99:
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.15e-85)
		tmp = Float64(t * Float64(Float64(y + Float64(x / t)) - z));
	elseif (t <= 4.4e-99)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.15e-85)
		tmp = t * ((y + (x / t)) - z);
	elseif (t <= 4.4e-99)
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.15e-85], N[(t * N[(N[(y + N[(x / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-99], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e-85

   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 86.7%

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

   4. Taylor expanded in t around inf 89.1%

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

   if -1.15e-85 < t < 4.40000000000000009e-99

   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 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   5. Simplified 89.5%

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

   if 4.40000000000000009e-99 < t

   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 85.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \left(\left(y + \frac{x}{t}\right) - z\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-46} \lor \neg \left(t \leq 4.5 \cdot 10^{-57}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.6e-46) (not (<= t 4.5e-57))) (* (- y z) t) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.6e-46) || !(t <= 4.5e-57)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	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 ((t <= (-3.6d-46)) .or. (.not. (t <= 4.5d-57))) then
        tmp = (y - z) * t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.6e-46) || !(t <= 4.5e-57)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.6e-46) or not (t <= 4.5e-57):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.6e-46) || !(t <= 4.5e-57))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.6e-46) || ~((t <= 4.5e-57)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.6e-46], N[Not[LessEqual[t, 4.5e-57]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6e-46 or 4.49999999999999973e-57 < t

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 97.9%

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in t around 0 95.9%

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

      1. associate-+r+ 95.9%

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

      2. *-rgt-identity 95.9%

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

      3. mul-1-neg 95.9%

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

      4. distribute-rgt-neg-in 95.9%

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

      5. distribute-lft-in 95.9%

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

      6. sub-neg 95.9%

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

      7. +-commutative 95.9%

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

      8. mul-1-neg 95.9%

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

      9. sub-neg 95.9%

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

      10. fma-define 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in x around 0 73.2%

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

   if -3.6e-46 < t < 4.49999999999999973e-57

   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 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in y around 0 65.9%

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

      1. +-commutative 65.9%

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

   8. Simplified 65.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-46} \lor \neg \left(t \leq 4.5 \cdot 10^{-57}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-118} \lor \neg \left(t \leq 4.4 \cdot 10^{-130}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3e-118) (not (<= t 4.4e-130))) (* (- y z) t) (* z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3e-118) || !(t <= 4.4e-130)) {
		tmp = (y - z) * t;
	} else {
		tmp = z * 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 ((t <= (-3d-118)) .or. (.not. (t <= 4.4d-130))) then
        tmp = (y - z) * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3e-118) || !(t <= 4.4e-130)) {
		tmp = (y - z) * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3e-118) or not (t <= 4.4e-130):
		tmp = (y - z) * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3e-118) || !(t <= 4.4e-130))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3e-118) || ~((t <= 4.4e-130)))
		tmp = (y - z) * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3e-118], N[Not[LessEqual[t, 4.4e-130]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.00000000000000018e-118 or 4.3999999999999997e-130 < t

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in t around 0 96.5%

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

      1. associate-+r+ 96.5%

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

      2. *-rgt-identity 96.5%

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

      3. mul-1-neg 96.5%

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

      4. distribute-rgt-neg-in 96.5%

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

      5. distribute-lft-in 96.5%

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

      6. sub-neg 96.5%

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

      7. +-commutative 96.5%

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

      8. mul-1-neg 96.5%

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

      9. sub-neg 96.5%

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

      10. fma-define 98.2%

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

   7. Simplified 98.2%

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

   8. Taylor expanded in x around 0 67.2%

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

   if -3.00000000000000018e-118 < t < 4.3999999999999997e-130

   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 93.3%

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

      1. mul-1-neg 93.3%

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

      2. unsub-neg 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in z around inf 45.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-118} \lor \neg \left(t \leq 4.4 \cdot 10^{-130}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-140} \lor \neg \left(y \leq 4.8 \cdot 10^{-43}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e-140) (not (<= y 4.8e-43))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-140) || !(y <= 4.8e-43)) {
		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 <= (-1.02d-140)) .or. (.not. (y <= 4.8d-43))) 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 <= -1.02e-140) || !(y <= 4.8e-43)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e-140) or not (y <= 4.8e-43):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e-140) || !(y <= 4.8e-43))
		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 <= -1.02e-140) || ~((y <= 4.8e-43)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e-140], N[Not[LessEqual[y, 4.8e-43]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.01999999999999995e-140 or 4.8000000000000004e-43 < y

   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 60.1%

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

   4. Taylor expanded in t around inf 65.1%

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

   5. Taylor expanded in y around inf 36.3%

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

   if -1.01999999999999995e-140 < y < 4.8000000000000004e-43

   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 74.0%

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

   4. Taylor expanded in x around inf 38.7%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-140} \lor \neg \left(y \leq 4.8 \cdot 10^{-43}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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 15: 18.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 66.0%

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

4. Taylor expanded in x around inf 20.2%

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

Developer Target 1: 96.3% 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 2024157 
(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))))