Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.2s

Alternatives: 15

Speedup: 1.0×

• 34.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 63.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;x \leq -1.56 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-182}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+17}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (- z y) 1.0))))
   (if (<= x -1.56e+41)
     t_1
     (if (<= x 1.45e-182)
       (+ x (* y t))
       (if (<= x 7.5e+17) (- x (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -1.56e+41) {
		tmp = t_1;
	} else if (x <= 1.45e-182) {
		tmp = x + (y * t);
	} else if (x <= 7.5e+17) {
		tmp = x - (z * 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 = x * ((z - y) + 1.0d0)
    if (x <= (-1.56d+41)) then
        tmp = t_1
    else if (x <= 1.45d-182) then
        tmp = x + (y * t)
    else if (x <= 7.5d+17) then
        tmp = x - (z * 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 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -1.56e+41) {
		tmp = t_1;
	} else if (x <= 1.45e-182) {
		tmp = x + (y * t);
	} else if (x <= 7.5e+17) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) + 1.0)
	tmp = 0
	if x <= -1.56e+41:
		tmp = t_1
	elif x <= 1.45e-182:
		tmp = x + (y * t)
	elif x <= 7.5e+17:
		tmp = x - (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (x <= -1.56e+41)
		tmp = t_1;
	elseif (x <= 1.45e-182)
		tmp = Float64(x + Float64(y * t));
	elseif (x <= 7.5e+17)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (x <= -1.56e+41)
		tmp = t_1;
	elseif (x <= 1.45e-182)
		tmp = x + (y * t);
	elseif (x <= 7.5e+17)
		tmp = x - (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.56e+41], t$95$1, If[LessEqual[x, 1.45e-182], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+17], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.56e41 or 7.5e17 < x

   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 85.5%

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

      1. mul-1-neg 85.5%

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

      2. unsub-neg 85.5%

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

   5. Simplified 85.5%

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

   if -1.56e41 < x < 1.44999999999999993e-182

   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 61.9%

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

      1. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in t around inf 58.6%

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

      1. *-commutative 58.6%

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

   8. Simplified 58.6%

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

   if 1.44999999999999993e-182 < x < 7.5e17

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 86.1%

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

   4. Taylor expanded in y around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

      3. *-commutative 57.4%

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

   6. Simplified 57.4%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-182}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+17}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-54} \lor \neg \left(z \leq 1.85 \cdot 10^{+32}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.8e-15)
   (* x (+ z 1.0))
   (if (or (<= z -1e-54) (not (<= z 1.85e+32))) (* z (- t)) (+ x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.8e-15) {
		tmp = x * (z + 1.0);
	} else if ((z <= -1e-54) || !(z <= 1.85e+32)) {
		tmp = z * -t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9.8d-15)) then
        tmp = x * (z + 1.0d0)
    else if ((z <= (-1d-54)) .or. (.not. (z <= 1.85d+32))) then
        tmp = z * -t
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.8e-15) {
		tmp = x * (z + 1.0);
	} else if ((z <= -1e-54) || !(z <= 1.85e+32)) {
		tmp = z * -t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.8e-15:
		tmp = x * (z + 1.0)
	elif (z <= -1e-54) or not (z <= 1.85e+32):
		tmp = z * -t
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.8e-15)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((z <= -1e-54) || !(z <= 1.85e+32))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.8e-15)
		tmp = x * (z + 1.0);
	elseif ((z <= -1e-54) || ~((z <= 1.85e+32)))
		tmp = z * -t;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.8e-15], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1e-54], N[Not[LessEqual[z, 1.85e+32]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.7999999999999999e-15

   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 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in y around 0 49.0%

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

      1. +-commutative 49.0%

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

   8. Simplified 49.0%

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

   if -9.7999999999999999e-15 < z < -1e-54 or 1.85e32 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in x around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. cancel-sign-sub-inv 78.2%

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

      3. metadata-eval 78.2%

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

      4. *-lft-identity 78.2%

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

      5. +-commutative 78.2%

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

      6. mul-1-neg 78.2%

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

      7. unsub-neg 78.2%

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

      8. associate-/l* 76.6%

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

   8. Simplified 76.6%

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

   9. Taylor expanded in x around 0 58.8%

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

       1. associate-*r* 58.8%

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

       2. neg-mul-1 58.8%

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

       3. *-commutative 58.8%

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

   11. Simplified 58.8%

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

   if -1e-54 < z < 1.85e32

   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 94.9%

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

      1. *-commutative 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in t around inf 72.6%

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

      1. *-commutative 72.6%

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

   8. Simplified 72.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-54} \lor \neg \left(z \leq 1.85 \cdot 10^{+32}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-45} \lor \neg \left(z \leq 1.3 \cdot 10^{+27}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-15)
   (* x (+ z 1.0))
   (if (or (<= z -1.7e-45) (not (<= z 1.3e+27))) (* z (- t)) (* x (- 1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-15) {
		tmp = x * (z + 1.0);
	} else if ((z <= -1.7e-45) || !(z <= 1.3e+27)) {
		tmp = z * -t;
	} else {
		tmp = x * (1.0 - 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 (z <= (-2.1d-15)) then
        tmp = x * (z + 1.0d0)
    else if ((z <= (-1.7d-45)) .or. (.not. (z <= 1.3d+27))) then
        tmp = z * -t
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-15) {
		tmp = x * (z + 1.0);
	} else if ((z <= -1.7e-45) || !(z <= 1.3e+27)) {
		tmp = z * -t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e-15:
		tmp = x * (z + 1.0)
	elif (z <= -1.7e-45) or not (z <= 1.3e+27):
		tmp = z * -t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e-15)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((z <= -1.7e-45) || !(z <= 1.3e+27))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e-15)
		tmp = x * (z + 1.0);
	elseif ((z <= -1.7e-45) || ~((z <= 1.3e+27)))
		tmp = z * -t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e-15], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.7e-45], N[Not[LessEqual[z, 1.3e+27]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.09999999999999981e-15

   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 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in y around 0 49.0%

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

      1. +-commutative 49.0%

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

   8. Simplified 49.0%

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

   if -2.09999999999999981e-15 < z < -1.70000000000000002e-45 or 1.30000000000000004e27 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 88.6%

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

      1. mul-1-neg 88.6%

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

      2. unsub-neg 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in x around inf 79.1%

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

      1. associate--l+ 79.1%

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

      2. cancel-sign-sub-inv 79.1%

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

      3. metadata-eval 79.1%

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

      4. *-lft-identity 79.1%

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

      5. +-commutative 79.1%

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

      6. mul-1-neg 79.1%

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

      7. unsub-neg 79.1%

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

      8. associate-/l* 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in x around 0 59.1%

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

       1. associate-*r* 59.1%

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

       2. neg-mul-1 59.1%

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

       3. *-commutative 59.1%

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

   11. Simplified 59.1%

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

   if -1.70000000000000002e-45 < z < 1.30000000000000004e27

   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 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unsub-neg 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in z around 0 57.2%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-45} \lor \neg \left(z \leq 1.3 \cdot 10^{+27}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+33}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e-13)
   (* x (+ z 1.0))
   (if (<= z -1e-54)
     (* z (- t))
     (if (<= z 2e+33) (+ x (* y t)) (- x (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e-13) {
		tmp = x * (z + 1.0);
	} else if (z <= -1e-54) {
		tmp = z * -t;
	} else if (z <= 2e+33) {
		tmp = x + (y * t);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4d-13)) then
        tmp = x * (z + 1.0d0)
    else if (z <= (-1d-54)) then
        tmp = z * -t
    else if (z <= 2d+33) then
        tmp = x + (y * t)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e-13) {
		tmp = x * (z + 1.0);
	} else if (z <= -1e-54) {
		tmp = z * -t;
	} else if (z <= 2e+33) {
		tmp = x + (y * t);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e-13:
		tmp = x * (z + 1.0)
	elif z <= -1e-54:
		tmp = z * -t
	elif z <= 2e+33:
		tmp = x + (y * t)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e-13)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= -1e-54)
		tmp = Float64(z * Float64(-t));
	elseif (z <= 2e+33)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e-13)
		tmp = x * (z + 1.0);
	elseif (z <= -1e-54)
		tmp = z * -t;
	elseif (z <= 2e+33)
		tmp = x + (y * t);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e-13], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e-54], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, 2e+33], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.0000000000000001e-13

   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 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in y around 0 49.0%

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

      1. +-commutative 49.0%

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

   8. Simplified 49.0%

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

   if -4.0000000000000001e-13 < z < -1e-54

   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 75.1%

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

      1. mul-1-neg 75.1%

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

      2. unsub-neg 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in x around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. cancel-sign-sub-inv 62.8%

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

      3. metadata-eval 62.8%

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

      4. *-lft-identity 62.8%

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

      5. +-commutative 62.8%

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

      6. mul-1-neg 62.8%

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

      7. unsub-neg 62.8%

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

      8. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in x around 0 75.2%

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

       1. associate-*r* 75.2%

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

       2. neg-mul-1 75.2%

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

       3. *-commutative 75.2%

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

   11. Simplified 75.2%

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

   if -1e-54 < z < 1.9999999999999999e33

   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 94.9%

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

      1. *-commutative 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in t around inf 72.6%

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

      1. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   if 1.9999999999999999e33 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 64.7%

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

   4. Taylor expanded in y around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

      3. *-commutative 57.1%

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

   6. Simplified 57.1%

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

Alternative 6: 37.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-55} \lor \neg \left(z \leq 116000000\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e+25)
   (* z x)
   (if (or (<= z -4.5e-55) (not (<= z 116000000.0))) (* z (- t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+25) {
		tmp = z * x;
	} else if ((z <= -4.5e-55) || !(z <= 116000000.0)) {
		tmp = z * -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 (z <= (-1.9d+25)) then
        tmp = z * x
    else if ((z <= (-4.5d-55)) .or. (.not. (z <= 116000000.0d0))) then
        tmp = z * -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 (z <= -1.9e+25) {
		tmp = z * x;
	} else if ((z <= -4.5e-55) || !(z <= 116000000.0)) {
		tmp = z * -t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.9e+25:
		tmp = z * x
	elif (z <= -4.5e-55) or not (z <= 116000000.0):
		tmp = z * -t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e+25)
		tmp = Float64(z * x);
	elseif ((z <= -4.5e-55) || !(z <= 116000000.0))
		tmp = Float64(z * Float64(-t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.9e+25)
		tmp = z * x;
	elseif ((z <= -4.5e-55) || ~((z <= 116000000.0)))
		tmp = z * -t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e+25], N[(z * x), $MachinePrecision], If[Or[LessEqual[z, -4.5e-55], N[Not[LessEqual[z, 116000000.0]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e25

   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 57.3%

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

      1. mul-1-neg 57.3%

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

      2. unsub-neg 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in z around inf 48.4%

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

   if -1.9e25 < z < -4.4999999999999997e-55 or 1.16e8 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in x around inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. cancel-sign-sub-inv 74.5%

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

      3. metadata-eval 74.5%

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

      4. *-lft-identity 74.5%

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

      5. +-commutative 74.5%

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

      6. mul-1-neg 74.5%

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

      7. unsub-neg 74.5%

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

      8. associate-/l* 73.2%

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

   8. Simplified 73.2%

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

   9. Taylor expanded in x around 0 55.0%

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

       1. associate-*r* 55.0%

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

       2. neg-mul-1 55.0%

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

       3. *-commutative 55.0%

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

   11. Simplified 55.0%

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

   if -4.4999999999999997e-55 < z < 1.16e8

   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 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in y around 0 33.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-55} \lor \neg \left(z \leq 116000000\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* z x)
   (if (<= z 7e-223) x (if (<= z 7.7e+31) (* x (- y)) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= 7e-223) {
		tmp = x;
	} else if (z <= 7.7e+31) {
		tmp = x * -y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = z * x
    else if (z <= 7d-223) then
        tmp = x
    else if (z <= 7.7d+31) then
        tmp = x * -y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= 7e-223) {
		tmp = x;
	} else if (z <= 7.7e+31) {
		tmp = x * -y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = z * x
	elif z <= 7e-223:
		tmp = x
	elif z <= 7.7e+31:
		tmp = x * -y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(z * x);
	elseif (z <= 7e-223)
		tmp = x;
	elseif (z <= 7.7e+31)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = z * x;
	elseif (z <= 7e-223)
		tmp = x;
	elseif (z <= 7.7e+31)
		tmp = x * -y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(z * x), $MachinePrecision], If[LessEqual[z, 7e-223], x, If[LessEqual[z, 7.7e+31], N[(x * (-y)), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 7.69999999999999967e31 < 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 52.8%

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

      1. mul-1-neg 52.8%

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

      2. unsub-neg 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in z around inf 46.1%

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

   if -1 < z < 7.00000000000000018e-223

   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 90.2%

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

      1. *-commutative 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in y around 0 33.5%

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

   if 7.00000000000000018e-223 < z < 7.69999999999999967e31

   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 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in y around inf 36.9%

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

      1. neg-mul-1 36.9%

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

   8. Simplified 36.9%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-45} \lor \neg \left(z \leq 1.9 \cdot 10^{+26}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-45) (not (<= z 1.9e+26)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-45) || !(z <= 1.9e+26)) {
		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 <= (-1.7d-45)) .or. (.not. (z <= 1.9d+26))) 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 <= -1.7e-45) || !(z <= 1.9e+26)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-45) or not (z <= 1.9e+26):
		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 <= -1.7e-45) || !(z <= 1.9e+26))
		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 <= -1.7e-45) || ~((z <= 1.9e+26)))
		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, -1.7e-45], N[Not[LessEqual[z, 1.9e+26]], $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 < -1.70000000000000002e-45 or 1.9000000000000001e26 < 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 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

   5. Simplified 83.2%

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

   if -1.70000000000000002e-45 < z < 1.9000000000000001e26

   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 94.2%

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

      1. *-commutative 94.2%

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

   5. Simplified 94.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-45} \lor \neg \left(z \leq 1.9 \cdot 10^{+26}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+44} \lor \neg \left(x \leq 2.5 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.75e+44) (not (<= x 2.5e+19)))
   (* x (+ (- z y) 1.0))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e+44) || !(x <= 2.5e+19)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.75d+44)) .or. (.not. (x <= 2.5d+19))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e+44) || !(x <= 2.5e+19)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.75e+44) or not (x <= 2.5e+19):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.75e+44) || !(x <= 2.5e+19))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.75e+44) || ~((x <= 2.5e+19)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.75e+44], N[Not[LessEqual[x, 2.5e+19]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75e44 or 2.5e19 < x

   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 86.1%

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

      1. mul-1-neg 86.1%

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

      2. unsub-neg 86.1%

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

   5. Simplified 86.1%

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

   if -1.75e44 < x < 2.5e19

   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 89.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+44} \lor \neg \left(x \leq 2.5 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+118)
   (* x (+ (- z y) 1.0))
   (if (<= z 5.8e+31) (+ x (* y (- t x))) (- x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+118) {
		tmp = x * ((z - y) + 1.0);
	} else if (z <= 5.8e+31) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4d+118)) then
        tmp = x * ((z - y) + 1.0d0)
    else if (z <= 5.8d+31) then
        tmp = x + (y * (t - x))
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+118) {
		tmp = x * ((z - y) + 1.0);
	} else if (z <= 5.8e+31) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e+118:
		tmp = x * ((z - y) + 1.0)
	elif z <= 5.8e+31:
		tmp = x + (y * (t - x))
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e+118)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (z <= 5.8e+31)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e+118)
		tmp = x * ((z - y) + 1.0);
	elseif (z <= 5.8e+31)
		tmp = x + (y * (t - x));
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e+118], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+31], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999987e118

   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 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

   5. Simplified 61.4%

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

   if -3.99999999999999987e118 < z < 5.8000000000000001e31

   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 84.0%

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

      1. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   if 5.8000000000000001e31 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 64.7%

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

   4. Taylor expanded in y around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

      3. *-commutative 57.1%

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

   6. Simplified 57.1%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+100} \lor \neg \left(t \leq 1.02 \cdot 10^{+33}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.6e+100) (not (<= t 1.02e+33))) (* z (- t)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e+100) || !(t <= 1.02e+33)) {
		tmp = z * -t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.6d+100)) .or. (.not. (t <= 1.02d+33))) then
        tmp = z * -t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e+100) || !(t <= 1.02e+33)) {
		tmp = z * -t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.6e+100) or not (t <= 1.02e+33):
		tmp = z * -t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.6e+100) || !(t <= 1.02e+33))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.6e+100) || ~((t <= 1.02e+33)))
		tmp = z * -t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.6e+100], N[Not[LessEqual[t, 1.02e+33]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5999999999999998e100 or 1.02000000000000001e33 < t

   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 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in x around inf 49.7%

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

      1. associate--l+ 49.7%

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

      2. cancel-sign-sub-inv 49.7%

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

      3. metadata-eval 49.7%

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

      4. *-lft-identity 49.7%

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

      5. +-commutative 49.7%

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

      6. mul-1-neg 49.7%

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

      7. unsub-neg 49.7%

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

      8. associate-/l* 50.6%

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

   8. Simplified 50.6%

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

   9. Taylor expanded in x around 0 50.5%

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

       1. associate-*r* 50.5%

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

       2. neg-mul-1 50.5%

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

       3. *-commutative 50.5%

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

   11. Simplified 50.5%

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

   if -4.5999999999999998e100 < t < 1.02000000000000001e33

   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 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in y around 0 53.8%

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

      1. +-commutative 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+100} \lor \neg \left(t \leq 1.02 \cdot 10^{+33}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.7 \cdot 10^{-10}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.7e-10))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.7e-10)) {
		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 <= 1.7d-10))) 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 <= 1.7e-10)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.7e-10):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.7e-10))
		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 <= 1.7e-10)))
		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, 1.7e-10]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.70000000000000007e-10 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.1%

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

      1. mul-1-neg 53.1%

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

      2. unsub-neg 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in z around inf 44.0%

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

   if -1 < z < 1.70000000000000007e-10

   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 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in y around 0 32.3%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.7 \cdot 10^{-10}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 14: 18.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y -4.5e+46) (* y x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e+46) {
		tmp = y * 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 (y <= (-4.5d+46)) then
        tmp = y * 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 (y <= -4.5e+46) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.5e+46:
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.5e+46], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000001e46

   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 43.7%

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

      1. mul-1-neg 43.7%

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

      2. unsub-neg 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in y around inf 31.9%

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

      1. neg-mul-1 31.9%

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

   8. Simplified 31.9%

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

      1. add-sqr-sqrt 31.9%

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

      2. sqrt-unprod 39.6%

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

      3. sqr-neg 39.6%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 15.8%

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

      6. pow1 15.8%

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

   10. Applied egg-rr 15.8%

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

       1. unpow1 15.8%

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

   12. Simplified 15.8%

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

   if -4.5000000000000001e46 < 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 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y around 0 20.1%

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

4. Final simplification 19.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 17.7% 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 y around inf 57.2%

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

   1. *-commutative 57.2%

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

5. Simplified 57.2%

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

6. Taylor expanded in y around 0 16.3%

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

Developer Target 1: 96.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024153 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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