Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 13

Speedup: 1.0×

• 35.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 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 2: 38.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.58 \cdot 10^{-58}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+28}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.4e+49)
   (* x z)
   (if (<= z -1.58e-58)
     (* y t)
     (if (<= z -1.12e-271) x (if (<= z 4.9e+28) (* y t) (* x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e+49) {
		tmp = x * z;
	} else if (z <= -1.58e-58) {
		tmp = y * t;
	} else if (z <= -1.12e-271) {
		tmp = x;
	} else if (z <= 4.9e+28) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	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 <= (-4.4d+49)) then
        tmp = x * z
    else if (z <= (-1.58d-58)) then
        tmp = y * t
    else if (z <= (-1.12d-271)) then
        tmp = x
    else if (z <= 4.9d+28) then
        tmp = y * t
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e+49) {
		tmp = x * z;
	} else if (z <= -1.58e-58) {
		tmp = y * t;
	} else if (z <= -1.12e-271) {
		tmp = x;
	} else if (z <= 4.9e+28) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.4e+49:
		tmp = x * z
	elif z <= -1.58e-58:
		tmp = y * t
	elif z <= -1.12e-271:
		tmp = x
	elif z <= 4.9e+28:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.4e+49)
		tmp = Float64(x * z);
	elseif (z <= -1.58e-58)
		tmp = Float64(y * t);
	elseif (z <= -1.12e-271)
		tmp = x;
	elseif (z <= 4.9e+28)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.4e+49)
		tmp = x * z;
	elseif (z <= -1.58e-58)
		tmp = y * t;
	elseif (z <= -1.12e-271)
		tmp = x;
	elseif (z <= 4.9e+28)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.4e+49], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.58e-58], N[(y * t), $MachinePrecision], If[LessEqual[z, -1.12e-271], x, If[LessEqual[z, 4.9e+28], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4000000000000001e49 or 4.8999999999999996e28 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 84.7%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 84.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]
   7. Step-by-step derivation

   8. Simplified 46.9%

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

   if -4.4000000000000001e49 < z < -1.57999999999999997e-58 or -1.11999999999999997e-271 < z < 4.8999999999999996e28

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 56.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 56.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 41.4%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{t}\right) \]

   8. Simplified 41.4%

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

   if -1.57999999999999997e-58 < z < -1.11999999999999997e-271

   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

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(t - x\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(t - x\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(t - x\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(x - t\right)\right)\right) \]

      12. --lowering--.f64 49.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 49.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 46.0%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.58 \cdot 10^{-58}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+28}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.95e-38)
     t_1
     (if (<= z -1.2e-122)
       (* x (- 1.0 y))
       (if (<= z 2.15e+22) (+ 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 <= -1.95e-38) {
		tmp = t_1;
	} else if (z <= -1.2e-122) {
		tmp = x * (1.0 - y);
	} else if (z <= 2.15e+22) {
		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 <= (-1.95d-38)) then
        tmp = t_1
    else if (z <= (-1.2d-122)) then
        tmp = x * (1.0d0 - y)
    else if (z <= 2.15d+22) 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 <= -1.95e-38) {
		tmp = t_1;
	} else if (z <= -1.2e-122) {
		tmp = x * (1.0 - y);
	} else if (z <= 2.15e+22) {
		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 <= -1.95e-38:
		tmp = t_1
	elif z <= -1.2e-122:
		tmp = x * (1.0 - y)
	elif z <= 2.15e+22:
		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 <= -1.95e-38)
		tmp = t_1;
	elseif (z <= -1.2e-122)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 2.15e+22)
		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 <= -1.95e-38)
		tmp = t_1;
	elseif (z <= -1.2e-122)
		tmp = x * (1.0 - y);
	elseif (z <= 2.15e+22)
		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, -1.95e-38], t$95$1, If[LessEqual[z, -1.2e-122], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+22], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e-38 or 2.1500000000000001e22 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 79.1%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 79.1%

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

   if -1.95e-38 < z < -1.19999999999999994e-122

   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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 79.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 79.4%

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

   6. Taylor expanded in z around 0

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

      1. *-rgt-identity N/A

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

      2. mul-1-neg N/A

         \[\leadsto x \cdot 1 + \left(\mathsf{neg}\left(x \cdot y\right)\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. distribute-lft-out N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{y}\right)\right) \]

      7. --lowering--.f64 79.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   8. Simplified 79.3%

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

   if -1.19999999999999994e-122 < z < 2.1500000000000001e22

   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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 81.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, t\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 73.6%

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

Alternative 4: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.5e-38)
     t_1
     (if (<= z -3.4e-270)
       (* x (- 1.0 y))
       (if (<= z 2.2e+22) (* y (- t x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.5e-38) {
		tmp = t_1;
	} else if (z <= -3.4e-270) {
		tmp = x * (1.0 - y);
	} else if (z <= 2.2e+22) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-1.5d-38)) then
        tmp = t_1
    else if (z <= (-3.4d-270)) then
        tmp = x * (1.0d0 - y)
    else if (z <= 2.2d+22) then
        tmp = y * (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.5e-38) {
		tmp = t_1;
	} else if (z <= -3.4e-270) {
		tmp = x * (1.0 - y);
	} else if (z <= 2.2e+22) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.5e-38:
		tmp = t_1
	elif z <= -3.4e-270:
		tmp = x * (1.0 - y)
	elif z <= 2.2e+22:
		tmp = y * (t - x)
	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 <= -1.5e-38)
		tmp = t_1;
	elseif (z <= -3.4e-270)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 2.2e+22)
		tmp = Float64(y * Float64(t - x));
	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 <= -1.5e-38)
		tmp = t_1;
	elseif (z <= -3.4e-270)
		tmp = x * (1.0 - y);
	elseif (z <= 2.2e+22)
		tmp = y * (t - x);
	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, -1.5e-38], t$95$1, If[LessEqual[z, -3.4e-270], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+22], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999994e-38 or 2.2e22 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 79.1%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 79.1%

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

   if -1.49999999999999994e-38 < z < -3.4000000000000001e-270

   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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 65.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 65.3%

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

   6. Taylor expanded in z around 0

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

      1. *-rgt-identity N/A

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

      2. mul-1-neg N/A

         \[\leadsto x \cdot 1 + \left(\mathsf{neg}\left(x \cdot y\right)\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. distribute-lft-out N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{y}\right)\right) \]

      7. --lowering--.f64 65.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   8. Simplified 65.3%

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

   if -3.4000000000000001e-270 < z < 2.2e22

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 65.8%

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

Alternative 5: 62.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -7.6e-10)
     t_1
     (if (<= t -2.95e-257)
       (* x (+ z 1.0))
       (if (<= t 2.4e+41) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -7.6e-10) {
		tmp = t_1;
	} else if (t <= -2.95e-257) {
		tmp = x * (z + 1.0);
	} else if (t <= 2.4e+41) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-7.6d-10)) then
        tmp = t_1
    else if (t <= (-2.95d-257)) then
        tmp = x * (z + 1.0d0)
    else if (t <= 2.4d+41) then
        tmp = x * (1.0d0 - y)
    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 tmp;
	if (t <= -7.6e-10) {
		tmp = t_1;
	} else if (t <= -2.95e-257) {
		tmp = x * (z + 1.0);
	} else if (t <= 2.4e+41) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -7.6e-10:
		tmp = t_1
	elif t <= -2.95e-257:
		tmp = x * (z + 1.0)
	elif t <= 2.4e+41:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -7.6e-10)
		tmp = t_1;
	elseif (t <= -2.95e-257)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (t <= 2.4e+41)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -7.6e-10)
		tmp = t_1;
	elseif (t <= -2.95e-257)
		tmp = x * (z + 1.0);
	elseif (t <= 2.4e+41)
		tmp = x * (1.0 - y);
	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]}, If[LessEqual[t, -7.6e-10], t$95$1, If[LessEqual[t, -2.95e-257], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+41], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999996e-10 or 2.4000000000000002e41 < 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 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 79.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 79.4%

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

   if -7.5999999999999996e-10 < t < -2.95e-257

   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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 87.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 87.0%

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

   6. Taylor expanded in y around 0

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

      1. *-rgt-identity N/A

         \[\leadsto x \cdot 1 + \color{blue}{x} \cdot z \]

      2. distribute-lft-in N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + z\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{1}\right)\right) \]

      5. +-lowering-+.f64 64.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \color{blue}{1}\right)\right) \]

   8. Simplified 64.9%

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

   if -2.95e-257 < t < 2.4000000000000002e41

   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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 80.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 80.4%

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

   6. Taylor expanded in z around 0

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

      1. *-rgt-identity N/A

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

      2. mul-1-neg N/A

         \[\leadsto x \cdot 1 + \left(\mathsf{neg}\left(x \cdot y\right)\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. distribute-lft-out N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{y}\right)\right) \]

      7. --lowering--.f64 64.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   8. Simplified 64.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-39}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+23}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -4.4e-39) (+ x t_1) (if (<= z 6.5e+23) (+ x (* y (- t x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.4e-39) {
		tmp = x + t_1;
	} else if (z <= 6.5e+23) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-4.4d-39)) then
        tmp = x + t_1
    else if (z <= 6.5d+23) then
        tmp = x + (y * (t - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.4e-39) {
		tmp = x + t_1;
	} else if (z <= 6.5e+23) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -4.4e-39:
		tmp = x + t_1
	elif z <= 6.5e+23:
		tmp = x + (y * (t - x))
	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 <= -4.4e-39)
		tmp = Float64(x + t_1);
	elseif (z <= 6.5e+23)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	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 <= -4.4e-39)
		tmp = x + t_1;
	elseif (z <= 6.5e+23)
		tmp = x + (y * (t - x));
	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, -4.4e-39], N[(x + t$95$1), $MachinePrecision], If[LessEqual[z, 6.5e+23], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000002e-39

   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

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(t - x\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(t - x\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(t - x\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(x - t\right)\right)\right) \]

      12. --lowering--.f64 78.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 78.4%

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

   if -4.40000000000000002e-39 < z < 6.4999999999999996e23

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 92.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 92.8%

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

   if 6.4999999999999996e23 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 87.0%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 87.0%

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

Alternative 7: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -4.2e+20) t_1 (if (<= z 2.3e+22) (+ x (* y (- t x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.2e+20) {
		tmp = t_1;
	} else if (z <= 2.3e+22) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-4.2d+20)) then
        tmp = t_1
    else if (z <= 2.3d+22) then
        tmp = x + (y * (t - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.2e+20) {
		tmp = t_1;
	} else if (z <= 2.3e+22) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -4.2e+20:
		tmp = t_1
	elif z <= 2.3e+22:
		tmp = x + (y * (t - x))
	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 <= -4.2e+20)
		tmp = t_1;
	elseif (z <= 2.3e+22)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	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 <= -4.2e+20)
		tmp = t_1;
	elseif (z <= 2.3e+22)
		tmp = x + (y * (t - x));
	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, -4.2e+20], t$95$1, If[LessEqual[z, 2.3e+22], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e20 or 2.3000000000000002e22 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 84.5%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 84.5%

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

   if -4.2e20 < z < 2.3000000000000002e22

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 88.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 88.2%

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

Alternative 8: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+41}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -6.2e-6) t_1 (if (<= t 3.3e+41) (+ x (* x (- z y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -6.2e-6) {
		tmp = t_1;
	} else if (t <= 3.3e+41) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-6.2d-6)) then
        tmp = t_1
    else if (t <= 3.3d+41) then
        tmp = x + (x * (z - y))
    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 tmp;
	if (t <= -6.2e-6) {
		tmp = t_1;
	} else if (t <= 3.3e+41) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -6.2e-6:
		tmp = t_1
	elif t <= 3.3e+41:
		tmp = x + (x * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -6.2e-6)
		tmp = t_1;
	elseif (t <= 3.3e+41)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -6.2e-6)
		tmp = t_1;
	elseif (t <= 3.3e+41)
		tmp = x + (x * (z - y));
	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]}, If[LessEqual[t, -6.2e-6], t$95$1, If[LessEqual[t, 3.3e+41], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.1999999999999999e-6 or 3.3e41 < 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 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 79.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 79.4%

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

   if -6.1999999999999999e-6 < t < 3.3e41

   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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 82.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 82.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+41}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -5e-9) t_1 (if (<= t 4.2e+41) (* x (+ (- z y) 1.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -5e-9) {
		tmp = t_1;
	} else if (t <= 4.2e+41) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-5d-9)) then
        tmp = t_1
    else if (t <= 4.2d+41) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -5e-9) {
		tmp = t_1;
	} else if (t <= 4.2e+41) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -5e-9:
		tmp = t_1
	elif t <= 4.2e+41:
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -5e-9)
		tmp = t_1;
	elseif (t <= 4.2e+41)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -5e-9)
		tmp = t_1;
	elseif (t <= 4.2e+41)
		tmp = x * ((z - y) + 1.0);
	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]}, If[LessEqual[t, -5e-9], t$95$1, If[LessEqual[t, 4.2e+41], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000001e-9 or 4.1999999999999999e41 < 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 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 79.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 79.4%

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

   if -5.0000000000000001e-9 < t < 4.1999999999999999e41

   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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(y - z\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\left(y - z\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(y - z\right)}\right)\right) \]

      5. --lowering--.f64 82.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 82.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-9}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.9e-8) t_1 (if (<= t 8.2e+41) (* x (+ z 1.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.9e-8) {
		tmp = t_1;
	} else if (t <= 8.2e+41) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-1.9d-8)) then
        tmp = t_1
    else if (t <= 8.2d+41) then
        tmp = x * (z + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.9e-8) {
		tmp = t_1;
	} else if (t <= 8.2e+41) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.9e-8:
		tmp = t_1
	elif t <= 8.2e+41:
		tmp = x * (z + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.9e-8)
		tmp = t_1;
	elseif (t <= 8.2e+41)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.9e-8)
		tmp = t_1;
	elseif (t <= 8.2e+41)
		tmp = x * (z + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.9e-8], t$95$1, If[LessEqual[t, 8.2e+41], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.90000000000000014e-8 or 8.2000000000000007e41 < 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 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 79.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 79.4%

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

   if -1.90000000000000014e-8 < t < 8.2000000000000007e41

   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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 82.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 82.6%

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

   6. Taylor expanded in y around 0

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

      1. *-rgt-identity N/A

         \[\leadsto x \cdot 1 + \color{blue}{x} \cdot z \]

      2. distribute-lft-in N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + z\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{1}\right)\right) \]

      5. +-lowering-+.f64 56.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \color{blue}{1}\right)\right) \]

   8. Simplified 56.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-8}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -3.5e-11) t_1 (if (<= t 2.1e-88) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -3.5e-11) {
		tmp = t_1;
	} else if (t <= 2.1e-88) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-3.5d-11)) then
        tmp = t_1
    else if (t <= 2.1d-88) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -3.5e-11) {
		tmp = t_1;
	} else if (t <= 2.1e-88) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -3.5e-11:
		tmp = t_1
	elif t <= 2.1e-88:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -3.5e-11)
		tmp = t_1;
	elseif (t <= 2.1e-88)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -3.5e-11)
		tmp = t_1;
	elseif (t <= 2.1e-88)
		tmp = x;
	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]}, If[LessEqual[t, -3.5e-11], t$95$1, If[LessEqual[t, 2.1e-88], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.50000000000000019e-11 or 2.1e-88 < 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 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 70.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 70.4%

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

   if -3.50000000000000019e-11 < t < 2.1e-88

   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

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(t - x\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(t - x\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(t - x\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(x - t\right)\right)\right) \]

      12. --lowering--.f64 69.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 69.0%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 35.5%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-11}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-58}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e-58) (* y t) (if (<= y 8.2e-31) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e-58) {
		tmp = y * t;
	} else if (y <= 8.2e-31) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.7d-58)) then
        tmp = y * t
    else if (y <= 8.2d-31) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e-58) {
		tmp = y * t;
	} else if (y <= 8.2e-31) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e-58:
		tmp = y * t
	elif y <= 8.2e-31:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e-58)
		tmp = Float64(y * t);
	elseif (y <= 8.2e-31)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.7e-58)
		tmp = y * t;
	elseif (y <= 8.2e-31)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e-58], N[(y * t), $MachinePrecision], If[LessEqual[y, 8.2e-31], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7000000000000003e-58 or 8.1999999999999993e-31 < 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 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 52.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 52.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 40.6%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{t}\right) \]

   8. Simplified 40.6%

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

   if -3.7000000000000003e-58 < y < 8.1999999999999993e-31

   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

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(t - x\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(t - x\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(t - x\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(x - t\right)\right)\right) \]

      12. --lowering--.f64 89.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 89.8%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 37.3%

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

Alternative 13: 18.4% 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 0

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(t - x\right)\right)\right)}\right) \]

   2. mul-1-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(t - x\right)\right)\right)\right) \]

   3. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}\right)\right) \]

   4. mul-1-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(t - x\right)}\right)\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right)\right) \]

   6. mul-1-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right)\right) \]

   8. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right)\right) \]

   9. distribute-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right)\right) \]

   10. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right)\right) \]

   11. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(x - t\right)\right)\right) \]

   12. --lowering--.f64 59.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

5. Simplified 59.8%

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

6. Taylor expanded in z around 0

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

8. Simplified 19.9%

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

Developer Target 1: 96.2% 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 2024191 
(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))))