Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.3s

Alternatives: 16

Speedup: 1.0×

• 34.0% 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: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+208}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+60}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -950000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-13}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (+ z 1.0))))
   (if (<= y -3.4e+208)
     (* y t)
     (if (<= y -1.02e+71)
       (* y (- x))
       (if (<= y -2.6e+60)
         (* y t)
         (if (<= y -950000.0)
           t_1
           (if (<= y -2.8e-13)
             (* y t)
             (if (<= y -2.65e-92)
               t_2
               (if (<= y -2.5e-187)
                 t_1
                 (if (<= y 1.05e+17) t_2 (* y t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -3.4e+208) {
		tmp = y * t;
	} else if (y <= -1.02e+71) {
		tmp = y * -x;
	} else if (y <= -2.6e+60) {
		tmp = y * t;
	} else if (y <= -950000.0) {
		tmp = t_1;
	} else if (y <= -2.8e-13) {
		tmp = y * t;
	} else if (y <= -2.65e-92) {
		tmp = t_2;
	} else if (y <= -2.5e-187) {
		tmp = t_1;
	} else if (y <= 1.05e+17) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x * (z + 1.0d0)
    if (y <= (-3.4d+208)) then
        tmp = y * t
    else if (y <= (-1.02d+71)) then
        tmp = y * -x
    else if (y <= (-2.6d+60)) then
        tmp = y * t
    else if (y <= (-950000.0d0)) then
        tmp = t_1
    else if (y <= (-2.8d-13)) then
        tmp = y * t
    else if (y <= (-2.65d-92)) then
        tmp = t_2
    else if (y <= (-2.5d-187)) then
        tmp = t_1
    else if (y <= 1.05d+17) then
        tmp = t_2
    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 = z * -t;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -3.4e+208) {
		tmp = y * t;
	} else if (y <= -1.02e+71) {
		tmp = y * -x;
	} else if (y <= -2.6e+60) {
		tmp = y * t;
	} else if (y <= -950000.0) {
		tmp = t_1;
	} else if (y <= -2.8e-13) {
		tmp = y * t;
	} else if (y <= -2.65e-92) {
		tmp = t_2;
	} else if (y <= -2.5e-187) {
		tmp = t_1;
	} else if (y <= 1.05e+17) {
		tmp = t_2;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -3.4e+208:
		tmp = y * t
	elif y <= -1.02e+71:
		tmp = y * -x
	elif y <= -2.6e+60:
		tmp = y * t
	elif y <= -950000.0:
		tmp = t_1
	elif y <= -2.8e-13:
		tmp = y * t
	elif y <= -2.65e-92:
		tmp = t_2
	elif y <= -2.5e-187:
		tmp = t_1
	elif y <= 1.05e+17:
		tmp = t_2
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -3.4e+208)
		tmp = Float64(y * t);
	elseif (y <= -1.02e+71)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -2.6e+60)
		tmp = Float64(y * t);
	elseif (y <= -950000.0)
		tmp = t_1;
	elseif (y <= -2.8e-13)
		tmp = Float64(y * t);
	elseif (y <= -2.65e-92)
		tmp = t_2;
	elseif (y <= -2.5e-187)
		tmp = t_1;
	elseif (y <= 1.05e+17)
		tmp = t_2;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -3.4e+208)
		tmp = y * t;
	elseif (y <= -1.02e+71)
		tmp = y * -x;
	elseif (y <= -2.6e+60)
		tmp = y * t;
	elseif (y <= -950000.0)
		tmp = t_1;
	elseif (y <= -2.8e-13)
		tmp = y * t;
	elseif (y <= -2.65e-92)
		tmp = t_2;
	elseif (y <= -2.5e-187)
		tmp = t_1;
	elseif (y <= 1.05e+17)
		tmp = t_2;
	else
		tmp = y * 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 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+208], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.02e+71], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -2.6e+60], N[(y * t), $MachinePrecision], If[LessEqual[y, -950000.0], t$95$1, If[LessEqual[y, -2.8e-13], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.65e-92], t$95$2, If[LessEqual[y, -2.5e-187], t$95$1, If[LessEqual[y, 1.05e+17], t$95$2, N[(y * t), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.3999999999999998e208 or -1.02000000000000003e71 < y < -2.60000000000000008e60 or -9.5e5 < y < -2.8000000000000002e-13 or 1.05e17 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 95.2%

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

   3. Applied egg-rr 95.2%

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

   4. Taylor expanded in y around inf 86.7%

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

   5. Taylor expanded in x around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. fma-def 88.0%

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

      3. mul-1-neg 88.0%

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

      4. unsub-neg 88.0%

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

      5. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in x around 0 53.5%

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

   if -3.3999999999999998e208 < y < -1.02000000000000003e71

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

   7. Simplified 56.8%

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

   if -2.60000000000000008e60 < y < -9.5e5 or -2.65000000000000015e-92 < y < -2.4999999999999998e-187

   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. add-sqr-sqrt 54.6%

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

      3. associate-*r* 54.5%

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

      4. fma-def 54.5%

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

   3. Applied egg-rr 54.5%

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

   4. Taylor expanded in x around 0 81.4%

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

      1. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in y around 0 71.9%

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

      1. associate-*r* 71.9%

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

      2. mul-1-neg 71.9%

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

   9. Simplified 71.9%

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

   if -2.8000000000000002e-13 < y < -2.65000000000000015e-92 or -2.4999999999999998e-187 < y < 1.05e17

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in y around 0 61.0%

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

      1. +-commutative 61.0%

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

   7. Simplified 61.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+208}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+60}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -950000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-13}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 3: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ t_3 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -245000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-13}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-187}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))) (t_3 (* z (- t))))
   (if (<= y -3.8e+61)
     t_1
     (if (<= y -245000.0)
       t_3
       (if (<= y -4.1e-13)
         (* y t)
         (if (<= y -4.2e-93)
           t_2
           (if (<= y -4.8e-187) t_3 (if (<= y 8e-11) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double t_3 = z * -t;
	double tmp;
	if (y <= -3.8e+61) {
		tmp = t_1;
	} else if (y <= -245000.0) {
		tmp = t_3;
	} else if (y <= -4.1e-13) {
		tmp = y * t;
	} else if (y <= -4.2e-93) {
		tmp = t_2;
	} else if (y <= -4.8e-187) {
		tmp = t_3;
	} else if (y <= 8e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x * (z + 1.0d0)
    t_3 = z * -t
    if (y <= (-3.8d+61)) then
        tmp = t_1
    else if (y <= (-245000.0d0)) then
        tmp = t_3
    else if (y <= (-4.1d-13)) then
        tmp = y * t
    else if (y <= (-4.2d-93)) then
        tmp = t_2
    else if (y <= (-4.8d-187)) then
        tmp = t_3
    else if (y <= 8d-11) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double t_3 = z * -t;
	double tmp;
	if (y <= -3.8e+61) {
		tmp = t_1;
	} else if (y <= -245000.0) {
		tmp = t_3;
	} else if (y <= -4.1e-13) {
		tmp = y * t;
	} else if (y <= -4.2e-93) {
		tmp = t_2;
	} else if (y <= -4.8e-187) {
		tmp = t_3;
	} else if (y <= 8e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * (z + 1.0)
	t_3 = z * -t
	tmp = 0
	if y <= -3.8e+61:
		tmp = t_1
	elif y <= -245000.0:
		tmp = t_3
	elif y <= -4.1e-13:
		tmp = y * t
	elif y <= -4.2e-93:
		tmp = t_2
	elif y <= -4.8e-187:
		tmp = t_3
	elif y <= 8e-11:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x * Float64(z + 1.0))
	t_3 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -3.8e+61)
		tmp = t_1;
	elseif (y <= -245000.0)
		tmp = t_3;
	elseif (y <= -4.1e-13)
		tmp = Float64(y * t);
	elseif (y <= -4.2e-93)
		tmp = t_2;
	elseif (y <= -4.8e-187)
		tmp = t_3;
	elseif (y <= 8e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x * (z + 1.0);
	t_3 = z * -t;
	tmp = 0.0;
	if (y <= -3.8e+61)
		tmp = t_1;
	elseif (y <= -245000.0)
		tmp = t_3;
	elseif (y <= -4.1e-13)
		tmp = y * t;
	elseif (y <= -4.2e-93)
		tmp = t_2;
	elseif (y <= -4.8e-187)
		tmp = t_3;
	elseif (y <= 8e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -3.8e+61], t$95$1, If[LessEqual[y, -245000.0], t$95$3, If[LessEqual[y, -4.1e-13], N[(y * t), $MachinePrecision], If[LessEqual[y, -4.2e-93], t$95$2, If[LessEqual[y, -4.8e-187], t$95$3, If[LessEqual[y, 8e-11], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.79999999999999995e61 or 7.99999999999999952e-11 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in y around inf 89.1%

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

   5. Taylor expanded in x around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. fma-def 91.6%

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

      3. mul-1-neg 91.6%

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

      4. unsub-neg 91.6%

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

      5. *-commutative 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in y around inf 83.8%

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

      1. neg-mul-1 83.8%

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

      2. sub-neg 83.8%

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

   10. Simplified 83.8%

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

   if -3.79999999999999995e61 < y < -245000 or -4.2000000000000002e-93 < y < -4.80000000000000027e-187

   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. add-sqr-sqrt 52.9%

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

      3. associate-*r* 52.8%

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

      4. fma-def 52.8%

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

   3. Applied egg-rr 52.8%

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

   4. Taylor expanded in x around 0 78.8%

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

      1. *-commutative 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in y around 0 69.7%

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

      1. associate-*r* 69.7%

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

      2. mul-1-neg 69.7%

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

   9. Simplified 69.7%

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

   if -245000 < y < -4.1000000000000002e-13

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 97.7%

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

   5. Taylor expanded in x around 0 97.7%

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

      1. +-commutative 97.7%

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

      2. fma-def 97.7%

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

      3. mul-1-neg 97.7%

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

      4. unsub-neg 97.7%

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

      5. *-commutative 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x around 0 91.4%

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

   if -4.1000000000000002e-13 < y < -4.2000000000000002e-93 or -4.80000000000000027e-187 < y < 7.99999999999999952e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. +-commutative 63.1%

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

   7. Simplified 63.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -245000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-13}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 35.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-175}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+210}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* y (- x))))
   (if (<= x -2.7e+86)
     t_2
     (if (<= x -1.55e-279)
       (* y t)
       (if (<= x 1.7e-303)
         t_1
         (if (<= x 1.95e-175)
           (* y t)
           (if (<= x 6.8e+31) t_1 (if (<= x 1.05e+210) (* z x) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = y * -x;
	double tmp;
	if (x <= -2.7e+86) {
		tmp = t_2;
	} else if (x <= -1.55e-279) {
		tmp = y * t;
	} else if (x <= 1.7e-303) {
		tmp = t_1;
	} else if (x <= 1.95e-175) {
		tmp = y * t;
	} else if (x <= 6.8e+31) {
		tmp = t_1;
	} else if (x <= 1.05e+210) {
		tmp = z * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = y * -x
    if (x <= (-2.7d+86)) then
        tmp = t_2
    else if (x <= (-1.55d-279)) then
        tmp = y * t
    else if (x <= 1.7d-303) then
        tmp = t_1
    else if (x <= 1.95d-175) then
        tmp = y * t
    else if (x <= 6.8d+31) then
        tmp = t_1
    else if (x <= 1.05d+210) then
        tmp = z * x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = y * -x;
	double tmp;
	if (x <= -2.7e+86) {
		tmp = t_2;
	} else if (x <= -1.55e-279) {
		tmp = y * t;
	} else if (x <= 1.7e-303) {
		tmp = t_1;
	} else if (x <= 1.95e-175) {
		tmp = y * t;
	} else if (x <= 6.8e+31) {
		tmp = t_1;
	} else if (x <= 1.05e+210) {
		tmp = z * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = y * -x
	tmp = 0
	if x <= -2.7e+86:
		tmp = t_2
	elif x <= -1.55e-279:
		tmp = y * t
	elif x <= 1.7e-303:
		tmp = t_1
	elif x <= 1.95e-175:
		tmp = y * t
	elif x <= 6.8e+31:
		tmp = t_1
	elif x <= 1.05e+210:
		tmp = z * x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -2.7e+86)
		tmp = t_2;
	elseif (x <= -1.55e-279)
		tmp = Float64(y * t);
	elseif (x <= 1.7e-303)
		tmp = t_1;
	elseif (x <= 1.95e-175)
		tmp = Float64(y * t);
	elseif (x <= 6.8e+31)
		tmp = t_1;
	elseif (x <= 1.05e+210)
		tmp = Float64(z * x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = y * -x;
	tmp = 0.0;
	if (x <= -2.7e+86)
		tmp = t_2;
	elseif (x <= -1.55e-279)
		tmp = y * t;
	elseif (x <= 1.7e-303)
		tmp = t_1;
	elseif (x <= 1.95e-175)
		tmp = y * t;
	elseif (x <= 6.8e+31)
		tmp = t_1;
	elseif (x <= 1.05e+210)
		tmp = z * x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -2.7e+86], t$95$2, If[LessEqual[x, -1.55e-279], N[(y * t), $MachinePrecision], If[LessEqual[x, 1.7e-303], t$95$1, If[LessEqual[x, 1.95e-175], N[(y * t), $MachinePrecision], If[LessEqual[x, 6.8e+31], t$95$1, If[LessEqual[x, 1.05e+210], N[(z * x), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.70000000000000018e86 or 1.0499999999999999e210 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

   4. Simplified 95.6%

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

   5. Taylor expanded in y around inf 46.0%

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

      1. mul-1-neg 46.0%

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

   7. Simplified 46.0%

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

   if -2.70000000000000018e86 < x < -1.55e-279 or 1.7e-303 < x < 1.94999999999999999e-175

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 73.2%

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

   5. Taylor expanded in x around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. fma-def 73.2%

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

      3. mul-1-neg 73.2%

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

      4. unsub-neg 73.2%

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

      5. *-commutative 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in x around 0 49.8%

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

   if -1.55e-279 < x < 1.7e-303 or 1.94999999999999999e-175 < x < 6.7999999999999996e31

   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. add-sqr-sqrt 35.2%

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

      3. associate-*r* 35.1%

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

      4. fma-def 35.1%

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

   3. Applied egg-rr 35.1%

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

   4. Taylor expanded in x around 0 70.3%

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

      1. *-commutative 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in y around 0 56.2%

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

      1. associate-*r* 56.2%

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

      2. mul-1-neg 56.2%

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

   9. Simplified 56.2%

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

   if 6.7999999999999996e31 < x < 1.0499999999999999e210

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in z around inf 41.3%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-175}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+210}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 44.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;x \leq -2.66 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-279}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-175}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= x -2.66e+82)
     (* x (- 1.0 y))
     (if (<= x -3.4e-279)
       (* y t)
       (if (<= x 4.3e-302)
         t_1
         (if (<= x 2.3e-175)
           (* y t)
           (if (<= x 1.2e-38) t_1 (* x (+ z 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (x <= -2.66e+82) {
		tmp = x * (1.0 - y);
	} else if (x <= -3.4e-279) {
		tmp = y * t;
	} else if (x <= 4.3e-302) {
		tmp = t_1;
	} else if (x <= 2.3e-175) {
		tmp = y * t;
	} else if (x <= 1.2e-38) {
		tmp = t_1;
	} 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 (x <= (-2.66d+82)) then
        tmp = x * (1.0d0 - y)
    else if (x <= (-3.4d-279)) then
        tmp = y * t
    else if (x <= 4.3d-302) then
        tmp = t_1
    else if (x <= 2.3d-175) then
        tmp = y * t
    else if (x <= 1.2d-38) then
        tmp = t_1
    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 (x <= -2.66e+82) {
		tmp = x * (1.0 - y);
	} else if (x <= -3.4e-279) {
		tmp = y * t;
	} else if (x <= 4.3e-302) {
		tmp = t_1;
	} else if (x <= 2.3e-175) {
		tmp = y * t;
	} else if (x <= 1.2e-38) {
		tmp = t_1;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if x <= -2.66e+82:
		tmp = x * (1.0 - y)
	elif x <= -3.4e-279:
		tmp = y * t
	elif x <= 4.3e-302:
		tmp = t_1
	elif x <= 2.3e-175:
		tmp = y * t
	elif x <= 1.2e-38:
		tmp = t_1
	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 (x <= -2.66e+82)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= -3.4e-279)
		tmp = Float64(y * t);
	elseif (x <= 4.3e-302)
		tmp = t_1;
	elseif (x <= 2.3e-175)
		tmp = Float64(y * t);
	elseif (x <= 1.2e-38)
		tmp = t_1;
	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 (x <= -2.66e+82)
		tmp = x * (1.0 - y);
	elseif (x <= -3.4e-279)
		tmp = y * t;
	elseif (x <= 4.3e-302)
		tmp = t_1;
	elseif (x <= 2.3e-175)
		tmp = y * t;
	elseif (x <= 1.2e-38)
		tmp = t_1;
	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[x, -2.66e+82], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e-279], N[(y * t), $MachinePrecision], If[LessEqual[x, 4.3e-302], t$95$1, If[LessEqual[x, 2.3e-175], N[(y * t), $MachinePrecision], If[LessEqual[x, 1.2e-38], t$95$1, N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.6600000000000001e82

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 93.5%

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

      1. mul-1-neg 93.5%

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

      2. unsub-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in z around 0 67.2%

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

   if -2.6600000000000001e82 < x < -3.40000000000000015e-279 or 4.3000000000000002e-302 < x < 2.3e-175

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 73.2%

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

   5. Taylor expanded in x around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. fma-def 73.2%

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

      3. mul-1-neg 73.2%

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

      4. unsub-neg 73.2%

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

      5. *-commutative 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in x around 0 49.8%

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

   if -3.40000000000000015e-279 < x < 4.3000000000000002e-302 or 2.3e-175 < x < 1.20000000000000011e-38

   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. add-sqr-sqrt 34.9%

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

      3. associate-*r* 34.9%

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

      4. fma-def 34.9%

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

   3. Applied egg-rr 34.9%

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

   4. Taylor expanded in x around 0 76.9%

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

      1. *-commutative 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in y around 0 61.3%

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

      1. associate-*r* 61.3%

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

      2. mul-1-neg 61.3%

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

   9. Simplified 61.3%

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

   if 1.20000000000000011e-38 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

   4. Simplified 81.7%

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

   5. Taylor expanded in y around 0 54.2%

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

      1. +-commutative 54.2%

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

   7. Simplified 54.2%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.66 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-279}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-175}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 6: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* y (- t x))))
   (if (<= y -1.55e+71)
     t_2
     (if (<= y -8.5e-15)
       (* (- y z) t)
       (if (<= y -4.2e-93)
         t_1
         (if (<= y -2.4e-187) (* z (- t)) (if (<= y 6.4e-11) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -1.55e+71) {
		tmp = t_2;
	} else if (y <= -8.5e-15) {
		tmp = (y - z) * t;
	} else if (y <= -4.2e-93) {
		tmp = t_1;
	} else if (y <= -2.4e-187) {
		tmp = z * -t;
	} else if (y <= 6.4e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = y * (t - x)
    if (y <= (-1.55d+71)) then
        tmp = t_2
    else if (y <= (-8.5d-15)) then
        tmp = (y - z) * t
    else if (y <= (-4.2d-93)) then
        tmp = t_1
    else if (y <= (-2.4d-187)) then
        tmp = z * -t
    else if (y <= 6.4d-11) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -1.55e+71) {
		tmp = t_2;
	} else if (y <= -8.5e-15) {
		tmp = (y - z) * t;
	} else if (y <= -4.2e-93) {
		tmp = t_1;
	} else if (y <= -2.4e-187) {
		tmp = z * -t;
	} else if (y <= 6.4e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = y * (t - x)
	tmp = 0
	if y <= -1.55e+71:
		tmp = t_2
	elif y <= -8.5e-15:
		tmp = (y - z) * t
	elif y <= -4.2e-93:
		tmp = t_1
	elif y <= -2.4e-187:
		tmp = z * -t
	elif y <= 6.4e-11:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1.55e+71)
		tmp = t_2;
	elseif (y <= -8.5e-15)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= -4.2e-93)
		tmp = t_1;
	elseif (y <= -2.4e-187)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 6.4e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = y * (t - x);
	tmp = 0.0;
	if (y <= -1.55e+71)
		tmp = t_2;
	elseif (y <= -8.5e-15)
		tmp = (y - z) * t;
	elseif (y <= -4.2e-93)
		tmp = t_1;
	elseif (y <= -2.4e-187)
		tmp = z * -t;
	elseif (y <= 6.4e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+71], t$95$2, If[LessEqual[y, -8.5e-15], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -4.2e-93], t$95$1, If[LessEqual[y, -2.4e-187], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 6.4e-11], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.55000000000000009e71 or 6.39999999999999987e-11 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in y around inf 88.9%

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

   5. Taylor expanded in x around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. fma-def 91.5%

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

      3. mul-1-neg 91.5%

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

      4. unsub-neg 91.5%

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

      5. *-commutative 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in y around inf 83.5%

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

      1. neg-mul-1 83.5%

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

      2. sub-neg 83.5%

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

   10. Simplified 83.5%

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

   if -1.55000000000000009e71 < y < -8.50000000000000007e-15

   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. add-sqr-sqrt 47.5%

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

      3. associate-*r* 47.5%

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

      4. fma-def 47.5%

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

   3. Applied egg-rr 47.5%

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

   4. Taylor expanded in x around 0 84.7%

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

      1. *-commutative 84.7%

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

   6. Simplified 84.7%

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

   if -8.50000000000000007e-15 < y < -4.2000000000000002e-93 or -2.40000000000000013e-187 < y < 6.39999999999999987e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. +-commutative 63.1%

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

   7. Simplified 63.1%

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

   if -4.2000000000000002e-93 < y < -2.40000000000000013e-187

   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. add-sqr-sqrt 58.5%

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

      3. associate-*r* 58.5%

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

      4. fma-def 58.5%

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

   3. Applied egg-rr 58.5%

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

   4. Taylor expanded in x around 0 77.0%

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

      1. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in y around 0 77.1%

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

      1. associate-*r* 77.1%

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

      2. mul-1-neg 77.1%

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

   9. Simplified 77.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-43}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* y (- t x))))
   (if (<= y -6.2e+71)
     t_2
     (if (<= y -5.8e-15)
       (* (- y z) t)
       (if (<= y -6.5e-90)
         t_1
         (if (<= y 6.7e-43) (- x (* z t)) (if (<= y 7.2e-11) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -6.2e+71) {
		tmp = t_2;
	} else if (y <= -5.8e-15) {
		tmp = (y - z) * t;
	} else if (y <= -6.5e-90) {
		tmp = t_1;
	} else if (y <= 6.7e-43) {
		tmp = x - (z * t);
	} else if (y <= 7.2e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = y * (t - x)
    if (y <= (-6.2d+71)) then
        tmp = t_2
    else if (y <= (-5.8d-15)) then
        tmp = (y - z) * t
    else if (y <= (-6.5d-90)) then
        tmp = t_1
    else if (y <= 6.7d-43) then
        tmp = x - (z * t)
    else if (y <= 7.2d-11) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -6.2e+71) {
		tmp = t_2;
	} else if (y <= -5.8e-15) {
		tmp = (y - z) * t;
	} else if (y <= -6.5e-90) {
		tmp = t_1;
	} else if (y <= 6.7e-43) {
		tmp = x - (z * t);
	} else if (y <= 7.2e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = y * (t - x)
	tmp = 0
	if y <= -6.2e+71:
		tmp = t_2
	elif y <= -5.8e-15:
		tmp = (y - z) * t
	elif y <= -6.5e-90:
		tmp = t_1
	elif y <= 6.7e-43:
		tmp = x - (z * t)
	elif y <= 7.2e-11:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -6.2e+71)
		tmp = t_2;
	elseif (y <= -5.8e-15)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= -6.5e-90)
		tmp = t_1;
	elseif (y <= 6.7e-43)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 7.2e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = y * (t - x);
	tmp = 0.0;
	if (y <= -6.2e+71)
		tmp = t_2;
	elseif (y <= -5.8e-15)
		tmp = (y - z) * t;
	elseif (y <= -6.5e-90)
		tmp = t_1;
	elseif (y <= 6.7e-43)
		tmp = x - (z * t);
	elseif (y <= 7.2e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+71], t$95$2, If[LessEqual[y, -5.8e-15], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -6.5e-90], t$95$1, If[LessEqual[y, 6.7e-43], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-11], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.20000000000000036e71 or 7.19999999999999969e-11 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in y around inf 88.9%

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

   5. Taylor expanded in x around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. fma-def 91.5%

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

      3. mul-1-neg 91.5%

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

      4. unsub-neg 91.5%

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

      5. *-commutative 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in y around inf 83.5%

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

      1. neg-mul-1 83.5%

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

      2. sub-neg 83.5%

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

   10. Simplified 83.5%

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

   if -6.20000000000000036e71 < y < -5.80000000000000037e-15

   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. add-sqr-sqrt 47.5%

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

      3. associate-*r* 47.5%

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

      4. fma-def 47.5%

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

   3. Applied egg-rr 47.5%

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

   4. Taylor expanded in x around 0 84.7%

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

      1. *-commutative 84.7%

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

   6. Simplified 84.7%

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

   if -5.80000000000000037e-15 < y < -6.4999999999999996e-90 or 6.6999999999999998e-43 < y < 7.19999999999999969e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. unsub-neg 74.7%

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

   4. Simplified 74.7%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. +-commutative 74.5%

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

   7. Simplified 74.5%

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

   if -6.4999999999999996e-90 < y < 6.6999999999999998e-43

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in t around inf 73.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-43}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-236}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -4.4e+70)
     t_1
     (if (<= y -8e-15)
       (* (- y z) t)
       (if (<= y -1.55e-92)
         (* x (+ z 1.0))
         (if (<= y 2.8e-236)
           (- x (* z t))
           (if (<= y 8e-11) (* z (- x t)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -4.4e+70) {
		tmp = t_1;
	} else if (y <= -8e-15) {
		tmp = (y - z) * t;
	} else if (y <= -1.55e-92) {
		tmp = x * (z + 1.0);
	} else if (y <= 2.8e-236) {
		tmp = x - (z * t);
	} else if (y <= 8e-11) {
		tmp = z * (x - 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 = y * (t - x)
    if (y <= (-4.4d+70)) then
        tmp = t_1
    else if (y <= (-8d-15)) then
        tmp = (y - z) * t
    else if (y <= (-1.55d-92)) then
        tmp = x * (z + 1.0d0)
    else if (y <= 2.8d-236) then
        tmp = x - (z * t)
    else if (y <= 8d-11) then
        tmp = z * (x - 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 = y * (t - x);
	double tmp;
	if (y <= -4.4e+70) {
		tmp = t_1;
	} else if (y <= -8e-15) {
		tmp = (y - z) * t;
	} else if (y <= -1.55e-92) {
		tmp = x * (z + 1.0);
	} else if (y <= 2.8e-236) {
		tmp = x - (z * t);
	} else if (y <= 8e-11) {
		tmp = z * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -4.4e+70:
		tmp = t_1
	elif y <= -8e-15:
		tmp = (y - z) * t
	elif y <= -1.55e-92:
		tmp = x * (z + 1.0)
	elif y <= 2.8e-236:
		tmp = x - (z * t)
	elif y <= 8e-11:
		tmp = z * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -4.4e+70)
		tmp = t_1;
	elseif (y <= -8e-15)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= -1.55e-92)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 2.8e-236)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 8e-11)
		tmp = Float64(z * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -4.4e+70)
		tmp = t_1;
	elseif (y <= -8e-15)
		tmp = (y - z) * t;
	elseif (y <= -1.55e-92)
		tmp = x * (z + 1.0);
	elseif (y <= 2.8e-236)
		tmp = x - (z * t);
	elseif (y <= 8e-11)
		tmp = z * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+70], t$95$1, If[LessEqual[y, -8e-15], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -1.55e-92], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-236], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-11], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.40000000000000001e70 or 7.99999999999999952e-11 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in y around inf 88.9%

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

   5. Taylor expanded in x around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. fma-def 91.5%

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

      3. mul-1-neg 91.5%

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

      4. unsub-neg 91.5%

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

      5. *-commutative 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in y around inf 83.5%

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

      1. neg-mul-1 83.5%

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

      2. sub-neg 83.5%

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

   10. Simplified 83.5%

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

   if -4.40000000000000001e70 < y < -8.0000000000000006e-15

   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. add-sqr-sqrt 47.5%

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

      3. associate-*r* 47.5%

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

      4. fma-def 47.5%

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

   3. Applied egg-rr 47.5%

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

   4. Taylor expanded in x around 0 84.7%

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

      1. *-commutative 84.7%

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

   6. Simplified 84.7%

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

   if -8.0000000000000006e-15 < y < -1.55e-92

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in y around 0 67.4%

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

      1. +-commutative 67.4%

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

   7. Simplified 67.4%

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

   if -1.55e-92 < y < 2.79999999999999986e-236

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 86.2%

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

   if 2.79999999999999986e-236 < y < 7.99999999999999952e-11

   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. add-sqr-sqrt 38.1%

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

      3. associate-*r* 38.2%

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

      4. fma-def 38.2%

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

   3. Applied egg-rr 38.2%

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

   4. Taylor expanded in z around inf 75.0%

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

      1. associate-*r* 75.0%

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

      2. neg-mul-1 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-236}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 9: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.65 \cdot 10^{-32}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -6.4e+69)
     t_1
     (if (<= y -4.65e-32)
       (+ x (* (- y z) t))
       (if (<= y 4.2e-16) (- x (* z (- t x))) (+ x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -6.4e+69) {
		tmp = t_1;
	} else if (y <= -4.65e-32) {
		tmp = x + ((y - z) * t);
	} else if (y <= 4.2e-16) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + 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 = y * (t - x)
    if (y <= (-6.4d+69)) then
        tmp = t_1
    else if (y <= (-4.65d-32)) then
        tmp = x + ((y - z) * t)
    else if (y <= 4.2d-16) then
        tmp = x - (z * (t - x))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -6.4e+69) {
		tmp = t_1;
	} else if (y <= -4.65e-32) {
		tmp = x + ((y - z) * t);
	} else if (y <= 4.2e-16) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -6.4e+69:
		tmp = t_1
	elif y <= -4.65e-32:
		tmp = x + ((y - z) * t)
	elif y <= 4.2e-16:
		tmp = x - (z * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -6.4e+69)
		tmp = t_1;
	elseif (y <= -4.65e-32)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	elseif (y <= 4.2e-16)
		tmp = Float64(x - Float64(z * Float64(t - x)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -6.4e+69)
		tmp = t_1;
	elseif (y <= -4.65e-32)
		tmp = x + ((y - z) * t);
	elseif (y <= 4.2e-16)
		tmp = x - (z * (t - x));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+69], t$95$1, If[LessEqual[y, -4.65e-32], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-16], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.3999999999999997e69

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.3%

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

   3. Applied egg-rr 94.3%

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

   4. Taylor expanded in y around inf 92.1%

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

   5. Taylor expanded in x around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. fma-def 95.9%

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

      3. mul-1-neg 95.9%

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

      4. unsub-neg 95.9%

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

      5. *-commutative 95.9%

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

   7. Simplified 95.9%

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

   8. Taylor expanded in y around inf 92.2%

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

      1. neg-mul-1 92.2%

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

      2. sub-neg 92.2%

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

   10. Simplified 92.2%

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

   if -6.3999999999999997e69 < y < -4.64999999999999988e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.1%

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

   if -4.64999999999999988e-32 < y < 4.2000000000000002e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.6%

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

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

   4. Simplified 95.6%

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

   if 4.2000000000000002e-16 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. *-commutative 78.2%

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

   4. Simplified 78.2%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+69}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -4.65 \cdot 10^{-32}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 10: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-275}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 31:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e+28)
   (* z x)
   (if (<= z -2.35e-275)
     (* y t)
     (if (<= z 2.3e-213) x (if (<= z 31.0) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+28) {
		tmp = z * x;
	} else if (z <= -2.35e-275) {
		tmp = y * t;
	} else if (z <= 2.3e-213) {
		tmp = x;
	} else if (z <= 31.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.8d+28)) then
        tmp = z * x
    else if (z <= (-2.35d-275)) then
        tmp = y * t
    else if (z <= 2.3d-213) then
        tmp = x
    else if (z <= 31.0d0) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+28) {
		tmp = z * x;
	} else if (z <= -2.35e-275) {
		tmp = y * t;
	} else if (z <= 2.3e-213) {
		tmp = x;
	} else if (z <= 31.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e+28:
		tmp = z * x
	elif z <= -2.35e-275:
		tmp = y * t
	elif z <= 2.3e-213:
		tmp = x
	elif z <= 31.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e+28)
		tmp = Float64(z * x);
	elseif (z <= -2.35e-275)
		tmp = Float64(y * t);
	elseif (z <= 2.3e-213)
		tmp = x;
	elseif (z <= 31.0)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.8e+28)
		tmp = z * x;
	elseif (z <= -2.35e-275)
		tmp = y * t;
	elseif (z <= 2.3e-213)
		tmp = x;
	elseif (z <= 31.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e+28], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.35e-275], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.3e-213], x, If[LessEqual[z, 31.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000002e28 or 31 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in z around inf 40.3%

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

   if -5.8000000000000002e28 < z < -2.3499999999999999e-275 or 2.30000000000000003e-213 < z < 31

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 98.0%

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

   3. Applied egg-rr 98.0%

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

   4. Taylor expanded in y around inf 89.4%

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

   5. Taylor expanded in x around 0 89.4%

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

      1. +-commutative 89.4%

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

      2. fma-def 90.4%

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

      3. mul-1-neg 90.4%

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

      4. unsub-neg 90.4%

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

      5. *-commutative 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in x around 0 45.7%

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

   if -2.3499999999999999e-275 < z < 2.30000000000000003e-213

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.9%

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

      1. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 55.8%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-275}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 31:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 11: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+37} \lor \neg \left(x \leq 2.3 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(1 - \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.08e+37) (not (<= x 2.3e-36)))
   (* x (- 1.0 (- y z)))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.08e+37) || !(x <= 2.3e-36)) {
		tmp = x * (1.0 - (y - z));
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.08d+37)) .or. (.not. (x <= 2.3d-36))) then
        tmp = x * (1.0d0 - (y - z))
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.08e+37) || !(x <= 2.3e-36)) {
		tmp = x * (1.0 - (y - z));
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.08e+37) or not (x <= 2.3e-36):
		tmp = x * (1.0 - (y - z))
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.08e+37) || !(x <= 2.3e-36))
		tmp = Float64(x * Float64(1.0 - Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.08e+37) || ~((x <= 2.3e-36)))
		tmp = x * (1.0 - (y - z));
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.08e+37], N[Not[LessEqual[x, 2.3e-36]], $MachinePrecision]], N[(x * N[(1.0 - N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.08e37 or 2.29999999999999996e-36 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 84.2%

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

      1. mul-1-neg 84.2%

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

      2. unsub-neg 84.2%

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

   4. Simplified 84.2%

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

   if -1.08e37 < x < 2.29999999999999996e-36

   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. add-sqr-sqrt 50.2%

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

      3. associate-*r* 50.1%

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

      4. fma-def 50.1%

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

   3. Applied egg-rr 50.1%

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

   4. Taylor expanded in x around 0 78.1%

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

      1. *-commutative 78.1%

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

   6. Simplified 78.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+37} \lor \neg \left(x \leq 2.3 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(1 - \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 12: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+43} \lor \neg \left(x \leq 5.2 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.25e+43) (not (<= x 5.2e+32)))
   (* x (- 1.0 (- y z)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e+43) || !(x <= 5.2e+32)) {
		tmp = x * (1.0 - (y - z));
	} 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 ((x <= (-1.25d+43)) .or. (.not. (x <= 5.2d+32))) then
        tmp = x * (1.0d0 - (y - z))
    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 ((x <= -1.25e+43) || !(x <= 5.2e+32)) {
		tmp = x * (1.0 - (y - z));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.25e+43) or not (x <= 5.2e+32):
		tmp = x * (1.0 - (y - z))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.25e+43) || !(x <= 5.2e+32))
		tmp = Float64(x * Float64(1.0 - Float64(y - z)));
	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 ((x <= -1.25e+43) || ~((x <= 5.2e+32)))
		tmp = x * (1.0 - (y - z));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.25e+43], N[Not[LessEqual[x, 5.2e+32]], $MachinePrecision]], N[(x * N[(1.0 - N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2500000000000001e43 or 5.2000000000000004e32 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. unsub-neg 87.1%

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

   4. Simplified 87.1%

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

   if -1.2500000000000001e43 < x < 5.2000000000000004e32

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.9%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+43} \lor \neg \left(x \leq 5.2 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 13: 34.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-43}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+208}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= x -3.1e+82)
     t_1
     (if (<= x 4e-43) (* y t) (if (<= x 6.4e+208) (* z x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (x <= -3.1e+82) {
		tmp = t_1;
	} else if (x <= 4e-43) {
		tmp = y * t;
	} else if (x <= 6.4e+208) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (x <= (-3.1d+82)) then
        tmp = t_1
    else if (x <= 4d-43) then
        tmp = y * t
    else if (x <= 6.4d+208) then
        tmp = z * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (x <= -3.1e+82) {
		tmp = t_1;
	} else if (x <= 4e-43) {
		tmp = y * t;
	} else if (x <= 6.4e+208) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if x <= -3.1e+82:
		tmp = t_1
	elif x <= 4e-43:
		tmp = y * t
	elif x <= 6.4e+208:
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -3.1e+82)
		tmp = t_1;
	elseif (x <= 4e-43)
		tmp = Float64(y * t);
	elseif (x <= 6.4e+208)
		tmp = Float64(z * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (x <= -3.1e+82)
		tmp = t_1;
	elseif (x <= 4e-43)
		tmp = y * t;
	elseif (x <= 6.4e+208)
		tmp = z * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -3.1e+82], t$95$1, If[LessEqual[x, 4e-43], N[(y * t), $MachinePrecision], If[LessEqual[x, 6.4e+208], N[(z * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.10000000000000032e82 or 6.4000000000000002e208 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

   4. Simplified 95.6%

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

   5. Taylor expanded in y around inf 46.0%

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

      1. mul-1-neg 46.0%

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

   7. Simplified 46.0%

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

   if -3.10000000000000032e82 < x < 4.00000000000000031e-43

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 65.4%

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

   5. Taylor expanded in x around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. fma-def 65.3%

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

      3. mul-1-neg 65.3%

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

      4. unsub-neg 65.3%

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

      5. *-commutative 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in x around 0 42.2%

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

   if 4.00000000000000031e-43 < x < 6.4000000000000002e208

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in z around inf 37.7%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-43}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+208}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 14: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 15: 37.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-65} \lor \neg \left(y \leq 4.15 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.6e-65) (not (<= y 4.15e-13))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e-65) || !(y <= 4.15e-13)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.6d-65)) .or. (.not. (y <= 4.15d-13))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e-65) || !(y <= 4.15e-13)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.6e-65) or not (y <= 4.15e-13):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.6e-65) || !(y <= 4.15e-13))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.6e-65) || ~((y <= 4.15e-13)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.6e-65], N[Not[LessEqual[y, 4.15e-13]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999999e-65 or 4.14999999999999999e-13 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.8%

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

   3. Applied egg-rr 94.8%

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

   4. Taylor expanded in y around inf 85.6%

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

   5. Taylor expanded in x around 0 85.6%

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

      1. +-commutative 85.6%

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

      2. fma-def 87.6%

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

      3. mul-1-neg 87.6%

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

      4. unsub-neg 87.6%

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

      5. *-commutative 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around 0 45.0%

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

   if -4.5999999999999999e-65 < y < 4.14999999999999999e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 32.3%

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

      1. *-commutative 32.3%

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

   4. Simplified 32.3%

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

   5. Taylor expanded in y around 0 29.2%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-65} \lor \neg \left(y \leq 4.15 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around inf 59.0%

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

   1. *-commutative 59.0%

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

4. Simplified 59.0%

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

5. Taylor expanded in y around 0 14.8%

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

6. Final simplification 14.8%

   \[\leadsto x \]

Developer target: 96.4% 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 2023331 
(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))))