Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.2s

Alternatives: 12

Speedup: 1.0×

• 35.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 69.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x - z \cdot t\\ \mathbf{if}\;y \leq -430:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-132}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-303}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-46}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* y (- t x))) (t_3 (- x (* z t))))
   (if (<= y -430.0)
     t_2
     (if (<= y -1.1e-132)
       t_3
       (if (<= y -3.2e-213)
         t_1
         (if (<= y -1.02e-303)
           t_3
           (if (<= y 2.6e-163) t_1 (if (<= y 5.5e-46) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -430.0) {
		tmp = t_2;
	} else if (y <= -1.1e-132) {
		tmp = t_3;
	} else if (y <= -3.2e-213) {
		tmp = t_1;
	} else if (y <= -1.02e-303) {
		tmp = t_3;
	} else if (y <= 2.6e-163) {
		tmp = t_1;
	} else if (y <= 5.5e-46) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = y * (t - x)
    t_3 = x - (z * t)
    if (y <= (-430.0d0)) then
        tmp = t_2
    else if (y <= (-1.1d-132)) then
        tmp = t_3
    else if (y <= (-3.2d-213)) then
        tmp = t_1
    else if (y <= (-1.02d-303)) then
        tmp = t_3
    else if (y <= 2.6d-163) then
        tmp = t_1
    else if (y <= 5.5d-46) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -430.0) {
		tmp = t_2;
	} else if (y <= -1.1e-132) {
		tmp = t_3;
	} else if (y <= -3.2e-213) {
		tmp = t_1;
	} else if (y <= -1.02e-303) {
		tmp = t_3;
	} else if (y <= 2.6e-163) {
		tmp = t_1;
	} else if (y <= 5.5e-46) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = y * (t - x)
	t_3 = x - (z * t)
	tmp = 0
	if y <= -430.0:
		tmp = t_2
	elif y <= -1.1e-132:
		tmp = t_3
	elif y <= -3.2e-213:
		tmp = t_1
	elif y <= -1.02e-303:
		tmp = t_3
	elif y <= 2.6e-163:
		tmp = t_1
	elif y <= 5.5e-46:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -430.0)
		tmp = t_2;
	elseif (y <= -1.1e-132)
		tmp = t_3;
	elseif (y <= -3.2e-213)
		tmp = t_1;
	elseif (y <= -1.02e-303)
		tmp = t_3;
	elseif (y <= 2.6e-163)
		tmp = t_1;
	elseif (y <= 5.5e-46)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = y * (t - x);
	t_3 = x - (z * t);
	tmp = 0.0;
	if (y <= -430.0)
		tmp = t_2;
	elseif (y <= -1.1e-132)
		tmp = t_3;
	elseif (y <= -3.2e-213)
		tmp = t_1;
	elseif (y <= -1.02e-303)
		tmp = t_3;
	elseif (y <= 2.6e-163)
		tmp = t_1;
	elseif (y <= 5.5e-46)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -430.0], t$95$2, If[LessEqual[y, -1.1e-132], t$95$3, If[LessEqual[y, -3.2e-213], t$95$1, If[LessEqual[y, -1.02e-303], t$95$3, If[LessEqual[y, 2.6e-163], t$95$1, If[LessEqual[y, 5.5e-46], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -430 or 5.49999999999999983e-46 < 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 79.4%

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

      1. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in x around -inf 76.4%

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

      1. +-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

      4. sub-neg 76.4%

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

      5. metadata-eval 76.4%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in y around inf 78.7%

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

   if -430 < y < -1.09999999999999995e-132 or -3.19999999999999972e-213 < y < -1.01999999999999996e-303 or 2.60000000000000002e-163 < y < 5.49999999999999983e-46

   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 84.7%

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

   4. Taylor expanded in y around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. unsub-neg 73.0%

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

   6. Simplified 73.0%

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

   if -1.09999999999999995e-132 < y < -3.19999999999999972e-213 or -1.01999999999999996e-303 < y < 2.60000000000000002e-163

   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 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in y around 0 74.4%

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

      1. +-commutative 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -430:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-132}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-303}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-46}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-49}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -1.05e+17)
     t_1
     (if (<= y -2.8e-44)
       t_2
       (if (<= y -9.5e-49)
         (* y t)
         (if (<= y -8.5e-130) (* z (- t)) (if (<= y 2.6e-9) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -1.05e+17) {
		tmp = t_1;
	} else if (y <= -2.8e-44) {
		tmp = t_2;
	} else if (y <= -9.5e-49) {
		tmp = y * t;
	} else if (y <= -8.5e-130) {
		tmp = z * -t;
	} else if (y <= 2.6e-9) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x * (z + 1.0d0)
    if (y <= (-1.05d+17)) then
        tmp = t_1
    else if (y <= (-2.8d-44)) then
        tmp = t_2
    else if (y <= (-9.5d-49)) then
        tmp = y * t
    else if (y <= (-8.5d-130)) then
        tmp = z * -t
    else if (y <= 2.6d-9) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -1.05e+17) {
		tmp = t_1;
	} else if (y <= -2.8e-44) {
		tmp = t_2;
	} else if (y <= -9.5e-49) {
		tmp = y * t;
	} else if (y <= -8.5e-130) {
		tmp = z * -t;
	} else if (y <= 2.6e-9) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -1.05e+17:
		tmp = t_1
	elif y <= -2.8e-44:
		tmp = t_2
	elif y <= -9.5e-49:
		tmp = y * t
	elif y <= -8.5e-130:
		tmp = z * -t
	elif y <= 2.6e-9:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -1.05e+17)
		tmp = t_1;
	elseif (y <= -2.8e-44)
		tmp = t_2;
	elseif (y <= -9.5e-49)
		tmp = Float64(y * t);
	elseif (y <= -8.5e-130)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 2.6e-9)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -1.05e+17)
		tmp = t_1;
	elseif (y <= -2.8e-44)
		tmp = t_2;
	elseif (y <= -9.5e-49)
		tmp = y * t;
	elseif (y <= -8.5e-130)
		tmp = z * -t;
	elseif (y <= 2.6e-9)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+17], t$95$1, If[LessEqual[y, -2.8e-44], t$95$2, If[LessEqual[y, -9.5e-49], N[(y * t), $MachinePrecision], If[LessEqual[y, -8.5e-130], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 2.6e-9], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05e17 or 2.6000000000000001e-9 < 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 83.6%

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

      1. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in x around -inf 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

      4. sub-neg 80.3%

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

      5. metadata-eval 80.3%

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

   8. Simplified 80.3%

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

   9. Taylor expanded in y around inf 83.2%

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

   if -1.05e17 < y < -2.8e-44 or -8.50000000000000033e-130 < y < 2.6000000000000001e-9

   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 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in y around 0 62.7%

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

      1. +-commutative 62.7%

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

   8. Simplified 62.7%

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

   if -2.8e-44 < y < -9.50000000000000006e-49

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

   if -9.50000000000000006e-49 < y < -8.50000000000000033e-130

   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 84.6%

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

   4. Taylor expanded in y around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. unsub-neg 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in x around 0 51.9%

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

      1. associate-*r* 51.9%

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

      2. neg-mul-1 51.9%

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

   9. Simplified 51.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-49}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-76}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -1.2e+17)
     t_1
     (if (<= y -1.16e-31)
       t_2
       (if (<= y -2e-76)
         (+ x (* y t))
         (if (<= y -1.3e-128) (* z (- t)) (if (<= y 1.02e-7) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -1.2e+17) {
		tmp = t_1;
	} else if (y <= -1.16e-31) {
		tmp = t_2;
	} else if (y <= -2e-76) {
		tmp = x + (y * t);
	} else if (y <= -1.3e-128) {
		tmp = z * -t;
	} else if (y <= 1.02e-7) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x * (z + 1.0d0)
    if (y <= (-1.2d+17)) then
        tmp = t_1
    else if (y <= (-1.16d-31)) then
        tmp = t_2
    else if (y <= (-2d-76)) then
        tmp = x + (y * t)
    else if (y <= (-1.3d-128)) then
        tmp = z * -t
    else if (y <= 1.02d-7) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -1.2e+17) {
		tmp = t_1;
	} else if (y <= -1.16e-31) {
		tmp = t_2;
	} else if (y <= -2e-76) {
		tmp = x + (y * t);
	} else if (y <= -1.3e-128) {
		tmp = z * -t;
	} else if (y <= 1.02e-7) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -1.2e+17:
		tmp = t_1
	elif y <= -1.16e-31:
		tmp = t_2
	elif y <= -2e-76:
		tmp = x + (y * t)
	elif y <= -1.3e-128:
		tmp = z * -t
	elif y <= 1.02e-7:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -1.2e+17)
		tmp = t_1;
	elseif (y <= -1.16e-31)
		tmp = t_2;
	elseif (y <= -2e-76)
		tmp = Float64(x + Float64(y * t));
	elseif (y <= -1.3e-128)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 1.02e-7)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -1.2e+17)
		tmp = t_1;
	elseif (y <= -1.16e-31)
		tmp = t_2;
	elseif (y <= -2e-76)
		tmp = x + (y * t);
	elseif (y <= -1.3e-128)
		tmp = z * -t;
	elseif (y <= 1.02e-7)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+17], t$95$1, If[LessEqual[y, -1.16e-31], t$95$2, If[LessEqual[y, -2e-76], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-128], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 1.02e-7], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2e17 or 1.02e-7 < 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 83.6%

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

      1. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in x around -inf 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

      4. sub-neg 80.3%

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

      5. metadata-eval 80.3%

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

   8. Simplified 80.3%

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

   9. Taylor expanded in y around inf 83.2%

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

   if -1.2e17 < y < -1.15999999999999998e-31 or -1.2999999999999999e-128 < y < 1.02e-7

   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 63.1%

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

      1. mul-1-neg 63.1%

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

      2. unsub-neg 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around 0 62.4%

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

      1. +-commutative 62.4%

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

   8. Simplified 62.4%

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

   if -1.15999999999999998e-31 < y < -1.99999999999999985e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

   4. Taylor expanded in z around 0 84.1%

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

   if -1.99999999999999985e-76 < y < -1.2999999999999999e-128

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.6%

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

   4. Taylor expanded in y around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in x around 0 54.8%

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

      1. associate-*r* 54.8%

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

      2. neg-mul-1 54.8%

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

   9. Simplified 54.8%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-76}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.82 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+108}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 26.5:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+59}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -1.82e+146)
     t_1
     (if (<= y -2.8e+108)
       (* y t)
       (if (<= y -8.2e+27)
         t_1
         (if (<= y 26.5) (* x (+ z 1.0)) (if (<= y 5e+59) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.82e+146) {
		tmp = t_1;
	} else if (y <= -2.8e+108) {
		tmp = y * t;
	} else if (y <= -8.2e+27) {
		tmp = t_1;
	} else if (y <= 26.5) {
		tmp = x * (z + 1.0);
	} else if (y <= 5e+59) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * -y
    if (y <= (-1.82d+146)) then
        tmp = t_1
    else if (y <= (-2.8d+108)) then
        tmp = y * t
    else if (y <= (-8.2d+27)) then
        tmp = t_1
    else if (y <= 26.5d0) then
        tmp = x * (z + 1.0d0)
    else if (y <= 5d+59) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.82e+146) {
		tmp = t_1;
	} else if (y <= -2.8e+108) {
		tmp = y * t;
	} else if (y <= -8.2e+27) {
		tmp = t_1;
	} else if (y <= 26.5) {
		tmp = x * (z + 1.0);
	} else if (y <= 5e+59) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -1.82e+146:
		tmp = t_1
	elif y <= -2.8e+108:
		tmp = y * t
	elif y <= -8.2e+27:
		tmp = t_1
	elif y <= 26.5:
		tmp = x * (z + 1.0)
	elif y <= 5e+59:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.82e+146)
		tmp = t_1;
	elseif (y <= -2.8e+108)
		tmp = Float64(y * t);
	elseif (y <= -8.2e+27)
		tmp = t_1;
	elseif (y <= 26.5)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 5e+59)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -1.82e+146)
		tmp = t_1;
	elseif (y <= -2.8e+108)
		tmp = y * t;
	elseif (y <= -8.2e+27)
		tmp = t_1;
	elseif (y <= 26.5)
		tmp = x * (z + 1.0);
	elseif (y <= 5e+59)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.82e+146], t$95$1, If[LessEqual[y, -2.8e+108], N[(y * t), $MachinePrecision], If[LessEqual[y, -8.2e+27], t$95$1, If[LessEqual[y, 26.5], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+59], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.82e146 or -2.7999999999999998e108 < y < -8.2000000000000005e27 or 4.9999999999999997e59 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in z around 0 60.0%

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

   7. Taylor expanded in y around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-out 60.0%

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

   9. Simplified 60.0%

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

   if -1.82e146 < y < -2.7999999999999998e108 or 26.5 < y < 4.9999999999999997e59

   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 66.9%

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

   4. Taylor expanded in z around 0 60.5%

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

   5. Taylor expanded in x around 0 61.0%

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

   if -8.2000000000000005e27 < y < 26.5

   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 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in y around 0 56.2%

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

      1. +-commutative 56.2%

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

   8. Simplified 56.2%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+108}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 26.5:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+59}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+92}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+243}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))))
   (if (<= t -4.1e+258)
     t_1
     (if (<= t -1.05e+92)
       (+ x (* y t))
       (if (<= t 5.5e+88)
         (* x (+ (- z y) 1.0))
         (if (<= t 6.2e+243) t_1 (* y (- t x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (t <= -4.1e+258) {
		tmp = t_1;
	} else if (t <= -1.05e+92) {
		tmp = x + (y * t);
	} else if (t <= 5.5e+88) {
		tmp = x * ((z - y) + 1.0);
	} else if (t <= 6.2e+243) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x - (z * t)
    if (t <= (-4.1d+258)) then
        tmp = t_1
    else if (t <= (-1.05d+92)) then
        tmp = x + (y * t)
    else if (t <= 5.5d+88) then
        tmp = x * ((z - y) + 1.0d0)
    else if (t <= 6.2d+243) then
        tmp = t_1
    else
        tmp = y * (t - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (t <= -4.1e+258) {
		tmp = t_1;
	} else if (t <= -1.05e+92) {
		tmp = x + (y * t);
	} else if (t <= 5.5e+88) {
		tmp = x * ((z - y) + 1.0);
	} else if (t <= 6.2e+243) {
		tmp = t_1;
	} else {
		tmp = y * (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	tmp = 0
	if t <= -4.1e+258:
		tmp = t_1
	elif t <= -1.05e+92:
		tmp = x + (y * t)
	elif t <= 5.5e+88:
		tmp = x * ((z - y) + 1.0)
	elif t <= 6.2e+243:
		tmp = t_1
	else:
		tmp = y * (t - x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (t <= -4.1e+258)
		tmp = t_1;
	elseif (t <= -1.05e+92)
		tmp = Float64(x + Float64(y * t));
	elseif (t <= 5.5e+88)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (t <= 6.2e+243)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	tmp = 0.0;
	if (t <= -4.1e+258)
		tmp = t_1;
	elseif (t <= -1.05e+92)
		tmp = x + (y * t);
	elseif (t <= 5.5e+88)
		tmp = x * ((z - y) + 1.0);
	elseif (t <= 6.2e+243)
		tmp = t_1;
	else
		tmp = y * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+258], t$95$1, If[LessEqual[t, -1.05e+92], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+88], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+243], t$95$1, N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.10000000000000008e258 or 5.5e88 < t < 6.2e243

   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 95.6%

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

   4. Taylor expanded in y around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

   6. Simplified 74.3%

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

   if -4.10000000000000008e258 < t < -1.04999999999999993e92

   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 90.9%

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

   4. Taylor expanded in z around 0 65.7%

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

   if -1.04999999999999993e92 < t < 5.5e88

   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 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

   5. Simplified 78.6%

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

   if 6.2e243 < 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 inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in x around -inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. sub-neg 64.8%

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

      5. metadata-eval 64.8%

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

   8. Simplified 64.8%

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

   9. Taylor expanded in y around inf 72.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+258}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+92}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+243}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-209}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 56000000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -4.7e-66)
     t_1
     (if (<= z 7.6e-209) (* y t) (if (<= z 56000000.0) (* x (- y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -4.7e-66) {
		tmp = t_1;
	} else if (z <= 7.6e-209) {
		tmp = y * t;
	} else if (z <= 56000000.0) {
		tmp = x * -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 = z * -t
    if (z <= (-4.7d-66)) then
        tmp = t_1
    else if (z <= 7.6d-209) then
        tmp = y * t
    else if (z <= 56000000.0d0) then
        tmp = x * -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 = z * -t;
	double tmp;
	if (z <= -4.7e-66) {
		tmp = t_1;
	} else if (z <= 7.6e-209) {
		tmp = y * t;
	} else if (z <= 56000000.0) {
		tmp = x * -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -4.7e-66:
		tmp = t_1
	elif z <= 7.6e-209:
		tmp = y * t
	elif z <= 56000000.0:
		tmp = x * -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -4.7e-66)
		tmp = t_1;
	elseif (z <= 7.6e-209)
		tmp = Float64(y * t);
	elseif (z <= 56000000.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -4.7e-66)
		tmp = t_1;
	elseif (z <= 7.6e-209)
		tmp = y * t;
	elseif (z <= 56000000.0)
		tmp = x * -y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -4.7e-66], t$95$1, If[LessEqual[z, 7.6e-209], N[(y * t), $MachinePrecision], If[LessEqual[z, 56000000.0], N[(x * (-y)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6999999999999999e-66 or 5.6e7 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 51.4%

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

   4. Taylor expanded in y around 0 44.2%

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

      1. mul-1-neg 44.2%

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

      2. unsub-neg 44.2%

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

   6. Simplified 44.2%

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

   7. Taylor expanded in x around 0 43.2%

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

      1. associate-*r* 43.2%

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

      2. neg-mul-1 43.2%

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

   9. Simplified 43.2%

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

   if -4.6999999999999999e-66 < z < 7.5999999999999998e-209

   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 75.5%

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

   4. Taylor expanded in z around 0 74.0%

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

   5. Taylor expanded in x around 0 48.8%

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

   if 7.5999999999999998e-209 < z < 5.6e7

   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 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in z around 0 72.8%

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

   7. Taylor expanded in y around inf 45.6%

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

      1. mul-1-neg 45.6%

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

      2. distribute-rgt-neg-out 45.6%

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

   9. Simplified 45.6%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-209}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 56000000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+70} \lor \neg \left(t \leq 2.7 \cdot 10^{-40}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.9e+70) (not (<= t 2.7e-40)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.9e+70) || !(t <= 2.7e-40)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 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 <= (-6.9d+70)) .or. (.not. (t <= 2.7d-40))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 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 <= -6.9e+70) || !(t <= 2.7e-40)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.9e+70) or not (t <= 2.7e-40):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.9e+70) || !(t <= 2.7e-40))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.9e+70) || ~((t <= 2.7e-40)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.9e+70], N[Not[LessEqual[t, 2.7e-40]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.8999999999999995e70 or 2.7e-40 < t

   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 84.4%

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

   if -6.8999999999999995e70 < t < 2.7e-40

   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 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+70} \lor \neg \left(t \leq 2.7 \cdot 10^{-40}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -270 \lor \neg \left(z \leq 1050000\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -270.0) (not (<= z 1050000.0)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -270.0) || !(z <= 1050000.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-270.0d0)) .or. (.not. (z <= 1050000.0d0))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -270.0) || !(z <= 1050000.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -270.0) or not (z <= 1050000.0):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -270.0) || !(z <= 1050000.0))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -270.0) || ~((z <= 1050000.0)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -270.0], N[Not[LessEqual[z, 1050000.0]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -270 or 1.05e6 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in y around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. associate-*r* 80.5%

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

      3. distribute-rgt-in 85.3%

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

      4. mul-1-neg 85.3%

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

      5. sub-neg 85.3%

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

   7. Simplified 85.3%

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

   if -270 < z < 1.05e6

   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 93.5%

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

      1. *-commutative 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -270 \lor \neg \left(z \leq 1050000\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{+72} \lor \neg \left(t \leq 3.8 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.46e+72) (not (<= t 3.8e+65))) (* y t) (* x (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.46e+72) || !(t <= 3.8e+65)) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.46d+72)) .or. (.not. (t <= 3.8d+65))) then
        tmp = y * t
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.46e+72) || !(t <= 3.8e+65)) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.46e+72) or not (t <= 3.8e+65):
		tmp = y * t
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.46e+72) || !(t <= 3.8e+65))
		tmp = Float64(y * t);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.46e+72) || ~((t <= 3.8e+65)))
		tmp = y * t;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.46e+72], N[Not[LessEqual[t, 3.8e+65]], $MachinePrecision]], N[(y * t), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45999999999999999e72 or 3.80000000000000011e65 < t

   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 91.1%

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

   4. Taylor expanded in z around 0 53.0%

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

   5. Taylor expanded in x around 0 46.4%

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

   if -1.45999999999999999e72 < t < 3.80000000000000011e65

   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 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in z around 0 52.5%

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

   7. Taylor expanded in y around inf 35.9%

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

      1. mul-1-neg 35.9%

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

      2. distribute-rgt-neg-out 35.9%

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

   9. Simplified 35.9%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{+72} \lor \neg \left(t \leq 3.8 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-91} \lor \neg \left(y \leq 1.12 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e-91) (not (<= y 1.12e-70))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e-91) || !(y <= 1.12e-70)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7.5d-91)) .or. (.not. (y <= 1.12d-70))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e-91) || !(y <= 1.12e-70)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e-91) or not (y <= 1.12e-70):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e-91) || !(y <= 1.12e-70))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e-91) || ~((y <= 1.12e-70)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e-91], N[Not[LessEqual[y, 1.12e-70]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000051e-91 or 1.12e-70 < y

   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 50.7%

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

   4. Taylor expanded in z around 0 37.9%

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

   5. Taylor expanded in x around 0 35.1%

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

   if -7.50000000000000051e-91 < y < 1.12e-70

   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 71.3%

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

   4. Taylor expanded in x around inf 31.8%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-91} \lor \neg \left(y \leq 1.12 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 18.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 58.7%

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

4. Taylor expanded in x around inf 15.7%

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

5. Final simplification 15.7%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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