Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.4s

Alternatives: 16

Speedup: 1.0×

• 34.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 36.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+118}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+184}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -7.2e+118)
     (* y t)
     (if (<= y -1.35e-196)
       t_1
       (if (<= y 9.6e-233)
         x
         (if (<= y 5.4e-169)
           t_1
           (if (<= y 2.35e-82) x (if (<= y 4e+184) (* y t) (* x (- y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -7.2e+118) {
		tmp = y * t;
	} else if (y <= -1.35e-196) {
		tmp = t_1;
	} else if (y <= 9.6e-233) {
		tmp = x;
	} else if (y <= 5.4e-169) {
		tmp = t_1;
	} else if (y <= 2.35e-82) {
		tmp = x;
	} else if (y <= 4e+184) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-7.2d+118)) then
        tmp = y * t
    else if (y <= (-1.35d-196)) then
        tmp = t_1
    else if (y <= 9.6d-233) then
        tmp = x
    else if (y <= 5.4d-169) then
        tmp = t_1
    else if (y <= 2.35d-82) then
        tmp = x
    else if (y <= 4d+184) then
        tmp = y * t
    else
        tmp = x * -y
    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 (y <= -7.2e+118) {
		tmp = y * t;
	} else if (y <= -1.35e-196) {
		tmp = t_1;
	} else if (y <= 9.6e-233) {
		tmp = x;
	} else if (y <= 5.4e-169) {
		tmp = t_1;
	} else if (y <= 2.35e-82) {
		tmp = x;
	} else if (y <= 4e+184) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -7.2e+118:
		tmp = y * t
	elif y <= -1.35e-196:
		tmp = t_1
	elif y <= 9.6e-233:
		tmp = x
	elif y <= 5.4e-169:
		tmp = t_1
	elif y <= 2.35e-82:
		tmp = x
	elif y <= 4e+184:
		tmp = y * t
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -7.2e+118)
		tmp = Float64(y * t);
	elseif (y <= -1.35e-196)
		tmp = t_1;
	elseif (y <= 9.6e-233)
		tmp = x;
	elseif (y <= 5.4e-169)
		tmp = t_1;
	elseif (y <= 2.35e-82)
		tmp = x;
	elseif (y <= 4e+184)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -7.2e+118)
		tmp = y * t;
	elseif (y <= -1.35e-196)
		tmp = t_1;
	elseif (y <= 9.6e-233)
		tmp = x;
	elseif (y <= 5.4e-169)
		tmp = t_1;
	elseif (y <= 2.35e-82)
		tmp = x;
	elseif (y <= 4e+184)
		tmp = y * t;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -7.2e+118], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.35e-196], t$95$1, If[LessEqual[y, 9.6e-233], x, If[LessEqual[y, 5.4e-169], t$95$1, If[LessEqual[y, 2.35e-82], x, If[LessEqual[y, 4e+184], N[(y * t), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.2e118 or 2.35e-82 < y < 4.00000000000000007e184

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.2%

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

      1. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in y around inf 80.1%

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

   7. Taylor expanded in t around inf 45.1%

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

      1. *-commutative 45.1%

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

   9. Simplified 45.1%

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

   if -7.2e118 < y < -1.34999999999999991e-196 or 9.5999999999999996e-233 < y < 5.4000000000000003e-169

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. *-commutative 86.8%

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

      3. *-commutative 86.8%

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

      4. associate-/l* 83.1%

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

      5. distribute-lft-out 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in z around inf 51.5%

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

      1. associate-*r* 51.5%

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

      2. neg-mul-1 51.5%

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

      3. sub-neg 51.5%

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

      4. metadata-eval 51.5%

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

      5. +-commutative 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in x around 0 43.2%

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

       1. associate-*r* 43.2%

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

       2. mul-1-neg 43.2%

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

   11. Simplified 43.2%

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

   if -1.34999999999999991e-196 < y < 9.5999999999999996e-233 or 5.4000000000000003e-169 < y < 2.35e-82

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 74.9%

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

   4. Taylor expanded in x around inf 48.1%

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

   if 4.00000000000000007e184 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.9%

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

      1. +-commutative 87.9%

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

      2. *-commutative 87.9%

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

      3. *-commutative 87.9%

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

      4. associate-/l* 94.2%

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

      5. distribute-lft-out 94.2%

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

   5. Simplified 94.2%

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

   6. Taylor expanded in y around inf 94.2%

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

   7. Taylor expanded in x around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-lft-neg-out 76.0%

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

      3. *-commutative 76.0%

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

   9. Simplified 76.0%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+118}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+184}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -1 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 10^{+188} \lor \neg \left(y - z \leq 10^{+222}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= (- y z) -1e-32)
     t_1
     (if (<= (- y z) 4e-51)
       x
       (if (or (<= (- y z) 1e+188) (not (<= (- y z) 1e+222))) t_1 (* z x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -1e-32) {
		tmp = t_1;
	} else if ((y - z) <= 4e-51) {
		tmp = x;
	} else if (((y - z) <= 1e+188) || !((y - z) <= 1e+222)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if ((y - z) <= (-1d-32)) then
        tmp = t_1
    else if ((y - z) <= 4d-51) then
        tmp = x
    else if (((y - z) <= 1d+188) .or. (.not. ((y - z) <= 1d+222))) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -1e-32) {
		tmp = t_1;
	} else if ((y - z) <= 4e-51) {
		tmp = x;
	} else if (((y - z) <= 1e+188) || !((y - z) <= 1e+222)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if (y - z) <= -1e-32:
		tmp = t_1
	elif (y - z) <= 4e-51:
		tmp = x
	elif ((y - z) <= 1e+188) or not ((y - z) <= 1e+222):
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (Float64(y - z) <= -1e-32)
		tmp = t_1;
	elseif (Float64(y - z) <= 4e-51)
		tmp = x;
	elseif ((Float64(y - z) <= 1e+188) || !(Float64(y - z) <= 1e+222))
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if ((y - z) <= -1e-32)
		tmp = t_1;
	elseif ((y - z) <= 4e-51)
		tmp = x;
	elseif (((y - z) <= 1e+188) || ~(((y - z) <= 1e+222)))
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -1e-32], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 4e-51], x, If[Or[LessEqual[N[(y - z), $MachinePrecision], 1e+188], N[Not[LessEqual[N[(y - z), $MachinePrecision], 1e+222]], $MachinePrecision]], t$95$1, N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 y z) < -1.00000000000000006e-32 or 4e-51 < (-.f64 y z) < 1e188 or 1e222 < (-.f64 y z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. *-commutative 83.5%

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

      3. *-commutative 83.5%

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

      4. associate-/l* 84.5%

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

      5. distribute-lft-out 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in x around 0 55.6%

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

   if -1.00000000000000006e-32 < (-.f64 y z) < 4e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

   4. Taylor expanded in x around inf 71.4%

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

   if 1e188 < (-.f64 y z) < 1e222

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-rgt-neg-in 81.7%

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

      3. neg-sub0 81.7%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 81.7%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 81.7%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 81.7%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 81.7%

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

      8. remove-double-neg 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in z around inf 81.7%

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

      1. *-commutative 81.7%

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

   8. Simplified 81.7%

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

   9. Taylor expanded in z around inf 81.7%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -1 \cdot 10^{-32}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 10^{+188} \lor \neg \left(y - z \leq 10^{+222}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-162}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* x (- 1.0 y))))
   (if (<= t -2.45e-17)
     t_1
     (if (<= t -6e-60)
       t_2
       (if (<= t -9.6e-111)
         t_1
         (if (<= t -4.8e-162) (* z x) (if (<= t 3.8e+16) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (t <= -2.45e-17) {
		tmp = t_1;
	} else if (t <= -6e-60) {
		tmp = t_2;
	} else if (t <= -9.6e-111) {
		tmp = t_1;
	} else if (t <= -4.8e-162) {
		tmp = z * x;
	} else if (t <= 3.8e+16) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * t
    t_2 = x * (1.0d0 - y)
    if (t <= (-2.45d-17)) then
        tmp = t_1
    else if (t <= (-6d-60)) then
        tmp = t_2
    else if (t <= (-9.6d-111)) then
        tmp = t_1
    else if (t <= (-4.8d-162)) then
        tmp = z * x
    else if (t <= 3.8d+16) 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 - z) * t;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (t <= -2.45e-17) {
		tmp = t_1;
	} else if (t <= -6e-60) {
		tmp = t_2;
	} else if (t <= -9.6e-111) {
		tmp = t_1;
	} else if (t <= -4.8e-162) {
		tmp = z * x;
	} else if (t <= 3.8e+16) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = x * (1.0 - y)
	tmp = 0
	if t <= -2.45e-17:
		tmp = t_1
	elif t <= -6e-60:
		tmp = t_2
	elif t <= -9.6e-111:
		tmp = t_1
	elif t <= -4.8e-162:
		tmp = z * x
	elif t <= 3.8e+16:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -2.45e-17)
		tmp = t_1;
	elseif (t <= -6e-60)
		tmp = t_2;
	elseif (t <= -9.6e-111)
		tmp = t_1;
	elseif (t <= -4.8e-162)
		tmp = Float64(z * x);
	elseif (t <= 3.8e+16)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (t <= -2.45e-17)
		tmp = t_1;
	elseif (t <= -6e-60)
		tmp = t_2;
	elseif (t <= -9.6e-111)
		tmp = t_1;
	elseif (t <= -4.8e-162)
		tmp = z * x;
	elseif (t <= 3.8e+16)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.45e-17], t$95$1, If[LessEqual[t, -6e-60], t$95$2, If[LessEqual[t, -9.6e-111], t$95$1, If[LessEqual[t, -4.8e-162], N[(z * x), $MachinePrecision], If[LessEqual[t, 3.8e+16], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.45000000000000006e-17 or -6.00000000000000038e-60 < t < -9.6000000000000003e-111 or 3.8e16 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.5%

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

      1. +-commutative 79.5%

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

      2. *-commutative 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-/l* 76.8%

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

      5. distribute-lft-out 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in x around 0 74.5%

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

   if -2.45000000000000006e-17 < t < -6.00000000000000038e-60 or -4.8000000000000004e-162 < t < 3.8e16

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. distribute-rgt-neg-in 81.1%

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

      3. neg-sub0 81.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 81.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 81.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 81.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 81.1%

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

      8. remove-double-neg 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in z around 0 58.6%

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

      1. *-rgt-identity 58.6%

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

      2. mul-1-neg 58.6%

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

      3. distribute-rgt-neg-out 58.6%

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

      4. distribute-lft-in 58.6%

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

      5. unsub-neg 58.6%

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

   8. Simplified 58.6%

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

   if -9.6000000000000003e-111 < t < -4.8000000000000004e-162

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 100.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 100.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 100.0%

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

      8. remove-double-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 88.3%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-17}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-111}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-162}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -4800000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-168}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-243}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 15.5:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))) (t_3 (* x (- 1.0 y))))
   (if (<= z -4800000.0)
     t_2
     (if (<= z -1.05e-168)
       t_3
       (if (<= z -1.9e-303)
         t_1
         (if (<= z 8.2e-243) t_3 (if (<= z 15.5) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -4800000.0) {
		tmp = t_2;
	} else if (z <= -1.05e-168) {
		tmp = t_3;
	} else if (z <= -1.9e-303) {
		tmp = t_1;
	} else if (z <= 8.2e-243) {
		tmp = t_3;
	} else if (z <= 15.5) {
		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) :: t_3
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    t_3 = x * (1.0d0 - y)
    if (z <= (-4800000.0d0)) then
        tmp = t_2
    else if (z <= (-1.05d-168)) then
        tmp = t_3
    else if (z <= (-1.9d-303)) then
        tmp = t_1
    else if (z <= 8.2d-243) then
        tmp = t_3
    else if (z <= 15.5d0) 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 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -4800000.0) {
		tmp = t_2;
	} else if (z <= -1.05e-168) {
		tmp = t_3;
	} else if (z <= -1.9e-303) {
		tmp = t_1;
	} else if (z <= 8.2e-243) {
		tmp = t_3;
	} else if (z <= 15.5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	t_3 = x * (1.0 - y)
	tmp = 0
	if z <= -4800000.0:
		tmp = t_2
	elif z <= -1.05e-168:
		tmp = t_3
	elif z <= -1.9e-303:
		tmp = t_1
	elif z <= 8.2e-243:
		tmp = t_3
	elif z <= 15.5:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -4800000.0)
		tmp = t_2;
	elseif (z <= -1.05e-168)
		tmp = t_3;
	elseif (z <= -1.9e-303)
		tmp = t_1;
	elseif (z <= 8.2e-243)
		tmp = t_3;
	elseif (z <= 15.5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -4800000.0)
		tmp = t_2;
	elseif (z <= -1.05e-168)
		tmp = t_3;
	elseif (z <= -1.9e-303)
		tmp = t_1;
	elseif (z <= 8.2e-243)
		tmp = t_3;
	elseif (z <= 15.5)
		tmp = t_1;
	else
		tmp = t_2;
	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[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4800000.0], t$95$2, If[LessEqual[z, -1.05e-168], t$95$3, If[LessEqual[z, -1.9e-303], t$95$1, If[LessEqual[z, 8.2e-243], t$95$3, If[LessEqual[z, 15.5], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e6 or 15.5 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. *-commutative 86.7%

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

      3. *-commutative 86.7%

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

      4. associate-/l* 87.5%

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

      5. distribute-lft-out 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in z around inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. neg-mul-1 70.6%

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

      3. sub-neg 70.6%

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

      4. metadata-eval 70.6%

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

      5. +-commutative 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in x around 0 77.0%

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

       1. +-commutative 77.0%

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

       2. mul-1-neg 77.0%

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

       3. unsub-neg 77.0%

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

       4. distribute-rgt-out-- 80.2%

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

   11. Simplified 80.2%

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

   if -4.8e6 < z < -1.04999999999999997e-168 or -1.90000000000000005e-303 < z < 8.19999999999999962e-243

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. distribute-rgt-neg-in 65.3%

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

      3. neg-sub0 65.3%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 65.3%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 65.3%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 65.3%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 65.3%

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

      8. remove-double-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in z around 0 65.1%

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

      1. *-rgt-identity 65.1%

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

      2. mul-1-neg 65.1%

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

      3. distribute-rgt-neg-out 65.1%

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

      4. distribute-lft-in 65.1%

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

      5. unsub-neg 65.1%

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

   8. Simplified 65.1%

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

   if -1.04999999999999997e-168 < z < -1.90000000000000005e-303 or 8.19999999999999962e-243 < z < 15.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in y around inf 85.9%

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

   7. Taylor expanded in y around inf 71.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4800000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 15.5:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -1.38 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.205:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y t))))
   (if (<= z -1.38e-6)
     t_1
     (if (<= z -6.8e-171)
       t_2
       (if (<= z -2.6e-275) (* y (- t x)) (if (<= z 0.205) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -1.38e-6) {
		tmp = t_1;
	} else if (z <= -6.8e-171) {
		tmp = t_2;
	} else if (z <= -2.6e-275) {
		tmp = y * (t - x);
	} else if (z <= 0.205) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = x + (y * t)
    if (z <= (-1.38d-6)) then
        tmp = t_1
    else if (z <= (-6.8d-171)) then
        tmp = t_2
    else if (z <= (-2.6d-275)) then
        tmp = y * (t - x)
    else if (z <= 0.205d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -1.38e-6) {
		tmp = t_1;
	} else if (z <= -6.8e-171) {
		tmp = t_2;
	} else if (z <= -2.6e-275) {
		tmp = y * (t - x);
	} else if (z <= 0.205) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -1.38e-6:
		tmp = t_1
	elif z <= -6.8e-171:
		tmp = t_2
	elif z <= -2.6e-275:
		tmp = y * (t - x)
	elif z <= 0.205:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -1.38e-6)
		tmp = t_1;
	elseif (z <= -6.8e-171)
		tmp = t_2;
	elseif (z <= -2.6e-275)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 0.205)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -1.38e-6)
		tmp = t_1;
	elseif (z <= -6.8e-171)
		tmp = t_2;
	elseif (z <= -2.6e-275)
		tmp = y * (t - x);
	elseif (z <= 0.205)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.38e-6], t$95$1, If[LessEqual[z, -6.8e-171], t$95$2, If[LessEqual[z, -2.6e-275], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.205], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3799999999999999e-6 or 0.204999999999999988 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.9%

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

      1. +-commutative 86.9%

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

      2. *-commutative 86.9%

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

      3. *-commutative 86.9%

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

      4. associate-/l* 87.6%

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

      5. distribute-lft-out 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in z around inf 70.1%

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

      1. associate-*r* 70.1%

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

      2. neg-mul-1 70.1%

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

      3. sub-neg 70.1%

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

      4. metadata-eval 70.1%

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

      5. +-commutative 70.1%

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

   8. Simplified 70.1%

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

   9. Taylor expanded in x around 0 76.4%

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

       1. +-commutative 76.4%

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

       2. mul-1-neg 76.4%

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

       3. unsub-neg 76.4%

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

       4. distribute-rgt-out-- 79.5%

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

   11. Simplified 79.5%

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

   if -1.3799999999999999e-6 < z < -6.7999999999999997e-171 or -2.59999999999999992e-275 < z < 0.204999999999999988

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.0%

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

   4. Taylor expanded in y around inf 72.5%

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

   if -6.7999999999999997e-171 < z < -2.59999999999999992e-275

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.7%

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

      1. *-commutative 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in y around inf 85.6%

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

   7. Taylor expanded in y around inf 77.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-171}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.205:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-168}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.225:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.0)
     t_1
     (if (<= z -2.5e-168)
       (- x (* z t))
       (if (<= z -3.2e-277)
         (* y (- t x))
         (if (<= z 0.225) (+ x (* y t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= -2.5e-168) {
		tmp = x - (z * t);
	} else if (z <= -3.2e-277) {
		tmp = y * (t - x);
	} else if (z <= 0.225) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= (-2.5d-168)) then
        tmp = x - (z * t)
    else if (z <= (-3.2d-277)) then
        tmp = y * (t - x)
    else if (z <= 0.225d0) then
        tmp = x + (y * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= -2.5e-168) {
		tmp = x - (z * t);
	} else if (z <= -3.2e-277) {
		tmp = y * (t - x);
	} else if (z <= 0.225) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= -2.5e-168:
		tmp = x - (z * t)
	elif z <= -3.2e-277:
		tmp = y * (t - x)
	elif z <= 0.225:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= -2.5e-168)
		tmp = Float64(x - Float64(z * t));
	elseif (z <= -3.2e-277)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 0.225)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= -2.5e-168)
		tmp = x - (z * t);
	elseif (z <= -3.2e-277)
		tmp = y * (t - x);
	elseif (z <= 0.225)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, -2.5e-168], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-277], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.225], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1 or 0.225000000000000006 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. *-commutative 86.7%

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

      3. *-commutative 86.7%

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

      4. associate-/l* 87.5%

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

      5. distribute-lft-out 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in z around inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. neg-mul-1 70.6%

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

      3. sub-neg 70.6%

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

      4. metadata-eval 70.6%

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

      5. +-commutative 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in x around 0 77.0%

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

       1. +-commutative 77.0%

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

       2. mul-1-neg 77.0%

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

       3. unsub-neg 77.0%

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

       4. distribute-rgt-out-- 80.2%

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

   11. Simplified 80.2%

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

   if -1 < z < -2.50000000000000001e-168

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 80.9%

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

   4. Taylor expanded in y around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

   6. Simplified 60.7%

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

   if -2.50000000000000001e-168 < z < -3.1999999999999998e-277

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.7%

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

      1. *-commutative 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in y around inf 85.6%

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

   7. Taylor expanded in y around inf 77.1%

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

   if -3.1999999999999998e-277 < z < 0.225000000000000006

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 79.8%

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

   4. Taylor expanded in y around inf 78.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-168}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.225:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+186}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-33)
   (* y t)
   (if (<= y 4.2e-75) x (if (<= y 1e+186) (* y t) (* x (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-33) {
		tmp = y * t;
	} else if (y <= 4.2e-75) {
		tmp = x;
	} else if (y <= 1e+186) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d-33)) then
        tmp = y * t
    else if (y <= 4.2d-75) then
        tmp = x
    else if (y <= 1d+186) then
        tmp = y * t
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-33) {
		tmp = y * t;
	} else if (y <= 4.2e-75) {
		tmp = x;
	} else if (y <= 1e+186) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-33:
		tmp = y * t
	elif y <= 4.2e-75:
		tmp = x
	elif y <= 1e+186:
		tmp = y * t
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-33)
		tmp = Float64(y * t);
	elseif (y <= 4.2e-75)
		tmp = x;
	elseif (y <= 1e+186)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-33)
		tmp = y * t;
	elseif (y <= 4.2e-75)
		tmp = x;
	elseif (y <= 1e+186)
		tmp = y * t;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-33], N[(y * t), $MachinePrecision], If[LessEqual[y, 4.2e-75], x, If[LessEqual[y, 1e+186], N[(y * t), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e-33 or 4.2000000000000002e-75 < y < 9.9999999999999998e185

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 71.7%

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

      1. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in y around inf 72.4%

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

   7. Taylor expanded in t around inf 40.4%

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

      1. *-commutative 40.4%

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

   9. Simplified 40.4%

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

   if -1.4e-33 < y < 4.2000000000000002e-75

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.7%

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

   4. Taylor expanded in x around inf 37.9%

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

   if 9.9999999999999998e185 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.9%

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

      1. +-commutative 87.9%

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

      2. *-commutative 87.9%

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

      3. *-commutative 87.9%

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

      4. associate-/l* 94.2%

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

      5. distribute-lft-out 94.2%

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

   5. Simplified 94.2%

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

   6. Taylor expanded in y around inf 94.2%

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

   7. Taylor expanded in x around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-lft-neg-out 76.0%

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

      3. *-commutative 76.0%

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

   9. Simplified 76.0%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+186}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-6} \lor \neg \left(z \leq 4 \cdot 10^{+77}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.75e-6) (not (<= z 4e+77)))
   (* z (- x t))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e-6) || !(z <= 4e+77)) {
		tmp = z * (x - t);
	} 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 ((z <= (-1.75d-6)) .or. (.not. (z <= 4d+77))) then
        tmp = z * (x - t)
    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 ((z <= -1.75e-6) || !(z <= 4e+77)) {
		tmp = z * (x - t);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.75e-6) or not (z <= 4e+77):
		tmp = z * (x - t)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.75e-6) || !(z <= 4e+77))
		tmp = Float64(z * Float64(x - t));
	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 ((z <= -1.75e-6) || ~((z <= 4e+77)))
		tmp = z * (x - t);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.75e-6], N[Not[LessEqual[z, 4e+77]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.74999999999999997e-6 or 3.99999999999999993e77 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. *-commutative 87.3%

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

      3. *-commutative 87.3%

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

      4. associate-/l* 88.2%

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

      5. distribute-lft-out 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in z around inf 71.5%

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

      1. associate-*r* 71.5%

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

      2. neg-mul-1 71.5%

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

      3. sub-neg 71.5%

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

      4. metadata-eval 71.5%

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

      5. +-commutative 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in x around 0 78.9%

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

       1. +-commutative 78.9%

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

       2. mul-1-neg 78.9%

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

       3. unsub-neg 78.9%

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

       4. distribute-rgt-out-- 82.4%

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

   11. Simplified 82.4%

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

   if -1.74999999999999997e-6 < z < 3.99999999999999993e77

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-6} \lor \neg \left(z \leq 4 \cdot 10^{+77}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+92} \lor \neg \left(x \leq 5.2 \cdot 10^{-44}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.35e+92) (not (<= x 5.2e-44)))
   (+ x (* x (- z y)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e+92) || !(x <= 5.2e-44)) {
		tmp = x + (x * (z - y));
	} 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 <= (-1.35d+92)) .or. (.not. (x <= 5.2d-44))) then
        tmp = x + (x * (z - y))
    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 <= -1.35e+92) || !(x <= 5.2e-44)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.35e+92) or not (x <= 5.2e-44):
		tmp = x + (x * (z - y))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.35e+92) || !(x <= 5.2e-44))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	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 <= -1.35e+92) || ~((x <= 5.2e-44)))
		tmp = x + (x * (z - y));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.35e+92], N[Not[LessEqual[x, 5.2e-44]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e92 or 5.1999999999999996e-44 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. distribute-rgt-neg-in 83.2%

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

      3. neg-sub0 83.2%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 83.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 83.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 83.2%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 83.2%

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

      8. remove-double-neg 83.2%

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

   5. Simplified 83.2%

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

   if -1.35e92 < x < 5.1999999999999996e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+92} \lor \neg \left(x \leq 5.2 \cdot 10^{-44}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+14} \lor \neg \left(z \leq 300\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e+14) (not (<= z 300.0)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e+14) || !(z <= 300.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - 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 <= (-7.2d+14)) .or. (.not. (z <= 300.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e+14) || !(z <= 300.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e+14) or not (z <= 300.0):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e+14) || !(z <= 300.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.2e+14) || ~((z <= 300.0)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e+14], N[Not[LessEqual[z, 300.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e14 or 300 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. *-commutative 86.7%

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

      3. *-commutative 86.7%

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

      4. associate-/l* 87.5%

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

      5. distribute-lft-out 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in z around inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. neg-mul-1 70.6%

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

      3. sub-neg 70.6%

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

      4. metadata-eval 70.6%

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

      5. +-commutative 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in x around 0 77.0%

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

       1. +-commutative 77.0%

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

       2. mul-1-neg 77.0%

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

       3. unsub-neg 77.0%

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

       4. distribute-rgt-out-- 80.2%

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

   11. Simplified 80.2%

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

   if -7.2e14 < z < 300

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.1%

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

      1. *-commutative 91.1%

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

   5. Simplified 91.1%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+14} \lor \neg \left(z \leq 300\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-30} \lor \neg \left(z \leq 135\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e-30) (not (<= z 135.0)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e-30) || !(z <= 135.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.6d-30)) .or. (.not. (z <= 135.0d0))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e-30) || !(z <= 135.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e-30) or not (z <= 135.0):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.6e-30) || !(z <= 135.0))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.6e-30) || ~((z <= 135.0)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.6e-30], N[Not[LessEqual[z, 135.0]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999987e-30 or 135 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

   if -2.59999999999999987e-30 < z < 135

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.5%

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

      1. *-commutative 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-30} \lor \neg \left(z \leq 135\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.003\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.003))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.003)) {
		tmp = z * x;
	} 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 ((z <= (-1.0d0)) .or. (.not. (z <= 0.003d0))) then
        tmp = z * x
    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 ((z <= -1.0) || !(z <= 0.003)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.003):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.003))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.003)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.003]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.0030000000000000001 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. distribute-rgt-neg-in 51.6%

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

      3. neg-sub0 51.6%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 51.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 51.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 51.6%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 51.6%

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

      8. remove-double-neg 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in z around inf 40.2%

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

      1. *-commutative 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in z around inf 40.2%

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

   if -1 < z < 0.0030000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.8%

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

   4. Taylor expanded in x around inf 35.3%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.003\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-33} \lor \neg \left(y \leq 6.2 \cdot 10^{-77}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e-33) (not (<= y 6.2e-77))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e-33) || !(y <= 6.2e-77)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.9d-33)) .or. (.not. (y <= 6.2d-77))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e-33) || !(y <= 6.2e-77)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e-33) or not (y <= 6.2e-77):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e-33) || !(y <= 6.2e-77))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.9e-33) || ~((y <= 6.2e-77)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e-33], N[Not[LessEqual[y, 6.2e-77]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999997e-33 or 6.20000000000000016e-77 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 74.9%

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

      1. *-commutative 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in y around inf 75.5%

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

   7. Taylor expanded in t around inf 40.9%

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

      1. *-commutative 40.9%

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

   9. Simplified 40.9%

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

   if -1.89999999999999997e-33 < y < 6.20000000000000016e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.7%

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

   4. Taylor expanded in x around inf 37.9%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-33} \lor \neg \left(y \leq 6.2 \cdot 10^{-77}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 16: 17.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 65.9%

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

4. Taylor expanded in x around inf 19.0%

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

5. Final simplification 19.0%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.1% 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 2024095 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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