Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

Alternatives: 12

Speedup: 1.0×

• 34.2% 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-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: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x + z \cdot x\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-122}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (+ x (* z x))))
   (if (<= z -7.8e+267)
     t_1
     (if (<= z -5.6e+236)
       t_2
       (if (<= z -9.4e+204)
         t_1
         (if (<= z -1.3e+28)
           t_2
           (if (<= z -2.7e-122)
             (- x (* y x))
             (if (<= z 9.5e+67) (+ x (* y t)) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x + (z * x);
	double tmp;
	if (z <= -7.8e+267) {
		tmp = t_1;
	} else if (z <= -5.6e+236) {
		tmp = t_2;
	} else if (z <= -9.4e+204) {
		tmp = t_1;
	} else if (z <= -1.3e+28) {
		tmp = t_2;
	} else if (z <= -2.7e-122) {
		tmp = x - (y * x);
	} else if (z <= 9.5e+67) {
		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) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x + (z * x)
    if (z <= (-7.8d+267)) then
        tmp = t_1
    else if (z <= (-5.6d+236)) then
        tmp = t_2
    else if (z <= (-9.4d+204)) then
        tmp = t_1
    else if (z <= (-1.3d+28)) then
        tmp = t_2
    else if (z <= (-2.7d-122)) then
        tmp = x - (y * x)
    else if (z <= 9.5d+67) 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 * -t;
	double t_2 = x + (z * x);
	double tmp;
	if (z <= -7.8e+267) {
		tmp = t_1;
	} else if (z <= -5.6e+236) {
		tmp = t_2;
	} else if (z <= -9.4e+204) {
		tmp = t_1;
	} else if (z <= -1.3e+28) {
		tmp = t_2;
	} else if (z <= -2.7e-122) {
		tmp = x - (y * x);
	} else if (z <= 9.5e+67) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x + (z * x)
	tmp = 0
	if z <= -7.8e+267:
		tmp = t_1
	elif z <= -5.6e+236:
		tmp = t_2
	elif z <= -9.4e+204:
		tmp = t_1
	elif z <= -1.3e+28:
		tmp = t_2
	elif z <= -2.7e-122:
		tmp = x - (y * x)
	elif z <= 9.5e+67:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x + Float64(z * x))
	tmp = 0.0
	if (z <= -7.8e+267)
		tmp = t_1;
	elseif (z <= -5.6e+236)
		tmp = t_2;
	elseif (z <= -9.4e+204)
		tmp = t_1;
	elseif (z <= -1.3e+28)
		tmp = t_2;
	elseif (z <= -2.7e-122)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 9.5e+67)
		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 * -t;
	t_2 = x + (z * x);
	tmp = 0.0;
	if (z <= -7.8e+267)
		tmp = t_1;
	elseif (z <= -5.6e+236)
		tmp = t_2;
	elseif (z <= -9.4e+204)
		tmp = t_1;
	elseif (z <= -1.3e+28)
		tmp = t_2;
	elseif (z <= -2.7e-122)
		tmp = x - (y * x);
	elseif (z <= 9.5e+67)
		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 * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+267], t$95$1, If[LessEqual[z, -5.6e+236], t$95$2, If[LessEqual[z, -9.4e+204], t$95$1, If[LessEqual[z, -1.3e+28], t$95$2, If[LessEqual[z, -2.7e-122], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+67], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.79999999999999961e267 or -5.59999999999999985e236 < z < -9.4000000000000003e204 or 9.5000000000000002e67 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 66.5%

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

   3. Taylor expanded in y around 0 60.3%

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

      1. associate-*r* 60.3%

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

      2. neg-mul-1 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around 0 59.5%

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

      1. associate-*r* 59.5%

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

      2. mul-1-neg 59.5%

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

   8. Simplified 59.5%

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

   if -7.79999999999999961e267 < z < -5.59999999999999985e236 or -9.4000000000000003e204 < z < -1.3000000000000001e28

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-rgt-neg-out 73.4%

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

      3. fma-def 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in t around 0 56.9%

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

   if -1.3000000000000001e28 < z < -2.70000000000000009e-122

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. distribute-lft-out-- 75.6%

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

      5. *-rgt-identity 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in y around inf 70.8%

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

   if -2.70000000000000009e-122 < z < 9.5000000000000002e67

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.4%

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

   3. Taylor expanded in z around 0 73.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+267}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+236}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+204}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-122}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 3: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x + z \cdot x\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-122}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (+ x (* z x))))
   (if (<= z -6.8e+267)
     t_1
     (if (<= z -4.1e+237)
       t_2
       (if (<= z -4.5e+205)
         t_1
         (if (<= z -1.06e+28)
           t_2
           (if (<= z -2.75e-122)
             (- x (* y x))
             (if (<= z 9.5e+65) (+ x (* y t)) (- x (* z t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x + (z * x);
	double tmp;
	if (z <= -6.8e+267) {
		tmp = t_1;
	} else if (z <= -4.1e+237) {
		tmp = t_2;
	} else if (z <= -4.5e+205) {
		tmp = t_1;
	} else if (z <= -1.06e+28) {
		tmp = t_2;
	} else if (z <= -2.75e-122) {
		tmp = x - (y * x);
	} else if (z <= 9.5e+65) {
		tmp = x + (y * t);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x + (z * x)
    if (z <= (-6.8d+267)) then
        tmp = t_1
    else if (z <= (-4.1d+237)) then
        tmp = t_2
    else if (z <= (-4.5d+205)) then
        tmp = t_1
    else if (z <= (-1.06d+28)) then
        tmp = t_2
    else if (z <= (-2.75d-122)) then
        tmp = x - (y * x)
    else if (z <= 9.5d+65) then
        tmp = x + (y * t)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x + (z * x);
	double tmp;
	if (z <= -6.8e+267) {
		tmp = t_1;
	} else if (z <= -4.1e+237) {
		tmp = t_2;
	} else if (z <= -4.5e+205) {
		tmp = t_1;
	} else if (z <= -1.06e+28) {
		tmp = t_2;
	} else if (z <= -2.75e-122) {
		tmp = x - (y * x);
	} else if (z <= 9.5e+65) {
		tmp = x + (y * t);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x + (z * x)
	tmp = 0
	if z <= -6.8e+267:
		tmp = t_1
	elif z <= -4.1e+237:
		tmp = t_2
	elif z <= -4.5e+205:
		tmp = t_1
	elif z <= -1.06e+28:
		tmp = t_2
	elif z <= -2.75e-122:
		tmp = x - (y * x)
	elif z <= 9.5e+65:
		tmp = x + (y * t)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x + Float64(z * x))
	tmp = 0.0
	if (z <= -6.8e+267)
		tmp = t_1;
	elseif (z <= -4.1e+237)
		tmp = t_2;
	elseif (z <= -4.5e+205)
		tmp = t_1;
	elseif (z <= -1.06e+28)
		tmp = t_2;
	elseif (z <= -2.75e-122)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 9.5e+65)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x + (z * x);
	tmp = 0.0;
	if (z <= -6.8e+267)
		tmp = t_1;
	elseif (z <= -4.1e+237)
		tmp = t_2;
	elseif (z <= -4.5e+205)
		tmp = t_1;
	elseif (z <= -1.06e+28)
		tmp = t_2;
	elseif (z <= -2.75e-122)
		tmp = x - (y * x);
	elseif (z <= 9.5e+65)
		tmp = x + (y * t);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+267], t$95$1, If[LessEqual[z, -4.1e+237], t$95$2, If[LessEqual[z, -4.5e+205], t$95$1, If[LessEqual[z, -1.06e+28], t$95$2, If[LessEqual[z, -2.75e-122], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+65], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.79999999999999964e267 or -4.10000000000000003e237 < z < -4.50000000000000035e205

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.2%

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

   3. Taylor expanded in y around 0 82.3%

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

      1. associate-*r* 82.3%

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

      2. neg-mul-1 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in x around 0 82.3%

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

      1. associate-*r* 82.3%

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

      2. mul-1-neg 82.3%

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

   8. Simplified 82.3%

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

   if -6.79999999999999964e267 < z < -4.10000000000000003e237 or -4.50000000000000035e205 < z < -1.0600000000000001e28

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-rgt-neg-out 73.4%

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

      3. fma-def 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in t around 0 56.9%

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

   if -1.0600000000000001e28 < z < -2.75000000000000026e-122

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. distribute-lft-out-- 75.6%

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

      5. *-rgt-identity 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in y around inf 70.8%

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

   if -2.75000000000000026e-122 < z < 9.5000000000000005e65

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.1%

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

   3. Taylor expanded in z around 0 74.2%

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

   if 9.5000000000000005e65 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 54.3%

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

   3. Taylor expanded in y around 0 46.9%

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

      1. associate-*r* 46.9%

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

      2. neg-mul-1 46.9%

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

   5. Simplified 46.9%

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

      1. add-sqr-sqrt 19.5%

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

      2. fma-def 19.5%

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

      3. distribute-lft-neg-out 19.5%

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

      4. add-sqr-sqrt 2.9%

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

      5. sqrt-unprod 3.5%

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

      6. sqr-neg 3.5%

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

      7. sqrt-unprod 0.6%

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

      8. add-sqr-sqrt 1.4%

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

      9. fma-neg 1.4%

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

      10. add-sqr-sqrt 4.5%

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

      11. *-commutative 4.5%

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

      12. add-sqr-sqrt 3.4%

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

      13. sqrt-unprod 16.9%

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

      14. sqr-neg 16.9%

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

      15. sqrt-unprod 13.5%

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

      16. add-sqr-sqrt 46.9%

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

   7. Applied egg-rr 46.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+267}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+237}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+28}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-122}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 4: 70.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ t_2 := x - y \cdot x\\ t_3 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))) (t_2 (- x (* y x))) (t_3 (+ x (* (- y z) t))))
   (if (<= t -6.5e-122)
     t_3
     (if (<= t -3.6e-205)
       t_1
       (if (<= t 2.6e-168)
         t_2
         (if (<= t 1.5e-76) t_1 (if (<= t 2.8e-62) t_2 t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x - (y * x);
	double t_3 = x + ((y - z) * t);
	double tmp;
	if (t <= -6.5e-122) {
		tmp = t_3;
	} else if (t <= -3.6e-205) {
		tmp = t_1;
	} else if (t <= 2.6e-168) {
		tmp = t_2;
	} else if (t <= 1.5e-76) {
		tmp = t_1;
	} else if (t <= 2.8e-62) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x + (z * x)
    t_2 = x - (y * x)
    t_3 = x + ((y - z) * t)
    if (t <= (-6.5d-122)) then
        tmp = t_3
    else if (t <= (-3.6d-205)) then
        tmp = t_1
    else if (t <= 2.6d-168) then
        tmp = t_2
    else if (t <= 1.5d-76) then
        tmp = t_1
    else if (t <= 2.8d-62) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x - (y * x);
	double t_3 = x + ((y - z) * t);
	double tmp;
	if (t <= -6.5e-122) {
		tmp = t_3;
	} else if (t <= -3.6e-205) {
		tmp = t_1;
	} else if (t <= 2.6e-168) {
		tmp = t_2;
	} else if (t <= 1.5e-76) {
		tmp = t_1;
	} else if (t <= 2.8e-62) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	t_2 = x - (y * x)
	t_3 = x + ((y - z) * t)
	tmp = 0
	if t <= -6.5e-122:
		tmp = t_3
	elif t <= -3.6e-205:
		tmp = t_1
	elif t <= 2.6e-168:
		tmp = t_2
	elif t <= 1.5e-76:
		tmp = t_1
	elif t <= 2.8e-62:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	t_2 = Float64(x - Float64(y * x))
	t_3 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t <= -6.5e-122)
		tmp = t_3;
	elseif (t <= -3.6e-205)
		tmp = t_1;
	elseif (t <= 2.6e-168)
		tmp = t_2;
	elseif (t <= 1.5e-76)
		tmp = t_1;
	elseif (t <= 2.8e-62)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	t_2 = x - (y * x);
	t_3 = x + ((y - z) * t);
	tmp = 0.0;
	if (t <= -6.5e-122)
		tmp = t_3;
	elseif (t <= -3.6e-205)
		tmp = t_1;
	elseif (t <= 2.6e-168)
		tmp = t_2;
	elseif (t <= 1.5e-76)
		tmp = t_1;
	elseif (t <= 2.8e-62)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e-122], t$95$3, If[LessEqual[t, -3.6e-205], t$95$1, If[LessEqual[t, 2.6e-168], t$95$2, If[LessEqual[t, 1.5e-76], t$95$1, If[LessEqual[t, 2.8e-62], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.49999999999999965e-122 or 2.80000000000000002e-62 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.4%

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

   if -6.49999999999999965e-122 < t < -3.5999999999999998e-205 or 2.6000000000000001e-168 < t < 1.50000000000000012e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-rgt-neg-out 73.1%

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

      3. fma-def 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in t around 0 69.4%

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

   if -3.5999999999999998e-205 < t < 2.6000000000000001e-168 or 1.50000000000000012e-76 < t < 2.80000000000000002e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.5%

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

      1. *-commutative 94.5%

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

      2. mul-1-neg 94.5%

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

      3. unsub-neg 94.5%

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

      4. distribute-lft-out-- 94.5%

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

      5. *-rgt-identity 94.5%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in y around inf 81.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-122}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-205}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-168}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-76}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-62}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 5: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x + z \cdot x\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+68}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (+ x (* z x))))
   (if (<= z -6.8e+267)
     t_1
     (if (<= z -6e+236)
       t_2
       (if (<= z -6.4e+205)
         t_1
         (if (<= z -4.5e+18) t_2 (if (<= z 1.25e+68) (+ x (* y t)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x + (z * x);
	double tmp;
	if (z <= -6.8e+267) {
		tmp = t_1;
	} else if (z <= -6e+236) {
		tmp = t_2;
	} else if (z <= -6.4e+205) {
		tmp = t_1;
	} else if (z <= -4.5e+18) {
		tmp = t_2;
	} else if (z <= 1.25e+68) {
		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) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x + (z * x)
    if (z <= (-6.8d+267)) then
        tmp = t_1
    else if (z <= (-6d+236)) then
        tmp = t_2
    else if (z <= (-6.4d+205)) then
        tmp = t_1
    else if (z <= (-4.5d+18)) then
        tmp = t_2
    else if (z <= 1.25d+68) 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 * -t;
	double t_2 = x + (z * x);
	double tmp;
	if (z <= -6.8e+267) {
		tmp = t_1;
	} else if (z <= -6e+236) {
		tmp = t_2;
	} else if (z <= -6.4e+205) {
		tmp = t_1;
	} else if (z <= -4.5e+18) {
		tmp = t_2;
	} else if (z <= 1.25e+68) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x + (z * x)
	tmp = 0
	if z <= -6.8e+267:
		tmp = t_1
	elif z <= -6e+236:
		tmp = t_2
	elif z <= -6.4e+205:
		tmp = t_1
	elif z <= -4.5e+18:
		tmp = t_2
	elif z <= 1.25e+68:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x + Float64(z * x))
	tmp = 0.0
	if (z <= -6.8e+267)
		tmp = t_1;
	elseif (z <= -6e+236)
		tmp = t_2;
	elseif (z <= -6.4e+205)
		tmp = t_1;
	elseif (z <= -4.5e+18)
		tmp = t_2;
	elseif (z <= 1.25e+68)
		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 * -t;
	t_2 = x + (z * x);
	tmp = 0.0;
	if (z <= -6.8e+267)
		tmp = t_1;
	elseif (z <= -6e+236)
		tmp = t_2;
	elseif (z <= -6.4e+205)
		tmp = t_1;
	elseif (z <= -4.5e+18)
		tmp = t_2;
	elseif (z <= 1.25e+68)
		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 * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+267], t$95$1, If[LessEqual[z, -6e+236], t$95$2, If[LessEqual[z, -6.4e+205], t$95$1, If[LessEqual[z, -4.5e+18], t$95$2, If[LessEqual[z, 1.25e+68], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999964e267 or -5.9999999999999996e236 < z < -6.39999999999999993e205 or 1.2500000000000001e68 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 66.5%

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

   3. Taylor expanded in y around 0 60.3%

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

      1. associate-*r* 60.3%

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

      2. neg-mul-1 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around 0 59.5%

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

      1. associate-*r* 59.5%

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

      2. mul-1-neg 59.5%

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

   8. Simplified 59.5%

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

   if -6.79999999999999964e267 < z < -5.9999999999999996e236 or -6.39999999999999993e205 < z < -4.5e18

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. distribute-rgt-neg-out 72.2%

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

      3. fma-def 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in t around 0 56.6%

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

   if -4.5e18 < z < 1.2500000000000001e68

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.9%

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

   3. Taylor expanded in z around 0 68.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+267}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+236}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+68}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 6: 38.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-61}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -8e-17)
     t_1
     (if (<= z -6e-156)
       x
       (if (<= z 2.9e-61)
         (* y t)
         (if (<= z 1.52e-18) x (if (<= z 5.5e+66) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -8e-17) {
		tmp = t_1;
	} else if (z <= -6e-156) {
		tmp = x;
	} else if (z <= 2.9e-61) {
		tmp = y * t;
	} else if (z <= 1.52e-18) {
		tmp = x;
	} else if (z <= 5.5e+66) {
		tmp = 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 * -t
    if (z <= (-8d-17)) then
        tmp = t_1
    else if (z <= (-6d-156)) then
        tmp = x
    else if (z <= 2.9d-61) then
        tmp = y * t
    else if (z <= 1.52d-18) then
        tmp = x
    else if (z <= 5.5d+66) then
        tmp = 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 * -t;
	double tmp;
	if (z <= -8e-17) {
		tmp = t_1;
	} else if (z <= -6e-156) {
		tmp = x;
	} else if (z <= 2.9e-61) {
		tmp = y * t;
	} else if (z <= 1.52e-18) {
		tmp = x;
	} else if (z <= 5.5e+66) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -8e-17:
		tmp = t_1
	elif z <= -6e-156:
		tmp = x
	elif z <= 2.9e-61:
		tmp = y * t
	elif z <= 1.52e-18:
		tmp = x
	elif z <= 5.5e+66:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -8e-17)
		tmp = t_1;
	elseif (z <= -6e-156)
		tmp = x;
	elseif (z <= 2.9e-61)
		tmp = Float64(y * t);
	elseif (z <= 1.52e-18)
		tmp = x;
	elseif (z <= 5.5e+66)
		tmp = Float64(y * t);
	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 <= -8e-17)
		tmp = t_1;
	elseif (z <= -6e-156)
		tmp = x;
	elseif (z <= 2.9e-61)
		tmp = y * t;
	elseif (z <= 1.52e-18)
		tmp = x;
	elseif (z <= 5.5e+66)
		tmp = y * t;
	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, -8e-17], t$95$1, If[LessEqual[z, -6e-156], x, If[LessEqual[z, 2.9e-61], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.52e-18], x, If[LessEqual[z, 5.5e+66], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.00000000000000057e-17 or 5.5e66 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 53.7%

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

   3. Taylor expanded in y around 0 44.9%

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

      1. associate-*r* 44.9%

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

      2. neg-mul-1 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in x around 0 44.0%

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

      1. associate-*r* 44.0%

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

      2. mul-1-neg 44.0%

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

   8. Simplified 44.0%

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

   if -8.00000000000000057e-17 < z < -6e-156 or 2.8999999999999999e-61 < z < 1.52e-18

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.8%

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

   3. Taylor expanded in x around inf 46.4%

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

   if -6e-156 < z < 2.8999999999999999e-61 or 1.52e-18 < z < 5.5e66

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.1%

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

   3. Taylor expanded in z around 0 74.5%

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

   4. Taylor expanded in y around inf 47.9%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-61}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 7: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+67} \lor \neg \left(y \leq 2.15 \cdot 10^{+68}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.8e+67) (not (<= y 2.15e+68)))
   (+ x (* y (- t x)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8e+67) || !(y <= 2.15e+68)) {
		tmp = x + (y * (t - x));
	} 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 ((y <= (-6.8d+67)) .or. (.not. (y <= 2.15d+68))) then
        tmp = x + (y * (t - x))
    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 ((y <= -6.8e+67) || !(y <= 2.15e+68)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.8e+67) or not (y <= 2.15e+68):
		tmp = x + (y * (t - x))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.8e+67) || !(y <= 2.15e+68))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	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 ((y <= -6.8e+67) || ~((y <= 2.15e+68)))
		tmp = x + (y * (t - x));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.8e+67], N[Not[LessEqual[y, 2.15e+68]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000003e67 or 2.1500000000000001e68 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 81.4%

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

   if -6.8000000000000003e67 < y < 2.1500000000000001e68

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+67} \lor \neg \left(y \leq 2.15 \cdot 10^{+68}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 8: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{-96} \lor \neg \left(t \leq 6.5 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.3e-96) (not (<= t 6.5e+29)))
   (+ x (* (- y z) t))
   (- x (* (- y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.3e-96) || !(t <= 6.5e+29)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x - ((y - 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 <= (-5.3d-96)) .or. (.not. (t <= 6.5d+29))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x - ((y - 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 <= -5.3e-96) || !(t <= 6.5e+29)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x - ((y - z) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.3e-96) or not (t <= 6.5e+29):
		tmp = x + ((y - z) * t)
	else:
		tmp = x - ((y - z) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.3e-96) || !(t <= 6.5e+29))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x - Float64(Float64(y - z) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.3e-96) || ~((t <= 6.5e+29)))
		tmp = x + ((y - z) * t);
	else
		tmp = x - ((y - z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.3e-96], N[Not[LessEqual[t, 6.5e+29]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.3000000000000001e-96 or 6.49999999999999971e29 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 88.1%

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

   if -5.3000000000000001e-96 < t < 6.49999999999999971e29

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.9%

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

      1. *-commutative 87.9%

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

      2. mul-1-neg 87.9%

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

      3. unsub-neg 87.9%

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

      4. distribute-lft-out-- 87.9%

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

      5. *-rgt-identity 87.9%

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

   4. Simplified 87.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{-96} \lor \neg \left(t \leq 6.5 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot x\\ \end{array} \]

Alternative 9: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+172} \lor \neg \left(z \leq 3.7 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.35e+172) (not (<= z 3.7e+70))) (* z (- t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e+172) || !(z <= 3.7e+70)) {
		tmp = z * -t;
	} else {
		tmp = x + (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 ((z <= (-1.35d+172)) .or. (.not. (z <= 3.7d+70))) then
        tmp = z * -t
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e+172) || !(z <= 3.7e+70)) {
		tmp = z * -t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.35e+172) or not (z <= 3.7e+70):
		tmp = z * -t
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.35e+172) || !(z <= 3.7e+70))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.35e+172) || ~((z <= 3.7e+70)))
		tmp = z * -t;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.35e+172], N[Not[LessEqual[z, 3.7e+70]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e172 or 3.69999999999999989e70 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 61.0%

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

   3. Taylor expanded in y around 0 55.4%

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

      1. associate-*r* 55.4%

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

      2. neg-mul-1 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in x around 0 54.8%

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

      1. associate-*r* 54.8%

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

      2. mul-1-neg 54.8%

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

   8. Simplified 54.8%

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

   if -1.35e172 < z < 3.69999999999999989e70

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 70.9%

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

   3. Taylor expanded in z around 0 60.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+172} \lor \neg \left(z \leq 3.7 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 11: 37.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-18) (* y t) (if (<= y 7.4e-39) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-18) {
		tmp = y * t;
	} else if (y <= 7.4e-39) {
		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 <= (-1.4d-18)) then
        tmp = y * t
    else if (y <= 7.4d-39) 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 <= -1.4e-18) {
		tmp = y * t;
	} else if (y <= 7.4e-39) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-18:
		tmp = y * t
	elif y <= 7.4e-39:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-18)
		tmp = Float64(y * t);
	elseif (y <= 7.4e-39)
		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 <= -1.4e-18)
		tmp = y * t;
	elseif (y <= 7.4e-39)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-18], N[(y * t), $MachinePrecision], If[LessEqual[y, 7.4e-39], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000006e-18 or 7.40000000000000029e-39 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 60.3%

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

   3. Taylor expanded in z around 0 42.6%

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

   4. Taylor expanded in y around inf 41.8%

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

   if -1.40000000000000006e-18 < y < 7.40000000000000029e-39

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 76.3%

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

   3. Taylor expanded in x around inf 37.9%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 12: 18.0% 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 67.6%

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

3. Taylor expanded in x around inf 18.9%

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

4. Final simplification 18.9%

   \[\leadsto x \]

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 2023252 
(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))))