Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.6s

Alternatives: 15

Speedup: 1.0×

• 35.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 52.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+29}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* y t))))
   (if (<= z -4.2e+113)
     (* z (- t))
     (if (<= z -3.9e+29)
       (* z x)
       (if (<= z -5.7e-167)
         t_1
         (if (<= z -1.95e-262)
           t_2
           (if (<= z 7.5e-254)
             t_1
             (if (<= z 9.2e-8) t_2 (* x (+ z 1.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -4.2e+113) {
		tmp = z * -t;
	} else if (z <= -3.9e+29) {
		tmp = z * x;
	} else if (z <= -5.7e-167) {
		tmp = t_1;
	} else if (z <= -1.95e-262) {
		tmp = t_2;
	} else if (z <= 7.5e-254) {
		tmp = t_1;
	} else if (z <= 9.2e-8) {
		tmp = t_2;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + (y * t)
    if (z <= (-4.2d+113)) then
        tmp = z * -t
    else if (z <= (-3.9d+29)) then
        tmp = z * x
    else if (z <= (-5.7d-167)) then
        tmp = t_1
    else if (z <= (-1.95d-262)) then
        tmp = t_2
    else if (z <= 7.5d-254) then
        tmp = t_1
    else if (z <= 9.2d-8) then
        tmp = t_2
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -4.2e+113) {
		tmp = z * -t;
	} else if (z <= -3.9e+29) {
		tmp = z * x;
	} else if (z <= -5.7e-167) {
		tmp = t_1;
	} else if (z <= -1.95e-262) {
		tmp = t_2;
	} else if (z <= 7.5e-254) {
		tmp = t_1;
	} else if (z <= 9.2e-8) {
		tmp = t_2;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -4.2e+113:
		tmp = z * -t
	elif z <= -3.9e+29:
		tmp = z * x
	elif z <= -5.7e-167:
		tmp = t_1
	elif z <= -1.95e-262:
		tmp = t_2
	elif z <= 7.5e-254:
		tmp = t_1
	elif z <= 9.2e-8:
		tmp = t_2
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -4.2e+113)
		tmp = Float64(z * Float64(-t));
	elseif (z <= -3.9e+29)
		tmp = Float64(z * x);
	elseif (z <= -5.7e-167)
		tmp = t_1;
	elseif (z <= -1.95e-262)
		tmp = t_2;
	elseif (z <= 7.5e-254)
		tmp = t_1;
	elseif (z <= 9.2e-8)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -4.2e+113)
		tmp = z * -t;
	elseif (z <= -3.9e+29)
		tmp = z * x;
	elseif (z <= -5.7e-167)
		tmp = t_1;
	elseif (z <= -1.95e-262)
		tmp = t_2;
	elseif (z <= 7.5e-254)
		tmp = t_1;
	elseif (z <= 9.2e-8)
		tmp = t_2;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+113], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, -3.9e+29], N[(z * x), $MachinePrecision], If[LessEqual[z, -5.7e-167], t$95$1, If[LessEqual[z, -1.95e-262], t$95$2, If[LessEqual[z, 7.5e-254], t$95$1, If[LessEqual[z, 9.2e-8], t$95$2, N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.1999999999999998e113

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 67.4%

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

   3. Taylor expanded in z around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. distribute-rgt-neg-out 64.7%

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

   5. Simplified 64.7%

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

   if -4.1999999999999998e113 < z < -3.89999999999999968e29

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

      4. distribute-lft-out-- 61.1%

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

      5. *-rgt-identity 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in z around inf 55.7%

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

   if -3.89999999999999968e29 < z < -5.69999999999999988e-167 or -1.94999999999999992e-262 < z < 7.5000000000000005e-254

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 86.0%

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

   3. Taylor expanded in t around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. sub-neg 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in x around 0 72.4%

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

   if -5.69999999999999988e-167 < z < -1.94999999999999992e-262 or 7.5000000000000005e-254 < z < 9.2000000000000003e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.4%

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

   3. Taylor expanded in z around 0 74.4%

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

   if 9.2000000000000003e-8 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.2%

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

      1. +-commutative 87.2%

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

      2. mul-1-neg 87.2%

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

      3. unsub-neg 87.2%

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

      4. *-commutative 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in x around -inf 53.7%

      \[\leadsto \color{blue}{\left(1 + z\right) \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+29}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-262}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 3: 52.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+116}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* y t))))
   (if (<= z -1.5e+116)
     (- x (* z t))
     (if (<= z -7.3e+28)
       (* z x)
       (if (<= z -2.2e-167)
         t_1
         (if (<= z -3.3e-263)
           t_2
           (if (<= z 7.8e-255)
             t_1
             (if (<= z 1.12e-7) t_2 (* x (+ z 1.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -1.5e+116) {
		tmp = x - (z * t);
	} else if (z <= -7.3e+28) {
		tmp = z * x;
	} else if (z <= -2.2e-167) {
		tmp = t_1;
	} else if (z <= -3.3e-263) {
		tmp = t_2;
	} else if (z <= 7.8e-255) {
		tmp = t_1;
	} else if (z <= 1.12e-7) {
		tmp = t_2;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + (y * t)
    if (z <= (-1.5d+116)) then
        tmp = x - (z * t)
    else if (z <= (-7.3d+28)) then
        tmp = z * x
    else if (z <= (-2.2d-167)) then
        tmp = t_1
    else if (z <= (-3.3d-263)) then
        tmp = t_2
    else if (z <= 7.8d-255) then
        tmp = t_1
    else if (z <= 1.12d-7) then
        tmp = t_2
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -1.5e+116) {
		tmp = x - (z * t);
	} else if (z <= -7.3e+28) {
		tmp = z * x;
	} else if (z <= -2.2e-167) {
		tmp = t_1;
	} else if (z <= -3.3e-263) {
		tmp = t_2;
	} else if (z <= 7.8e-255) {
		tmp = t_1;
	} else if (z <= 1.12e-7) {
		tmp = t_2;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -1.5e+116:
		tmp = x - (z * t)
	elif z <= -7.3e+28:
		tmp = z * x
	elif z <= -2.2e-167:
		tmp = t_1
	elif z <= -3.3e-263:
		tmp = t_2
	elif z <= 7.8e-255:
		tmp = t_1
	elif z <= 1.12e-7:
		tmp = t_2
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -1.5e+116)
		tmp = Float64(x - Float64(z * t));
	elseif (z <= -7.3e+28)
		tmp = Float64(z * x);
	elseif (z <= -2.2e-167)
		tmp = t_1;
	elseif (z <= -3.3e-263)
		tmp = t_2;
	elseif (z <= 7.8e-255)
		tmp = t_1;
	elseif (z <= 1.12e-7)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -1.5e+116)
		tmp = x - (z * t);
	elseif (z <= -7.3e+28)
		tmp = z * x;
	elseif (z <= -2.2e-167)
		tmp = t_1;
	elseif (z <= -3.3e-263)
		tmp = t_2;
	elseif (z <= 7.8e-255)
		tmp = t_1;
	elseif (z <= 1.12e-7)
		tmp = t_2;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+116], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.3e+28], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.2e-167], t$95$1, If[LessEqual[z, -3.3e-263], t$95$2, If[LessEqual[z, 7.8e-255], t$95$1, If[LessEqual[z, 1.12e-7], t$95$2, N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.4999999999999999e116

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. mul-1-neg 85.1%

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

      3. unsub-neg 85.1%

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

      4. *-commutative 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in t around inf 64.7%

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

      1. *-commutative 64.7%

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

   7. Simplified 64.7%

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

   if -1.4999999999999999e116 < z < -7.2999999999999998e28

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

      4. distribute-lft-out-- 61.1%

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

      5. *-rgt-identity 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in z around inf 55.7%

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

   if -7.2999999999999998e28 < z < -2.2e-167 or -3.2999999999999997e-263 < z < 7.8000000000000001e-255

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 86.0%

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

   3. Taylor expanded in t around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. sub-neg 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in x around 0 72.4%

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

   if -2.2e-167 < z < -3.2999999999999997e-263 or 7.8000000000000001e-255 < z < 1.12e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.4%

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

   3. Taylor expanded in z around 0 74.4%

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

   if 1.12e-7 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.2%

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

      1. +-commutative 87.2%

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

      2. mul-1-neg 87.2%

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

      3. unsub-neg 87.2%

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

      4. *-commutative 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in x around -inf 53.7%

      \[\leadsto \color{blue}{\left(1 + z\right) \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+116}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-263}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-7}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 4: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= z -9.2e+113)
     (* z (- t))
     (if (<= z -2.45e+28)
       (* z x)
       (if (<= z -8.6e-218)
         t_1
         (if (<= z -5.4e-258)
           (* y t)
           (if (<= z 9.2e-8) t_1 (* x (+ z 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (z <= -9.2e+113) {
		tmp = z * -t;
	} else if (z <= -2.45e+28) {
		tmp = z * x;
	} else if (z <= -8.6e-218) {
		tmp = t_1;
	} else if (z <= -5.4e-258) {
		tmp = y * t;
	} else if (z <= 9.2e-8) {
		tmp = t_1;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    if (z <= (-9.2d+113)) then
        tmp = z * -t
    else if (z <= (-2.45d+28)) then
        tmp = z * x
    else if (z <= (-8.6d-218)) then
        tmp = t_1
    else if (z <= (-5.4d-258)) then
        tmp = y * t
    else if (z <= 9.2d-8) then
        tmp = t_1
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (z <= -9.2e+113) {
		tmp = z * -t;
	} else if (z <= -2.45e+28) {
		tmp = z * x;
	} else if (z <= -8.6e-218) {
		tmp = t_1;
	} else if (z <= -5.4e-258) {
		tmp = y * t;
	} else if (z <= 9.2e-8) {
		tmp = t_1;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	tmp = 0
	if z <= -9.2e+113:
		tmp = z * -t
	elif z <= -2.45e+28:
		tmp = z * x
	elif z <= -8.6e-218:
		tmp = t_1
	elif z <= -5.4e-258:
		tmp = y * t
	elif z <= 9.2e-8:
		tmp = t_1
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -9.2e+113)
		tmp = Float64(z * Float64(-t));
	elseif (z <= -2.45e+28)
		tmp = Float64(z * x);
	elseif (z <= -8.6e-218)
		tmp = t_1;
	elseif (z <= -5.4e-258)
		tmp = Float64(y * t);
	elseif (z <= 9.2e-8)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -9.2e+113)
		tmp = z * -t;
	elseif (z <= -2.45e+28)
		tmp = z * x;
	elseif (z <= -8.6e-218)
		tmp = t_1;
	elseif (z <= -5.4e-258)
		tmp = y * t;
	elseif (z <= 9.2e-8)
		tmp = t_1;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+113], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, -2.45e+28], N[(z * x), $MachinePrecision], If[LessEqual[z, -8.6e-218], t$95$1, If[LessEqual[z, -5.4e-258], N[(y * t), $MachinePrecision], If[LessEqual[z, 9.2e-8], t$95$1, N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.19999999999999987e113

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 67.4%

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

   3. Taylor expanded in z around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. distribute-rgt-neg-out 64.7%

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

   5. Simplified 64.7%

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

   if -9.19999999999999987e113 < z < -2.4499999999999998e28

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

      4. distribute-lft-out-- 61.1%

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

      5. *-rgt-identity 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in z around inf 55.7%

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

   if -2.4499999999999998e28 < z < -8.6e-218 or -5.39999999999999991e-258 < z < 9.2000000000000003e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 89.2%

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

   3. Taylor expanded in t around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. sub-neg 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in x around 0 67.5%

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

   if -8.6e-218 < z < -5.39999999999999991e-258

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 90.1%

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

   3. Taylor expanded in y around inf 80.5%

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

   if 9.2000000000000003e-8 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.2%

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

      1. +-commutative 87.2%

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

      2. mul-1-neg 87.2%

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

      3. unsub-neg 87.2%

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

      4. *-commutative 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in x around -inf 53.7%

      \[\leadsto \color{blue}{\left(1 + z\right) \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 5: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -4000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 27:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+156} \lor \neg \left(y \leq 3.3 \cdot 10^{+243}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -4000000000000.0)
     t_1
     (if (<= y 27.0)
       (* x (+ z 1.0))
       (if (<= y 1.7e+124)
         (* z (- t))
         (if (or (<= y 6e+156) (not (<= y 3.3e+243))) t_1 (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -4000000000000.0) {
		tmp = t_1;
	} else if (y <= 27.0) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.7e+124) {
		tmp = z * -t;
	} else if ((y <= 6e+156) || !(y <= 3.3e+243)) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (y <= (-4000000000000.0d0)) then
        tmp = t_1
    else if (y <= 27.0d0) then
        tmp = x * (z + 1.0d0)
    else if (y <= 1.7d+124) then
        tmp = z * -t
    else if ((y <= 6d+156) .or. (.not. (y <= 3.3d+243))) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -4000000000000.0) {
		tmp = t_1;
	} else if (y <= 27.0) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.7e+124) {
		tmp = z * -t;
	} else if ((y <= 6e+156) || !(y <= 3.3e+243)) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -4000000000000.0:
		tmp = t_1
	elif y <= 27.0:
		tmp = x * (z + 1.0)
	elif y <= 1.7e+124:
		tmp = z * -t
	elif (y <= 6e+156) or not (y <= 3.3e+243):
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -4000000000000.0)
		tmp = t_1;
	elseif (y <= 27.0)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 1.7e+124)
		tmp = Float64(z * Float64(-t));
	elseif ((y <= 6e+156) || !(y <= 3.3e+243))
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -4000000000000.0)
		tmp = t_1;
	elseif (y <= 27.0)
		tmp = x * (z + 1.0);
	elseif (y <= 1.7e+124)
		tmp = z * -t;
	elseif ((y <= 6e+156) || ~((y <= 3.3e+243)))
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -4000000000000.0], t$95$1, If[LessEqual[y, 27.0], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+124], N[(z * (-t)), $MachinePrecision], If[Or[LessEqual[y, 6e+156], N[Not[LessEqual[y, 3.3e+243]], $MachinePrecision]], t$95$1, N[(y * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4e12 or 1.7e124 < y < 5.9999999999999999e156 or 3.29999999999999994e243 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 82.8%

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

   3. Taylor expanded in t around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. sub-neg 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y around inf 58.6%

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

      1. associate-*r* 58.6%

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

      2. neg-mul-1 58.6%

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

      3. *-commutative 58.6%

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

   8. Simplified 58.6%

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

   if -4e12 < y < 27

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.9%

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

      1. +-commutative 87.9%

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

      2. mul-1-neg 87.9%

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

      3. unsub-neg 87.9%

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

      4. *-commutative 87.9%

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

   4. Simplified 87.9%

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

   5. Taylor expanded in x around -inf 61.3%

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

   if 27 < y < 1.7e124

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 58.2%

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

   3. Taylor expanded in z around inf 40.9%

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

      1. mul-1-neg 40.9%

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

      2. distribute-rgt-neg-out 40.9%

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

   5. Simplified 40.9%

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

   if 5.9999999999999999e156 < y < 3.29999999999999994e243

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.4%

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

   3. Taylor expanded in y around inf 71.3%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 27:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+156} \lor \neg \left(y \leq 3.3 \cdot 10^{+243}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 6: 37.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-266}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 800:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -3e+113)
     t_1
     (if (<= z -1.1e+92)
       (* z x)
       (if (<= z -2.55e+57)
         t_1
         (if (<= z -5.8e-266) (* y t) (if (<= z 800.0) x (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -3e+113) {
		tmp = t_1;
	} else if (z <= -1.1e+92) {
		tmp = z * x;
	} else if (z <= -2.55e+57) {
		tmp = t_1;
	} else if (z <= -5.8e-266) {
		tmp = y * t;
	} else if (z <= 800.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-3d+113)) then
        tmp = t_1
    else if (z <= (-1.1d+92)) then
        tmp = z * x
    else if (z <= (-2.55d+57)) then
        tmp = t_1
    else if (z <= (-5.8d-266)) then
        tmp = y * t
    else if (z <= 800.0d0) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -3e+113) {
		tmp = t_1;
	} else if (z <= -1.1e+92) {
		tmp = z * x;
	} else if (z <= -2.55e+57) {
		tmp = t_1;
	} else if (z <= -5.8e-266) {
		tmp = y * t;
	} else if (z <= 800.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -3e+113:
		tmp = t_1
	elif z <= -1.1e+92:
		tmp = z * x
	elif z <= -2.55e+57:
		tmp = t_1
	elif z <= -5.8e-266:
		tmp = y * t
	elif z <= 800.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -3e+113)
		tmp = t_1;
	elseif (z <= -1.1e+92)
		tmp = Float64(z * x);
	elseif (z <= -2.55e+57)
		tmp = t_1;
	elseif (z <= -5.8e-266)
		tmp = Float64(y * t);
	elseif (z <= 800.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -3e+113)
		tmp = t_1;
	elseif (z <= -1.1e+92)
		tmp = z * x;
	elseif (z <= -2.55e+57)
		tmp = t_1;
	elseif (z <= -5.8e-266)
		tmp = y * t;
	elseif (z <= 800.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -3e+113], t$95$1, If[LessEqual[z, -1.1e+92], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.55e+57], t$95$1, If[LessEqual[z, -5.8e-266], N[(y * t), $MachinePrecision], If[LessEqual[z, 800.0], x, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3e113 or -1.09999999999999996e92 < z < -2.55000000000000011e57

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 69.8%

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

   3. Taylor expanded in z around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. distribute-rgt-neg-out 67.2%

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

   5. Simplified 67.2%

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

   if -3e113 < z < -1.09999999999999996e92 or 800 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 58.5%

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

      1. *-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. distribute-lft-out-- 58.5%

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

      5. *-rgt-identity 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in z around inf 55.6%

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

   if -2.55000000000000011e57 < z < -5.79999999999999991e-266

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 68.1%

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

   3. Taylor expanded in y around inf 37.6%

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

   if -5.79999999999999991e-266 < z < 800

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.1%

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

   3. Taylor expanded in x around inf 46.3%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-266}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 800:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 7: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-267}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 800:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e+115)
   (* z (- t))
   (if (<= z -3.2e+29)
     (* z x)
     (if (<= z -1.45e-167)
       (* y (- x))
       (if (<= z -9e-267) (* y t) (if (<= z 800.0) x (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e+115) {
		tmp = z * -t;
	} else if (z <= -3.2e+29) {
		tmp = z * x;
	} else if (z <= -1.45e-167) {
		tmp = y * -x;
	} else if (z <= -9e-267) {
		tmp = y * t;
	} else if (z <= 800.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.5d+115)) then
        tmp = z * -t
    else if (z <= (-3.2d+29)) then
        tmp = z * x
    else if (z <= (-1.45d-167)) then
        tmp = y * -x
    else if (z <= (-9d-267)) then
        tmp = y * t
    else if (z <= 800.0d0) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e+115) {
		tmp = z * -t;
	} else if (z <= -3.2e+29) {
		tmp = z * x;
	} else if (z <= -1.45e-167) {
		tmp = y * -x;
	} else if (z <= -9e-267) {
		tmp = y * t;
	} else if (z <= 800.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e+115:
		tmp = z * -t
	elif z <= -3.2e+29:
		tmp = z * x
	elif z <= -1.45e-167:
		tmp = y * -x
	elif z <= -9e-267:
		tmp = y * t
	elif z <= 800.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e+115)
		tmp = Float64(z * Float64(-t));
	elseif (z <= -3.2e+29)
		tmp = Float64(z * x);
	elseif (z <= -1.45e-167)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -9e-267)
		tmp = Float64(y * t);
	elseif (z <= 800.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e+115)
		tmp = z * -t;
	elseif (z <= -3.2e+29)
		tmp = z * x;
	elseif (z <= -1.45e-167)
		tmp = y * -x;
	elseif (z <= -9e-267)
		tmp = y * t;
	elseif (z <= 800.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e+115], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, -3.2e+29], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.45e-167], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -9e-267], N[(y * t), $MachinePrecision], If[LessEqual[z, 800.0], x, N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.4999999999999997e115

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 67.4%

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

   3. Taylor expanded in z around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. distribute-rgt-neg-out 64.7%

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

   5. Simplified 64.7%

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

   if -7.4999999999999997e115 < z < -3.19999999999999987e29 or 800 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 56.4%

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

      1. *-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. distribute-lft-out-- 56.4%

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

      5. *-rgt-identity 56.4%

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

   4. Simplified 56.4%

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

   5. Taylor expanded in z around inf 53.8%

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

   if -3.19999999999999987e29 < z < -1.45000000000000001e-167

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.7%

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

   3. Taylor expanded in t around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. sub-neg 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in y around inf 39.8%

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

      1. associate-*r* 39.8%

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

      2. neg-mul-1 39.8%

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

      3. *-commutative 39.8%

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

   8. Simplified 39.8%

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

   if -1.45000000000000001e-167 < z < -8.9999999999999999e-267

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 71.8%

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

   3. Taylor expanded in y around inf 56.9%

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

   if -8.9999999999999999e-267 < z < 800

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.1%

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

   3. Taylor expanded in x around inf 46.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-267}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 800:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 8: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+254}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+226}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))))
   (if (<= t -7.2e+254)
     (* y t)
     (if (<= t -9e+112)
       t_1
       (if (<= t 1.2e+31)
         (* x (- (+ z 1.0) y))
         (if (<= t 1.55e+226) (+ x (* y t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (t <= -7.2e+254) {
		tmp = y * t;
	} else if (t <= -9e+112) {
		tmp = t_1;
	} else if (t <= 1.2e+31) {
		tmp = x * ((z + 1.0) - y);
	} else if (t <= 1.55e+226) {
		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 = x - (z * t)
    if (t <= (-7.2d+254)) then
        tmp = y * t
    else if (t <= (-9d+112)) then
        tmp = t_1
    else if (t <= 1.2d+31) then
        tmp = x * ((z + 1.0d0) - y)
    else if (t <= 1.55d+226) 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 = x - (z * t);
	double tmp;
	if (t <= -7.2e+254) {
		tmp = y * t;
	} else if (t <= -9e+112) {
		tmp = t_1;
	} else if (t <= 1.2e+31) {
		tmp = x * ((z + 1.0) - y);
	} else if (t <= 1.55e+226) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	tmp = 0
	if t <= -7.2e+254:
		tmp = y * t
	elif t <= -9e+112:
		tmp = t_1
	elif t <= 1.2e+31:
		tmp = x * ((z + 1.0) - y)
	elif t <= 1.55e+226:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (t <= -7.2e+254)
		tmp = Float64(y * t);
	elseif (t <= -9e+112)
		tmp = t_1;
	elseif (t <= 1.2e+31)
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	elseif (t <= 1.55e+226)
		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 = x - (z * t);
	tmp = 0.0;
	if (t <= -7.2e+254)
		tmp = y * t;
	elseif (t <= -9e+112)
		tmp = t_1;
	elseif (t <= 1.2e+31)
		tmp = x * ((z + 1.0) - y);
	elseif (t <= 1.55e+226)
		tmp = x + (y * t);
	else
		tmp = t_1;
	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, -7.2e+254], N[(y * t), $MachinePrecision], If[LessEqual[t, -9e+112], t$95$1, If[LessEqual[t, 1.2e+31], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+226], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.19999999999999954e254

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

   3. Taylor expanded in y around inf 82.4%

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

   if -7.19999999999999954e254 < t < -8.9999999999999998e112 or 1.54999999999999988e226 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.3%

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

      1. +-commutative 79.3%

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

      2. mul-1-neg 79.3%

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

      3. unsub-neg 79.3%

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

      4. *-commutative 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in t around inf 76.2%

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

      1. *-commutative 76.2%

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

   7. Simplified 76.2%

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

   if -8.9999999999999998e112 < t < 1.19999999999999991e31

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. distribute-lft-out-- 72.9%

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

      5. *-rgt-identity 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in x around 0 72.9%

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

   if 1.19999999999999991e31 < t < 1.54999999999999988e226

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.1%

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

   3. Taylor expanded in z around 0 61.0%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+254}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+112}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+226}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 9: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+19} \lor \neg \left(x \leq 1.28 \cdot 10^{+188}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.5e+19) (not (<= x 1.28e+188)))
   (* x (- (+ z 1.0) y))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e+19) || !(x <= 1.28e+188)) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.5d+19)) .or. (.not. (x <= 1.28d+188))) then
        tmp = x * ((z + 1.0d0) - y)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e+19) || !(x <= 1.28e+188)) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.5e+19) or not (x <= 1.28e+188):
		tmp = x * ((z + 1.0) - y)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.5e+19) || !(x <= 1.28e+188))
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.5e+19) || ~((x <= 1.28e+188)))
		tmp = x * ((z + 1.0) - y);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.5e+19], N[Not[LessEqual[x, 1.28e+188]], $MachinePrecision]], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e19 or 1.27999999999999997e188 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.8%

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

      1. *-commutative 95.8%

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

      2. mul-1-neg 95.8%

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

      3. unsub-neg 95.8%

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

      4. distribute-lft-out-- 95.8%

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

      5. *-rgt-identity 95.8%

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

   4. Simplified 95.8%

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

   5. Taylor expanded in x around 0 95.8%

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

   if -5.5e19 < x < 1.27999999999999997e188

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.7%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+19} \lor \neg \left(x \leq 1.28 \cdot 10^{+188}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 10: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+29} \lor \neg \left(z \leq 1.15 \cdot 10^{-7}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e+29) (not (<= z 1.15e-7)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e+29) || !(z <= 1.15e-7)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.95d+29)) .or. (.not. (z <= 1.15d-7))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e+29) || !(z <= 1.15e-7)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e+29) or not (z <= 1.15e-7):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e+29) || !(z <= 1.15e-7))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e+29) || ~((z <= 1.15e-7)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e+29], N[Not[LessEqual[z, 1.15e-7]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999984e29 or 1.14999999999999997e-7 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. mul-1-neg 85.3%

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

      3. unsub-neg 85.3%

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

      4. *-commutative 85.3%

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

   4. Simplified 85.3%

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

   if -1.94999999999999984e29 < z < 1.14999999999999997e-7

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 90.1%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+29} \lor \neg \left(z \leq 1.15 \cdot 10^{-7}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 11: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{+188}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.8e+19)
   (* x (- (+ z 1.0) y))
   (if (<= x 1.28e+188) (+ x (* (- y z) t)) (+ x (* x (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e+19) {
		tmp = x * ((z + 1.0) - y);
	} else if (x <= 1.28e+188) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.8d+19)) then
        tmp = x * ((z + 1.0d0) - y)
    else if (x <= 1.28d+188) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e+19) {
		tmp = x * ((z + 1.0) - y);
	} else if (x <= 1.28e+188) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.8e+19:
		tmp = x * ((z + 1.0) - y)
	elif x <= 1.28e+188:
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.8e+19)
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	elseif (x <= 1.28e+188)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.8e+19)
		tmp = x * ((z + 1.0) - y);
	elseif (x <= 1.28e+188)
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.8e+19], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.28e+188], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e19

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.4%

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

      1. *-commutative 94.4%

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

      2. mul-1-neg 94.4%

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

      3. unsub-neg 94.4%

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

      4. distribute-lft-out-- 94.4%

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

      5. *-rgt-identity 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in x around 0 94.4%

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

   if -4.8e19 < x < 1.27999999999999997e188

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.7%

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

   if 1.27999999999999997e188 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-lft-out-- 100.0%

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

      5. *-rgt-identity 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{+188}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 12: 37.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+93}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-268}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 800:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.2e+93)
   (* z x)
   (if (<= z -9.5e-268) (* y t) (if (<= z 800.0) x (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e+93) {
		tmp = z * x;
	} else if (z <= -9.5e-268) {
		tmp = y * t;
	} else if (z <= 800.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8.2d+93)) then
        tmp = z * x
    else if (z <= (-9.5d-268)) then
        tmp = y * t
    else if (z <= 800.0d0) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e+93) {
		tmp = z * x;
	} else if (z <= -9.5e-268) {
		tmp = y * t;
	} else if (z <= 800.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.2e+93:
		tmp = z * x
	elif z <= -9.5e-268:
		tmp = y * t
	elif z <= 800.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.2e+93)
		tmp = Float64(z * x);
	elseif (z <= -9.5e-268)
		tmp = Float64(y * t);
	elseif (z <= 800.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.2e+93)
		tmp = z * x;
	elseif (z <= -9.5e-268)
		tmp = y * t;
	elseif (z <= 800.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.2e+93], N[(z * x), $MachinePrecision], If[LessEqual[z, -9.5e-268], N[(y * t), $MachinePrecision], If[LessEqual[z, 800.0], x, N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000002e93 or 800 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. distribute-lft-out-- 52.7%

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

      5. *-rgt-identity 52.7%

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

   4. Simplified 52.7%

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

   5. Taylor expanded in z around inf 46.4%

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

   if -8.2000000000000002e93 < z < -9.50000000000000007e-268

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 68.9%

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

   3. Taylor expanded in y around inf 39.0%

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

   if -9.50000000000000007e-268 < z < 800

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.1%

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

   3. Taylor expanded in x around inf 46.3%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+93}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-268}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 800:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 13: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 14: 38.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e-15) (* y t) (if (<= y 3.2e-60) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e-15) {
		tmp = y * t;
	} else if (y <= 3.2e-60) {
		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 <= (-8d-15)) then
        tmp = y * t
    else if (y <= 3.2d-60) 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 <= -8e-15) {
		tmp = y * t;
	} else if (y <= 3.2e-60) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e-15:
		tmp = y * t
	elif y <= 3.2e-60:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e-15)
		tmp = Float64(y * t);
	elseif (y <= 3.2e-60)
		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 <= -8e-15)
		tmp = y * t;
	elseif (y <= 3.2e-60)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e-15], N[(y * t), $MachinePrecision], If[LessEqual[y, 3.2e-60], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000006e-15 or 3.2000000000000001e-60 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 58.2%

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

   3. Taylor expanded in y around inf 40.8%

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

   if -8.0000000000000006e-15 < y < 3.2000000000000001e-60

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.1%

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

   3. Taylor expanded in x around inf 36.1%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 15: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 65.3%

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

3. Taylor expanded in x around inf 19.4%

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

4. Final simplification 19.4%

   \[\leadsto x \]

Developer target: 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 2023223 
(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))))