Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.7s

Alternatives: 15

Speedup: 1.0×

• 33.9% 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-def 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. Final simplification 100.0%

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

Alternative 2: 39.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{+131}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-115}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -4.8e+268)
     t_1
     (if (<= z -1.38e+131)
       (* z x)
       (if (<= z -1.1e-26)
         t_1
         (if (<= z -3.8e-39)
           (* y (- x))
           (if (<= z -8e-42)
             t_1
             (if (<= z 3.9e-115)
               (* y t)
               (if (<= z 5.2e-43) x (if (<= z 1.36e+247) t_1 (* z x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -4.8e+268) {
		tmp = t_1;
	} else if (z <= -1.38e+131) {
		tmp = z * x;
	} else if (z <= -1.1e-26) {
		tmp = t_1;
	} else if (z <= -3.8e-39) {
		tmp = y * -x;
	} else if (z <= -8e-42) {
		tmp = t_1;
	} else if (z <= 3.9e-115) {
		tmp = y * t;
	} else if (z <= 5.2e-43) {
		tmp = x;
	} else if (z <= 1.36e+247) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-4.8d+268)) then
        tmp = t_1
    else if (z <= (-1.38d+131)) then
        tmp = z * x
    else if (z <= (-1.1d-26)) then
        tmp = t_1
    else if (z <= (-3.8d-39)) then
        tmp = y * -x
    else if (z <= (-8d-42)) then
        tmp = t_1
    else if (z <= 3.9d-115) then
        tmp = y * t
    else if (z <= 5.2d-43) then
        tmp = x
    else if (z <= 1.36d+247) then
        tmp = t_1
    else
        tmp = z * x
    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 <= -4.8e+268) {
		tmp = t_1;
	} else if (z <= -1.38e+131) {
		tmp = z * x;
	} else if (z <= -1.1e-26) {
		tmp = t_1;
	} else if (z <= -3.8e-39) {
		tmp = y * -x;
	} else if (z <= -8e-42) {
		tmp = t_1;
	} else if (z <= 3.9e-115) {
		tmp = y * t;
	} else if (z <= 5.2e-43) {
		tmp = x;
	} else if (z <= 1.36e+247) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -4.8e+268:
		tmp = t_1
	elif z <= -1.38e+131:
		tmp = z * x
	elif z <= -1.1e-26:
		tmp = t_1
	elif z <= -3.8e-39:
		tmp = y * -x
	elif z <= -8e-42:
		tmp = t_1
	elif z <= 3.9e-115:
		tmp = y * t
	elif z <= 5.2e-43:
		tmp = x
	elif z <= 1.36e+247:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -4.8e+268)
		tmp = t_1;
	elseif (z <= -1.38e+131)
		tmp = Float64(z * x);
	elseif (z <= -1.1e-26)
		tmp = t_1;
	elseif (z <= -3.8e-39)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -8e-42)
		tmp = t_1;
	elseif (z <= 3.9e-115)
		tmp = Float64(y * t);
	elseif (z <= 5.2e-43)
		tmp = x;
	elseif (z <= 1.36e+247)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -4.8e+268)
		tmp = t_1;
	elseif (z <= -1.38e+131)
		tmp = z * x;
	elseif (z <= -1.1e-26)
		tmp = t_1;
	elseif (z <= -3.8e-39)
		tmp = y * -x;
	elseif (z <= -8e-42)
		tmp = t_1;
	elseif (z <= 3.9e-115)
		tmp = y * t;
	elseif (z <= 5.2e-43)
		tmp = x;
	elseif (z <= 1.36e+247)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -4.8e+268], t$95$1, If[LessEqual[z, -1.38e+131], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.1e-26], t$95$1, If[LessEqual[z, -3.8e-39], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -8e-42], t$95$1, If[LessEqual[z, 3.9e-115], N[(y * t), $MachinePrecision], If[LessEqual[z, 5.2e-43], x, If[LessEqual[z, 1.36e+247], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.7999999999999999e268 or -1.38e131 < z < -1.1e-26 or -3.8000000000000002e-39 < z < -8.0000000000000003e-42 or 5.2e-43 < z < 1.35999999999999995e247

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 64.2%

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

   3. Taylor expanded in z around inf 45.8%

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

      1. mul-1-neg 45.8%

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

      2. distribute-rgt-neg-out 45.8%

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

   5. Simplified 45.8%

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

   if -4.7999999999999999e268 < z < -1.38e131 or 1.35999999999999995e247 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. distribute-lft-out-- 70.5%

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

      5. *-rgt-identity 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in z around inf 64.8%

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

   if -1.1e-26 < z < -3.8000000000000002e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.3%

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

      1. *-commutative 94.3%

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

      2. mul-1-neg 94.3%

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

      3. unsub-neg 94.3%

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

      4. distribute-lft-out-- 94.3%

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

      5. *-rgt-identity 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in z around 0 94.3%

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

   6. Taylor expanded in y around inf 87.9%

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

      1. mul-1-neg 87.9%

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

      2. distribute-rgt-neg-in 87.9%

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

   8. Simplified 87.9%

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

   if -8.0000000000000003e-42 < z < 3.8999999999999998e-115

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.3%

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

   3. Taylor expanded in y around inf 50.7%

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

   if 3.8999999999999998e-115 < z < 5.2e-43

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.4%

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

   3. Taylor expanded in x around inf 46.6%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+268}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{+131}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-115}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+247}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 53.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot x\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{+130}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-198}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+243}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y x))) (t_2 (* z (- t))))
   (if (<= z -3e+267)
     t_2
     (if (<= z -1.04e+130)
       (* z x)
       (if (<= z -5.2e-23)
         t_2
         (if (<= z -1.02e-36)
           t_1
           (if (<= z 2.15e-198)
             (+ x (* y t))
             (if (<= z 3.1e+56) t_1 (if (<= z 6.2e+243) t_2 (* z x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * x);
	double t_2 = z * -t;
	double tmp;
	if (z <= -3e+267) {
		tmp = t_2;
	} else if (z <= -1.04e+130) {
		tmp = z * x;
	} else if (z <= -5.2e-23) {
		tmp = t_2;
	} else if (z <= -1.02e-36) {
		tmp = t_1;
	} else if (z <= 2.15e-198) {
		tmp = x + (y * t);
	} else if (z <= 3.1e+56) {
		tmp = t_1;
	} else if (z <= 6.2e+243) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * x)
    t_2 = z * -t
    if (z <= (-3d+267)) then
        tmp = t_2
    else if (z <= (-1.04d+130)) then
        tmp = z * x
    else if (z <= (-5.2d-23)) then
        tmp = t_2
    else if (z <= (-1.02d-36)) then
        tmp = t_1
    else if (z <= 2.15d-198) then
        tmp = x + (y * t)
    else if (z <= 3.1d+56) then
        tmp = t_1
    else if (z <= 6.2d+243) then
        tmp = t_2
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * x);
	double t_2 = z * -t;
	double tmp;
	if (z <= -3e+267) {
		tmp = t_2;
	} else if (z <= -1.04e+130) {
		tmp = z * x;
	} else if (z <= -5.2e-23) {
		tmp = t_2;
	} else if (z <= -1.02e-36) {
		tmp = t_1;
	} else if (z <= 2.15e-198) {
		tmp = x + (y * t);
	} else if (z <= 3.1e+56) {
		tmp = t_1;
	} else if (z <= 6.2e+243) {
		tmp = t_2;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * x)
	t_2 = z * -t
	tmp = 0
	if z <= -3e+267:
		tmp = t_2
	elif z <= -1.04e+130:
		tmp = z * x
	elif z <= -5.2e-23:
		tmp = t_2
	elif z <= -1.02e-36:
		tmp = t_1
	elif z <= 2.15e-198:
		tmp = x + (y * t)
	elif z <= 3.1e+56:
		tmp = t_1
	elif z <= 6.2e+243:
		tmp = t_2
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * x))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -3e+267)
		tmp = t_2;
	elseif (z <= -1.04e+130)
		tmp = Float64(z * x);
	elseif (z <= -5.2e-23)
		tmp = t_2;
	elseif (z <= -1.02e-36)
		tmp = t_1;
	elseif (z <= 2.15e-198)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.1e+56)
		tmp = t_1;
	elseif (z <= 6.2e+243)
		tmp = t_2;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * x);
	t_2 = z * -t;
	tmp = 0.0;
	if (z <= -3e+267)
		tmp = t_2;
	elseif (z <= -1.04e+130)
		tmp = z * x;
	elseif (z <= -5.2e-23)
		tmp = t_2;
	elseif (z <= -1.02e-36)
		tmp = t_1;
	elseif (z <= 2.15e-198)
		tmp = x + (y * t);
	elseif (z <= 3.1e+56)
		tmp = t_1;
	elseif (z <= 6.2e+243)
		tmp = t_2;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -3e+267], t$95$2, If[LessEqual[z, -1.04e+130], N[(z * x), $MachinePrecision], If[LessEqual[z, -5.2e-23], t$95$2, If[LessEqual[z, -1.02e-36], t$95$1, If[LessEqual[z, 2.15e-198], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+56], t$95$1, If[LessEqual[z, 6.2e+243], t$95$2, N[(z * x), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9999999999999999e267 or -1.04000000000000005e130 < z < -5.2e-23 or 3.10000000000000005e56 < z < 6.2e243

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 66.2%

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

   3. Taylor expanded in z around inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. distribute-rgt-neg-out 50.7%

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

   5. Simplified 50.7%

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

   if -2.9999999999999999e267 < z < -1.04000000000000005e130 or 6.2e243 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. distribute-lft-out-- 70.5%

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

      5. *-rgt-identity 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in z around inf 64.8%

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

   if -5.2e-23 < z < -1.02e-36 or 2.1500000000000002e-198 < z < 3.10000000000000005e56

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.5%

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

   3. Taylor expanded in t around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. sub-neg 66.1%

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

   5. Simplified 66.1%

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

   if -1.02e-36 < z < 2.1500000000000002e-198

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.5%

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

   3. Taylor expanded in z around 0 70.5%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+267}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{+130}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-36}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-198}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+243}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 4: 43.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-205}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-131}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+112} \lor \neg \left(x \leq 8 \cdot 10^{+238}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))))
   (if (<= x -3.3e-24)
     t_1
     (if (<= x -3.3e-205)
       (* y t)
       (if (<= x -1.95e-285)
         (* z (- t))
         (if (<= x 1.05e-131)
           (* y t)
           (if (or (<= x 2e+112) (not (<= x 8e+238))) t_1 (* y (- x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (x <= -3.3e-24) {
		tmp = t_1;
	} else if (x <= -3.3e-205) {
		tmp = y * t;
	} else if (x <= -1.95e-285) {
		tmp = z * -t;
	} else if (x <= 1.05e-131) {
		tmp = y * t;
	} else if ((x <= 2e+112) || !(x <= 8e+238)) {
		tmp = t_1;
	} else {
		tmp = y * -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) :: t_1
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    if (x <= (-3.3d-24)) then
        tmp = t_1
    else if (x <= (-3.3d-205)) then
        tmp = y * t
    else if (x <= (-1.95d-285)) then
        tmp = z * -t
    else if (x <= 1.05d-131) then
        tmp = y * t
    else if ((x <= 2d+112) .or. (.not. (x <= 8d+238))) then
        tmp = t_1
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (x <= -3.3e-24) {
		tmp = t_1;
	} else if (x <= -3.3e-205) {
		tmp = y * t;
	} else if (x <= -1.95e-285) {
		tmp = z * -t;
	} else if (x <= 1.05e-131) {
		tmp = y * t;
	} else if ((x <= 2e+112) || !(x <= 8e+238)) {
		tmp = t_1;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	tmp = 0
	if x <= -3.3e-24:
		tmp = t_1
	elif x <= -3.3e-205:
		tmp = y * t
	elif x <= -1.95e-285:
		tmp = z * -t
	elif x <= 1.05e-131:
		tmp = y * t
	elif (x <= 2e+112) or not (x <= 8e+238):
		tmp = t_1
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (x <= -3.3e-24)
		tmp = t_1;
	elseif (x <= -3.3e-205)
		tmp = Float64(y * t);
	elseif (x <= -1.95e-285)
		tmp = Float64(z * Float64(-t));
	elseif (x <= 1.05e-131)
		tmp = Float64(y * t);
	elseif ((x <= 2e+112) || !(x <= 8e+238))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	tmp = 0.0;
	if (x <= -3.3e-24)
		tmp = t_1;
	elseif (x <= -3.3e-205)
		tmp = y * t;
	elseif (x <= -1.95e-285)
		tmp = z * -t;
	elseif (x <= 1.05e-131)
		tmp = y * t;
	elseif ((x <= 2e+112) || ~((x <= 8e+238)))
		tmp = t_1;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e-24], t$95$1, If[LessEqual[x, -3.3e-205], N[(y * t), $MachinePrecision], If[LessEqual[x, -1.95e-285], N[(z * (-t)), $MachinePrecision], If[LessEqual[x, 1.05e-131], N[(y * t), $MachinePrecision], If[Or[LessEqual[x, 2e+112], N[Not[LessEqual[x, 8e+238]], $MachinePrecision]], t$95$1, N[(y * (-x)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.29999999999999984e-24 or 1.04999999999999999e-131 < x < 1.9999999999999999e112 or 8.0000000000000004e238 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. mul-1-neg 67.0%

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

      3. unsub-neg 67.0%

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

      4. *-commutative 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in x around -inf 48.8%

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

   if -3.29999999999999984e-24 < x < -3.2999999999999999e-205 or -1.94999999999999993e-285 < x < 1.04999999999999999e-131

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.8%

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

   3. Taylor expanded in y around inf 57.6%

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

   if -3.2999999999999999e-205 < x < -1.94999999999999993e-285

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 91.0%

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

   3. Taylor expanded in z around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-rgt-neg-out 63.2%

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

   5. Simplified 63.2%

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

   if 1.9999999999999999e112 < x < 8.0000000000000004e238

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. mul-1-neg 88.7%

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

      3. unsub-neg 88.7%

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

      4. distribute-lft-out-- 88.6%

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

      5. *-rgt-identity 88.6%

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

   4. Simplified 88.6%

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

   5. Taylor expanded in z around 0 88.6%

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

   6. Taylor expanded in y around inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. distribute-rgt-neg-in 66.2%

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

   8. Simplified 66.2%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-205}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-131}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+112} \lor \neg \left(x \leq 8 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 39.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+129}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -8e+271)
     t_1
     (if (<= z -1.22e+129)
       (* z x)
       (if (<= z -5.8e-41)
         t_1
         (if (<= z 2.2e-113)
           (* y t)
           (if (<= z 9e-43) x (if (<= z 4e+247) t_1 (* z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -8e+271) {
		tmp = t_1;
	} else if (z <= -1.22e+129) {
		tmp = z * x;
	} else if (z <= -5.8e-41) {
		tmp = t_1;
	} else if (z <= 2.2e-113) {
		tmp = y * t;
	} else if (z <= 9e-43) {
		tmp = x;
	} else if (z <= 4e+247) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-8d+271)) then
        tmp = t_1
    else if (z <= (-1.22d+129)) then
        tmp = z * x
    else if (z <= (-5.8d-41)) then
        tmp = t_1
    else if (z <= 2.2d-113) then
        tmp = y * t
    else if (z <= 9d-43) then
        tmp = x
    else if (z <= 4d+247) then
        tmp = t_1
    else
        tmp = z * x
    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 <= -8e+271) {
		tmp = t_1;
	} else if (z <= -1.22e+129) {
		tmp = z * x;
	} else if (z <= -5.8e-41) {
		tmp = t_1;
	} else if (z <= 2.2e-113) {
		tmp = y * t;
	} else if (z <= 9e-43) {
		tmp = x;
	} else if (z <= 4e+247) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -8e+271:
		tmp = t_1
	elif z <= -1.22e+129:
		tmp = z * x
	elif z <= -5.8e-41:
		tmp = t_1
	elif z <= 2.2e-113:
		tmp = y * t
	elif z <= 9e-43:
		tmp = x
	elif z <= 4e+247:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -8e+271)
		tmp = t_1;
	elseif (z <= -1.22e+129)
		tmp = Float64(z * x);
	elseif (z <= -5.8e-41)
		tmp = t_1;
	elseif (z <= 2.2e-113)
		tmp = Float64(y * t);
	elseif (z <= 9e-43)
		tmp = x;
	elseif (z <= 4e+247)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -8e+271)
		tmp = t_1;
	elseif (z <= -1.22e+129)
		tmp = z * x;
	elseif (z <= -5.8e-41)
		tmp = t_1;
	elseif (z <= 2.2e-113)
		tmp = y * t;
	elseif (z <= 9e-43)
		tmp = x;
	elseif (z <= 4e+247)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -8e+271], t$95$1, If[LessEqual[z, -1.22e+129], N[(z * x), $MachinePrecision], If[LessEqual[z, -5.8e-41], t$95$1, If[LessEqual[z, 2.2e-113], N[(y * t), $MachinePrecision], If[LessEqual[z, 9e-43], x, If[LessEqual[z, 4e+247], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.99999999999999962e271 or -1.2200000000000001e129 < z < -5.79999999999999955e-41 or 9.0000000000000005e-43 < z < 3.99999999999999981e247

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 61.4%

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

   3. Taylor expanded in z around inf 43.7%

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

      1. mul-1-neg 43.7%

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

      2. distribute-rgt-neg-out 43.7%

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

   5. Simplified 43.7%

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

   if -7.99999999999999962e271 < z < -1.2200000000000001e129 or 3.99999999999999981e247 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. distribute-lft-out-- 70.5%

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

      5. *-rgt-identity 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in z around inf 64.8%

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

   if -5.79999999999999955e-41 < z < 2.20000000000000004e-113

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.3%

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

   3. Taylor expanded in y around inf 50.7%

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

   if 2.20000000000000004e-113 < z < 9.0000000000000005e-43

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.4%

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

   3. Taylor expanded in x around inf 46.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+271}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+129}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+247}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 6: 53.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 145000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -8.5e+266)
     t_1
     (if (<= z -3.5e+131)
       (* z x)
       (if (<= z -7.2e-24)
         t_1
         (if (<= z 145000.0) (+ x (* y t)) (* x (+ z 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -8.5e+266) {
		tmp = t_1;
	} else if (z <= -3.5e+131) {
		tmp = z * x;
	} else if (z <= -7.2e-24) {
		tmp = t_1;
	} else if (z <= 145000.0) {
		tmp = x + (y * 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-8.5d+266)) then
        tmp = t_1
    else if (z <= (-3.5d+131)) then
        tmp = z * x
    else if (z <= (-7.2d-24)) then
        tmp = t_1
    else if (z <= 145000.0d0) then
        tmp = x + (y * 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 t_1 = z * -t;
	double tmp;
	if (z <= -8.5e+266) {
		tmp = t_1;
	} else if (z <= -3.5e+131) {
		tmp = z * x;
	} else if (z <= -7.2e-24) {
		tmp = t_1;
	} else if (z <= 145000.0) {
		tmp = x + (y * t);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -8.5e+266:
		tmp = t_1
	elif z <= -3.5e+131:
		tmp = z * x
	elif z <= -7.2e-24:
		tmp = t_1
	elif z <= 145000.0:
		tmp = x + (y * t)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -8.5e+266)
		tmp = t_1;
	elseif (z <= -3.5e+131)
		tmp = Float64(z * x);
	elseif (z <= -7.2e-24)
		tmp = t_1;
	elseif (z <= 145000.0)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -8.5e+266)
		tmp = t_1;
	elseif (z <= -3.5e+131)
		tmp = z * x;
	elseif (z <= -7.2e-24)
		tmp = t_1;
	elseif (z <= 145000.0)
		tmp = x + (y * t);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -8.5e+266], t$95$1, If[LessEqual[z, -3.5e+131], N[(z * x), $MachinePrecision], If[LessEqual[z, -7.2e-24], t$95$1, If[LessEqual[z, 145000.0], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.49999999999999955e266 or -3.4999999999999999e131 < z < -7.2000000000000002e-24

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 70.1%

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

   3. Taylor expanded in z around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-rgt-neg-out 50.1%

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

   5. Simplified 50.1%

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

   if -8.49999999999999955e266 < z < -3.4999999999999999e131

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

      4. distribute-lft-out-- 65.4%

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

      5. *-rgt-identity 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in z around inf 58.2%

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

   if -7.2000000000000002e-24 < z < 145000

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.4%

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

   3. Taylor expanded in z around 0 64.5%

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

   if 145000 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.5%

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

      1. +-commutative 82.5%

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

      2. mul-1-neg 82.5%

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

      3. unsub-neg 82.5%

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

      4. *-commutative 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in x around -inf 47.1%

      \[\leadsto \color{blue}{\left(1 + z\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+266}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 145000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 7: 70.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-149}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* t (- z y)))))
   (if (<= t -3.5e-107)
     t_1
     (if (<= t 3.3e-149)
       (- x (* y x))
       (if (<= t 1.16e-64) (* x (+ z 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (t * (z - y));
	double tmp;
	if (t <= -3.5e-107) {
		tmp = t_1;
	} else if (t <= 3.3e-149) {
		tmp = x - (y * x);
	} else if (t <= 1.16e-64) {
		tmp = x * (z + 1.0);
	} 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 = x - (t * (z - y))
    if (t <= (-3.5d-107)) then
        tmp = t_1
    else if (t <= 3.3d-149) then
        tmp = x - (y * x)
    else if (t <= 1.16d-64) then
        tmp = x * (z + 1.0d0)
    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 = x - (t * (z - y));
	double tmp;
	if (t <= -3.5e-107) {
		tmp = t_1;
	} else if (t <= 3.3e-149) {
		tmp = x - (y * x);
	} else if (t <= 1.16e-64) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (t * (z - y))
	tmp = 0
	if t <= -3.5e-107:
		tmp = t_1
	elif t <= 3.3e-149:
		tmp = x - (y * x)
	elif t <= 1.16e-64:
		tmp = x * (z + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(t * Float64(z - y)))
	tmp = 0.0
	if (t <= -3.5e-107)
		tmp = t_1;
	elseif (t <= 3.3e-149)
		tmp = Float64(x - Float64(y * x));
	elseif (t <= 1.16e-64)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (t * (z - y));
	tmp = 0.0;
	if (t <= -3.5e-107)
		tmp = t_1;
	elseif (t <= 3.3e-149)
		tmp = x - (y * x);
	elseif (t <= 1.16e-64)
		tmp = x * (z + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-107], t$95$1, If[LessEqual[t, 3.3e-149], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e-64], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.49999999999999985e-107 or 1.15999999999999992e-64 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.1%

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

   if -3.49999999999999985e-107 < t < 3.30000000000000017e-149

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 71.6%

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

   3. Taylor expanded in t around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. sub-neg 59.5%

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

   5. Simplified 59.5%

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

   if 3.30000000000000017e-149 < t < 1.15999999999999992e-64

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

      4. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in x around -inf 72.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-107}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-149}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]

Alternative 8: 53.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-70}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))))
   (if (<= y -1.35e+48)
     t_1
     (if (<= y 3.2e-70)
       (- x (* z t))
       (if (<= y 2.9e+36) t_1 (if (<= y 3.6e+121) (* y (- x)) (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double tmp;
	if (y <= -1.35e+48) {
		tmp = t_1;
	} else if (y <= 3.2e-70) {
		tmp = x - (z * t);
	} else if (y <= 2.9e+36) {
		tmp = t_1;
	} else if (y <= 3.6e+121) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * t)
    if (y <= (-1.35d+48)) then
        tmp = t_1
    else if (y <= 3.2d-70) then
        tmp = x - (z * t)
    else if (y <= 2.9d+36) then
        tmp = t_1
    else if (y <= 3.6d+121) then
        tmp = y * -x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double tmp;
	if (y <= -1.35e+48) {
		tmp = t_1;
	} else if (y <= 3.2e-70) {
		tmp = x - (z * t);
	} else if (y <= 2.9e+36) {
		tmp = t_1;
	} else if (y <= 3.6e+121) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	tmp = 0
	if y <= -1.35e+48:
		tmp = t_1
	elif y <= 3.2e-70:
		tmp = x - (z * t)
	elif y <= 2.9e+36:
		tmp = t_1
	elif y <= 3.6e+121:
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (y <= -1.35e+48)
		tmp = t_1;
	elseif (y <= 3.2e-70)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 2.9e+36)
		tmp = t_1;
	elseif (y <= 3.6e+121)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	tmp = 0.0;
	if (y <= -1.35e+48)
		tmp = t_1;
	elseif (y <= 3.2e-70)
		tmp = x - (z * t);
	elseif (y <= 2.9e+36)
		tmp = t_1;
	elseif (y <= 3.6e+121)
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+48], t$95$1, If[LessEqual[y, 3.2e-70], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+36], t$95$1, If[LessEqual[y, 3.6e+121], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000002e48 or 3.1999999999999997e-70 < y < 2.9e36

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 60.8%

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

   3. Taylor expanded in z around 0 49.4%

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

   if -1.35000000000000002e48 < y < 3.1999999999999997e-70

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.8%

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

      1. +-commutative 88.8%

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

      2. mul-1-neg 88.8%

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

      3. unsub-neg 88.8%

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

      4. *-commutative 88.8%

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

   4. Simplified 88.8%

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

   5. Taylor expanded in t around inf 66.2%

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

      1. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if 2.9e36 < y < 3.59999999999999981e121

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 71.8%

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

      1. *-commutative 71.8%

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

      2. mul-1-neg 71.8%

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

      3. unsub-neg 71.8%

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

      4. distribute-lft-out-- 71.8%

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

      5. *-rgt-identity 71.8%

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

   4. Simplified 71.8%

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

   5. Taylor expanded in z around 0 67.6%

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

   6. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. distribute-rgt-neg-in 51.7%

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

   8. Simplified 51.7%

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

   if 3.59999999999999981e121 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 67.4%

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

   3. Taylor expanded in y around inf 67.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-70}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 9: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+23} \lor \neg \left(y \leq 0.002\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.7e+23) (not (<= y 0.002)))
   (- x (* y (- x t)))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.7e+23) || !(y <= 0.002)) {
		tmp = x - (y * (x - t));
	} 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 ((y <= (-1.7d+23)) .or. (.not. (y <= 0.002d0))) then
        tmp = x - (y * (x - t))
    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 ((y <= -1.7e+23) || !(y <= 0.002)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.7e+23) or not (y <= 0.002):
		tmp = x - (y * (x - t))
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.7e+23) || !(y <= 0.002))
		tmp = Float64(x - Float64(y * Float64(x - t)));
	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 ((y <= -1.7e+23) || ~((y <= 0.002)))
		tmp = x - (y * (x - t));
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.7e+23], N[Not[LessEqual[y, 0.002]], $MachinePrecision]], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999996e23 or 2e-3 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 83.1%

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

   if -1.69999999999999996e23 < y < 2e-3

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+23} \lor \neg \left(y \leq 0.002\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]

Alternative 10: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-35} \lor \neg \left(t \leq 2.15 \cdot 10^{-13}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e-35) (not (<= t 2.15e-13)))
   (- x (* t (- z y)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-35) || !(t <= 2.15e-13)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (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 ((t <= (-3.5d-35)) .or. (.not. (t <= 2.15d-13))) then
        tmp = x - (t * (z - y))
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-35) || !(t <= 2.15e-13)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e-35) or not (t <= 2.15e-13):
		tmp = x - (t * (z - y))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e-35) || !(t <= 2.15e-13))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e-35) || ~((t <= 2.15e-13)))
		tmp = x - (t * (z - y));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e-35], N[Not[LessEqual[t, 2.15e-13]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999996e-35 or 2.1499999999999999e-13 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.9%

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

   if -3.49999999999999996e-35 < t < 2.1499999999999999e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. *-commutative 78.3%

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

      2. mul-1-neg 78.3%

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

      3. unsub-neg 78.3%

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

      4. distribute-lft-out-- 78.3%

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

      5. *-rgt-identity 78.3%

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

   4. Simplified 78.3%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-35} \lor \neg \left(t \leq 2.15 \cdot 10^{-13}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 11: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+19} \lor \neg \left(y \leq 4.4 \cdot 10^{-26}\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+19) (not (<= y 4.4e-26)))
   (- x (* y (- x t)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+19) || !(y <= 4.4e-26)) {
		tmp = x - (y * (x - t));
	} 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 <= (-1.9d+19)) .or. (.not. (y <= 4.4d-26))) then
        tmp = x - (y * (x - t))
    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 <= -1.9e+19) || !(y <= 4.4e-26)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e+19) or not (y <= 4.4e-26):
		tmp = x - (y * (x - t))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+19) || !(y <= 4.4e-26))
		tmp = Float64(x - Float64(y * Float64(x - t)));
	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 <= -1.9e+19) || ~((y <= 4.4e-26)))
		tmp = x - (y * (x - t));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e+19], N[Not[LessEqual[y, 4.4e-26]], $MachinePrecision]], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e19 or 4.4000000000000002e-26 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 82.6%

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

   if -1.9e19 < y < 4.4000000000000002e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.6%

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

      1. +-commutative 91.6%

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

      2. mul-1-neg 91.6%

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

      3. unsub-neg 91.6%

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

      4. *-commutative 91.6%

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

   4. Simplified 91.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+19} \lor \neg \left(y \leq 4.4 \cdot 10^{-26}\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 12: 38.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-114}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 24:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.5e+61)
   (* z x)
   (if (<= z 2.85e-114) (* y t) (if (<= z 24.0) x (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+61) {
		tmp = z * x;
	} else if (z <= 2.85e-114) {
		tmp = y * t;
	} else if (z <= 24.0) {
		tmp = x;
	} 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 <= (-8.5d+61)) then
        tmp = z * x
    else if (z <= 2.85d-114) then
        tmp = y * t
    else if (z <= 24.0d0) then
        tmp = x
    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 <= -8.5e+61) {
		tmp = z * x;
	} else if (z <= 2.85e-114) {
		tmp = y * t;
	} else if (z <= 24.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.5e+61:
		tmp = z * x
	elif z <= 2.85e-114:
		tmp = y * t
	elif z <= 24.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.5e+61)
		tmp = Float64(z * x);
	elseif (z <= 2.85e-114)
		tmp = Float64(y * t);
	elseif (z <= 24.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.5e+61)
		tmp = z * x;
	elseif (z <= 2.85e-114)
		tmp = y * t;
	elseif (z <= 24.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.5e+61], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.85e-114], N[(y * t), $MachinePrecision], If[LessEqual[z, 24.0], x, N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000035e61 or 24 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 53.8%

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

      1. *-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. distribute-lft-out-- 53.7%

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

      5. *-rgt-identity 53.7%

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

   4. Simplified 53.7%

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

   5. Taylor expanded in z around inf 45.1%

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

   if -8.50000000000000035e61 < z < 2.8499999999999999e-114

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 70.5%

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

   3. Taylor expanded in y around inf 45.1%

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

   if 2.8499999999999999e-114 < z < 24

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.5%

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

   3. Taylor expanded in x around inf 35.5%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-114}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 24:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 13: 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. Final simplification 100.0%

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

Alternative 14: 36.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-109}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e-109) (* y t) (if (<= y 1.85e-38) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-109) {
		tmp = y * t;
	} else if (y <= 1.85e-38) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.5d-109)) then
        tmp = y * t
    else if (y <= 1.85d-38) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-109) {
		tmp = y * t;
	} else if (y <= 1.85e-38) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e-109:
		tmp = y * t
	elif y <= 1.85e-38:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e-109)
		tmp = Float64(y * t);
	elseif (y <= 1.85e-38)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.5e-109)
		tmp = y * t;
	elseif (y <= 1.85e-38)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e-109], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.85e-38], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5e-109 or 1.85e-38 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 58.7%

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

   3. Taylor expanded in y around inf 43.7%

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

   if -3.5e-109 < y < 1.85e-38

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.6%

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

   3. Taylor expanded in x around inf 30.8%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-109}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 15: 17.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 65.3%

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

3. Taylor expanded in x around inf 14.2%

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

4. Final simplification 14.2%

   \[\leadsto x \]

Developer target: 96.6% 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 2023274 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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