Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 11

Speedup: 1.0×

• 34.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 69.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + x \cdot z\\ t_3 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-44}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* x z))) (t_3 (+ x (* (- y z) t))))
   (if (<= t -6.8e-44)
     t_3
     (if (<= t -1.5e-82)
       t_1
       (if (<= t -2.9e-134)
         t_2
         (if (<= t -3.2e-296) t_1 (if (<= t 4.5e-29) t_2 t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + ((y - z) * t);
	double tmp;
	if (t <= -6.8e-44) {
		tmp = t_3;
	} else if (t <= -1.5e-82) {
		tmp = t_1;
	} else if (t <= -2.9e-134) {
		tmp = t_2;
	} else if (t <= -3.2e-296) {
		tmp = t_1;
	} else if (t <= 4.5e-29) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 * (1.0d0 - y)
    t_2 = x + (x * z)
    t_3 = x + ((y - z) * t)
    if (t <= (-6.8d-44)) then
        tmp = t_3
    else if (t <= (-1.5d-82)) then
        tmp = t_1
    else if (t <= (-2.9d-134)) then
        tmp = t_2
    else if (t <= (-3.2d-296)) then
        tmp = t_1
    else if (t <= 4.5d-29) then
        tmp = t_2
    else
        tmp = t_3
    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 + (x * z);
	double t_3 = x + ((y - z) * t);
	double tmp;
	if (t <= -6.8e-44) {
		tmp = t_3;
	} else if (t <= -1.5e-82) {
		tmp = t_1;
	} else if (t <= -2.9e-134) {
		tmp = t_2;
	} else if (t <= -3.2e-296) {
		tmp = t_1;
	} else if (t <= 4.5e-29) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (x * z)
	t_3 = x + ((y - z) * t)
	tmp = 0
	if t <= -6.8e-44:
		tmp = t_3
	elif t <= -1.5e-82:
		tmp = t_1
	elif t <= -2.9e-134:
		tmp = t_2
	elif t <= -3.2e-296:
		tmp = t_1
	elif t <= 4.5e-29:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(x * z))
	t_3 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t <= -6.8e-44)
		tmp = t_3;
	elseif (t <= -1.5e-82)
		tmp = t_1;
	elseif (t <= -2.9e-134)
		tmp = t_2;
	elseif (t <= -3.2e-296)
		tmp = t_1;
	elseif (t <= 4.5e-29)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + (x * z);
	t_3 = x + ((y - z) * t);
	tmp = 0.0;
	if (t <= -6.8e-44)
		tmp = t_3;
	elseif (t <= -1.5e-82)
		tmp = t_1;
	elseif (t <= -2.9e-134)
		tmp = t_2;
	elseif (t <= -3.2e-296)
		tmp = t_1;
	elseif (t <= 4.5e-29)
		tmp = t_2;
	else
		tmp = t_3;
	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[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-44], t$95$3, If[LessEqual[t, -1.5e-82], t$95$1, If[LessEqual[t, -2.9e-134], t$95$2, If[LessEqual[t, -3.2e-296], t$95$1, If[LessEqual[t, 4.5e-29], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.80000000000000033e-44 or 4.4999999999999998e-29 < 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 91.9%

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

   if -6.80000000000000033e-44 < t < -1.4999999999999999e-82 or -2.89999999999999993e-134 < t < -3.20000000000000013e-296

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 88.6%

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

      1. mul-1-neg 88.6%

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

      2. distribute-rgt-neg-in 88.6%

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

      3. sub-neg 88.6%

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

      4. +-commutative 88.6%

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

      5. distribute-neg-in 88.6%

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

      6. remove-double-neg 88.6%

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

      7. sub-neg 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in z around 0 63.8%

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

      1. *-rgt-identity 63.8%

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

      2. mul-1-neg 63.8%

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

      3. distribute-rgt-neg-out 63.8%

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

      4. distribute-lft-in 63.8%

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

      5. unsub-neg 63.8%

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

   8. Simplified 63.8%

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

   if -1.4999999999999999e-82 < t < -2.89999999999999993e-134 or -3.20000000000000013e-296 < t < 4.4999999999999998e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. distribute-rgt-neg-in 81.9%

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

      3. sub-neg 81.9%

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

      4. +-commutative 81.9%

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

      5. distribute-neg-in 81.9%

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

      6. remove-double-neg 81.9%

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

      7. sub-neg 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in y around 0 68.5%

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

      1. *-commutative 68.5%

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

   8. Simplified 68.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-44}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-134}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-29}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+168}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1100000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+115}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= z -6.8e+184)
     t_1
     (if (<= z -5.6e+168)
       (* x z)
       (if (<= z -1.6e+100)
         t_1
         (if (<= z 1100000000.0)
           (+ x (* y t))
           (if (<= z 5.2e+115) (+ x (* x z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -6.8e+184) {
		tmp = t_1;
	} else if (z <= -5.6e+168) {
		tmp = x * z;
	} else if (z <= -1.6e+100) {
		tmp = t_1;
	} else if (z <= 1100000000.0) {
		tmp = x + (y * t);
	} else if (z <= 5.2e+115) {
		tmp = x + (x * z);
	} 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 = t * -z
    if (z <= (-6.8d+184)) then
        tmp = t_1
    else if (z <= (-5.6d+168)) then
        tmp = x * z
    else if (z <= (-1.6d+100)) then
        tmp = t_1
    else if (z <= 1100000000.0d0) then
        tmp = x + (y * t)
    else if (z <= 5.2d+115) then
        tmp = x + (x * z)
    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 = t * -z;
	double tmp;
	if (z <= -6.8e+184) {
		tmp = t_1;
	} else if (z <= -5.6e+168) {
		tmp = x * z;
	} else if (z <= -1.6e+100) {
		tmp = t_1;
	} else if (z <= 1100000000.0) {
		tmp = x + (y * t);
	} else if (z <= 5.2e+115) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if z <= -6.8e+184:
		tmp = t_1
	elif z <= -5.6e+168:
		tmp = x * z
	elif z <= -1.6e+100:
		tmp = t_1
	elif z <= 1100000000.0:
		tmp = x + (y * t)
	elif z <= 5.2e+115:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (z <= -6.8e+184)
		tmp = t_1;
	elseif (z <= -5.6e+168)
		tmp = Float64(x * z);
	elseif (z <= -1.6e+100)
		tmp = t_1;
	elseif (z <= 1100000000.0)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 5.2e+115)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (z <= -6.8e+184)
		tmp = t_1;
	elseif (z <= -5.6e+168)
		tmp = x * z;
	elseif (z <= -1.6e+100)
		tmp = t_1;
	elseif (z <= 1100000000.0)
		tmp = x + (y * t);
	elseif (z <= 5.2e+115)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[z, -6.8e+184], t$95$1, If[LessEqual[z, -5.6e+168], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.6e+100], t$95$1, If[LessEqual[z, 1100000000.0], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+115], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.8000000000000003e184 or -5.5999999999999998e168 < z < -1.5999999999999999e100 or 5.2000000000000001e115 < 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 64.2%

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

   4. Taylor expanded in y around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in x around 0 58.4%

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

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

      3. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -6.8000000000000003e184 < z < -5.5999999999999998e168

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 86.1%

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

      1. mul-1-neg 86.1%

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

      2. distribute-rgt-neg-in 86.1%

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

      3. sub-neg 86.1%

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

      4. +-commutative 86.1%

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

      5. distribute-neg-in 86.1%

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

      6. remove-double-neg 86.1%

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

      7. sub-neg 86.1%

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

   5. Simplified 86.1%

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

      1. sub-neg 86.1%

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

      2. distribute-rgt-in 71.8%

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

   7. Applied egg-rr 71.8%

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

      1. associate-+r+ 71.8%

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

      2. distribute-lft-neg-out 71.8%

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

      3. unsub-neg 71.8%

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

      4. *-un-lft-identity 71.8%

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

      5. distribute-rgt-out 71.8%

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

   9. Applied egg-rr 71.8%

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

   10. Taylor expanded in z around inf 86.1%

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

       1. *-commutative 86.1%

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

   12. Simplified 86.1%

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

   if -1.5999999999999999e100 < z < 1.1e9

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.4%

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

   4. Taylor expanded in y around inf 62.8%

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

   if 1.1e9 < z < 5.2000000000000001e115

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. distribute-rgt-neg-in 62.7%

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

      3. sub-neg 62.7%

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

      4. +-commutative 62.7%

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

      5. distribute-neg-in 62.7%

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

      6. remove-double-neg 62.7%

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

      7. sub-neg 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y around 0 58.6%

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

      1. *-commutative 58.6%

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

   8. Simplified 58.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+168}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1100000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+115}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+168}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1450000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= z -3.1e+184)
     t_1
     (if (<= z -6e+168)
       (* x z)
       (if (<= z -2.2e+101)
         t_1
         (if (<= z 1450000000.0)
           (+ x (* y t))
           (if (<= z 7.5e+116) (* x z) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -3.1e+184) {
		tmp = t_1;
	} else if (z <= -6e+168) {
		tmp = x * z;
	} else if (z <= -2.2e+101) {
		tmp = t_1;
	} else if (z <= 1450000000.0) {
		tmp = x + (y * t);
	} else if (z <= 7.5e+116) {
		tmp = x * z;
	} 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 = t * -z
    if (z <= (-3.1d+184)) then
        tmp = t_1
    else if (z <= (-6d+168)) then
        tmp = x * z
    else if (z <= (-2.2d+101)) then
        tmp = t_1
    else if (z <= 1450000000.0d0) then
        tmp = x + (y * t)
    else if (z <= 7.5d+116) then
        tmp = x * z
    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 = t * -z;
	double tmp;
	if (z <= -3.1e+184) {
		tmp = t_1;
	} else if (z <= -6e+168) {
		tmp = x * z;
	} else if (z <= -2.2e+101) {
		tmp = t_1;
	} else if (z <= 1450000000.0) {
		tmp = x + (y * t);
	} else if (z <= 7.5e+116) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if z <= -3.1e+184:
		tmp = t_1
	elif z <= -6e+168:
		tmp = x * z
	elif z <= -2.2e+101:
		tmp = t_1
	elif z <= 1450000000.0:
		tmp = x + (y * t)
	elif z <= 7.5e+116:
		tmp = x * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (z <= -3.1e+184)
		tmp = t_1;
	elseif (z <= -6e+168)
		tmp = Float64(x * z);
	elseif (z <= -2.2e+101)
		tmp = t_1;
	elseif (z <= 1450000000.0)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 7.5e+116)
		tmp = Float64(x * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (z <= -3.1e+184)
		tmp = t_1;
	elseif (z <= -6e+168)
		tmp = x * z;
	elseif (z <= -2.2e+101)
		tmp = t_1;
	elseif (z <= 1450000000.0)
		tmp = x + (y * t);
	elseif (z <= 7.5e+116)
		tmp = x * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[z, -3.1e+184], t$95$1, If[LessEqual[z, -6e+168], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.2e+101], t$95$1, If[LessEqual[z, 1450000000.0], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+116], N[(x * z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0999999999999998e184 or -5.9999999999999996e168 < z < -2.2000000000000001e101 or 7.5e116 < 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 64.2%

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

   4. Taylor expanded in y around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in x around 0 58.4%

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

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

      3. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -3.0999999999999998e184 < z < -5.9999999999999996e168 or 1.45e9 < z < 7.5e116

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. distribute-rgt-neg-in 68.6%

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

      3. sub-neg 68.6%

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

      4. +-commutative 68.6%

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

      5. distribute-neg-in 68.6%

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

      6. remove-double-neg 68.6%

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

      7. sub-neg 68.6%

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

   5. Simplified 68.6%

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

      1. sub-neg 68.6%

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

      2. distribute-rgt-in 65.0%

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

   7. Applied egg-rr 65.0%

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

      1. associate-+r+ 65.0%

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

      2. distribute-lft-neg-out 65.0%

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

      3. unsub-neg 65.0%

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

      4. *-un-lft-identity 65.0%

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

      5. distribute-rgt-out 65.0%

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

   9. Applied egg-rr 65.0%

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

   10. Taylor expanded in z around inf 63.3%

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

       1. *-commutative 63.3%

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

   12. Simplified 63.3%

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

   if -2.2000000000000001e101 < z < 1.45e9

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.4%

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

   4. Taylor expanded in y around inf 62.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+168}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1450000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 44.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -0.0071:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4200000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))) (t_2 (* x (- 1.0 y))))
   (if (<= t -0.0071)
     t_1
     (if (<= t 3.2e-81)
       t_2
       (if (<= t 4200000000000.0) (* x z) (if (<= t 3.3e+39) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (t <= -0.0071) {
		tmp = t_1;
	} else if (t <= 3.2e-81) {
		tmp = t_2;
	} else if (t <= 4200000000000.0) {
		tmp = x * z;
	} else if (t <= 3.3e+39) {
		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 = t * -z
    t_2 = x * (1.0d0 - y)
    if (t <= (-0.0071d0)) then
        tmp = t_1
    else if (t <= 3.2d-81) then
        tmp = t_2
    else if (t <= 4200000000000.0d0) then
        tmp = x * z
    else if (t <= 3.3d+39) 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 = t * -z;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (t <= -0.0071) {
		tmp = t_1;
	} else if (t <= 3.2e-81) {
		tmp = t_2;
	} else if (t <= 4200000000000.0) {
		tmp = x * z;
	} else if (t <= 3.3e+39) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	t_2 = x * (1.0 - y)
	tmp = 0
	if t <= -0.0071:
		tmp = t_1
	elif t <= 3.2e-81:
		tmp = t_2
	elif t <= 4200000000000.0:
		tmp = x * z
	elif t <= 3.3e+39:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -0.0071)
		tmp = t_1;
	elseif (t <= 3.2e-81)
		tmp = t_2;
	elseif (t <= 4200000000000.0)
		tmp = Float64(x * z);
	elseif (t <= 3.3e+39)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (t <= -0.0071)
		tmp = t_1;
	elseif (t <= 3.2e-81)
		tmp = t_2;
	elseif (t <= 4200000000000.0)
		tmp = x * z;
	elseif (t <= 3.3e+39)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.0071], t$95$1, If[LessEqual[t, 3.2e-81], t$95$2, If[LessEqual[t, 4200000000000.0], N[(x * z), $MachinePrecision], If[LessEqual[t, 3.3e+39], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.0071000000000000004 or 3.30000000000000021e39 < 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 95.6%

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

   4. Taylor expanded in y around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   6. Simplified 58.5%

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

   7. Taylor expanded in x around 0 51.4%

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

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

      3. *-commutative 51.4%

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

   9. Simplified 51.4%

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

   if -0.0071000000000000004 < t < 3.2e-81 or 4.2e12 < t < 3.30000000000000021e39

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. distribute-rgt-neg-in 84.9%

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

      3. sub-neg 84.9%

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

      4. +-commutative 84.9%

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

      5. distribute-neg-in 84.9%

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

      6. remove-double-neg 84.9%

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

      7. sub-neg 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in z around 0 55.3%

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

      1. *-rgt-identity 55.3%

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

      2. mul-1-neg 55.3%

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

      3. distribute-rgt-neg-out 55.3%

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

      4. distribute-lft-in 55.3%

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

      5. unsub-neg 55.3%

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

   8. Simplified 55.3%

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

   if 3.2e-81 < t < 4.2e12

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-rgt-neg-in 61.2%

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

      3. sub-neg 61.2%

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

      4. +-commutative 61.2%

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

      5. distribute-neg-in 61.2%

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

      6. remove-double-neg 61.2%

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

      7. sub-neg 61.2%

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

   5. Simplified 61.2%

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

      1. sub-neg 61.2%

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

      2. distribute-rgt-in 54.7%

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

   7. Applied egg-rr 54.7%

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

      1. associate-+r+ 54.7%

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

      2. distribute-lft-neg-out 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-un-lft-identity 54.7%

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

      5. distribute-rgt-out 54.7%

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

   9. Applied egg-rr 54.7%

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

   10. Taylor expanded in z around inf 51.5%

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

       1. *-commutative 51.5%

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

   12. Simplified 51.5%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0071:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 4200000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3500:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= t -2.15e-18)
     t_1
     (if (<= t -1.2e-148)
       (* x z)
       (if (<= t -1.25e-235) x (if (<= t 3500.0) (* x z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (t <= -2.15e-18) {
		tmp = t_1;
	} else if (t <= -1.2e-148) {
		tmp = x * z;
	} else if (t <= -1.25e-235) {
		tmp = x;
	} else if (t <= 3500.0) {
		tmp = x * z;
	} 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 = t * -z
    if (t <= (-2.15d-18)) then
        tmp = t_1
    else if (t <= (-1.2d-148)) then
        tmp = x * z
    else if (t <= (-1.25d-235)) then
        tmp = x
    else if (t <= 3500.0d0) then
        tmp = x * z
    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 = t * -z;
	double tmp;
	if (t <= -2.15e-18) {
		tmp = t_1;
	} else if (t <= -1.2e-148) {
		tmp = x * z;
	} else if (t <= -1.25e-235) {
		tmp = x;
	} else if (t <= 3500.0) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if t <= -2.15e-18:
		tmp = t_1
	elif t <= -1.2e-148:
		tmp = x * z
	elif t <= -1.25e-235:
		tmp = x
	elif t <= 3500.0:
		tmp = x * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (t <= -2.15e-18)
		tmp = t_1;
	elseif (t <= -1.2e-148)
		tmp = Float64(x * z);
	elseif (t <= -1.25e-235)
		tmp = x;
	elseif (t <= 3500.0)
		tmp = Float64(x * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (t <= -2.15e-18)
		tmp = t_1;
	elseif (t <= -1.2e-148)
		tmp = x * z;
	elseif (t <= -1.25e-235)
		tmp = x;
	elseif (t <= 3500.0)
		tmp = x * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[t, -2.15e-18], t$95$1, If[LessEqual[t, -1.2e-148], N[(x * z), $MachinePrecision], If[LessEqual[t, -1.25e-235], x, If[LessEqual[t, 3500.0], N[(x * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1500000000000001e-18 or 3500 < 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 92.4%

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

   4. Taylor expanded in y around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unsub-neg 57.2%

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

   6. Simplified 57.2%

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

   7. Taylor expanded in x around 0 49.3%

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

      1. associate-*r* 49.3%

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

      2. neg-mul-1 49.3%

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

      3. *-commutative 49.3%

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

   9. Simplified 49.3%

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

   if -2.1500000000000001e-18 < t < -1.2000000000000001e-148 or -1.2499999999999999e-235 < t < 3500

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. distribute-rgt-neg-in 83.7%

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

      3. sub-neg 83.7%

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

      4. +-commutative 83.7%

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

      5. distribute-neg-in 83.7%

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

      6. remove-double-neg 83.7%

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

      7. sub-neg 83.7%

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

   5. Simplified 83.7%

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

      1. sub-neg 83.7%

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

      2. distribute-rgt-in 81.6%

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

   7. Applied egg-rr 81.6%

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

      1. associate-+r+ 81.6%

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

      2. distribute-lft-neg-out 81.6%

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

      3. unsub-neg 81.6%

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

      4. *-un-lft-identity 81.6%

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

      5. distribute-rgt-out 81.6%

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

   9. Applied egg-rr 81.6%

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

   10. Taylor expanded in z around inf 43.4%

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

       1. *-commutative 43.4%

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

   12. Simplified 43.4%

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

   if -1.2000000000000001e-148 < t < -1.2499999999999999e-235

   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 58.4%

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

   4. Taylor expanded in x around inf 38.5%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3500:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+177}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-14} \lor \neg \left(t \leq 114\right):\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e+177)
   (+ x (* y t))
   (if (or (<= t -2.55e-14) (not (<= t 114.0))) (- x (* z t)) (+ x (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e+177) {
		tmp = x + (y * t);
	} else if ((t <= -2.55e-14) || !(t <= 114.0)) {
		tmp = x - (z * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.8d+177)) then
        tmp = x + (y * t)
    else if ((t <= (-2.55d-14)) .or. (.not. (t <= 114.0d0))) then
        tmp = x - (z * t)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e+177) {
		tmp = x + (y * t);
	} else if ((t <= -2.55e-14) || !(t <= 114.0)) {
		tmp = x - (z * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e+177:
		tmp = x + (y * t)
	elif (t <= -2.55e-14) or not (t <= 114.0):
		tmp = x - (z * t)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e+177)
		tmp = Float64(x + Float64(y * t));
	elseif ((t <= -2.55e-14) || !(t <= 114.0))
		tmp = Float64(x - Float64(z * t));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e+177)
		tmp = x + (y * t);
	elseif ((t <= -2.55e-14) || ~((t <= 114.0)))
		tmp = x - (z * t);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e+177], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.55e-14], N[Not[LessEqual[t, 114.0]], $MachinePrecision]], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000001e177

   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 y around inf 67.4%

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

   if -1.80000000000000001e177 < t < -2.5499999999999999e-14 or 114 < 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 90.8%

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

   4. Taylor expanded in y around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. unsub-neg 59.5%

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

   6. Simplified 59.5%

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

   if -2.5499999999999999e-14 < t < 114

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. distribute-rgt-neg-in 83.0%

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

      3. sub-neg 83.0%

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

      4. +-commutative 83.0%

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

      5. distribute-neg-in 83.0%

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

      6. remove-double-neg 83.0%

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

      7. sub-neg 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in y around 0 58.2%

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

      1. *-commutative 58.2%

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

   8. Simplified 58.2%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+177}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-14} \lor \neg \left(t \leq 114\right):\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.44:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 12200000000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.44)
   (* x z)
   (if (<= z 5.8e-243) x (if (<= z 12200000000.0) (* x (- y)) (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.44) {
		tmp = x * z;
	} else if (z <= 5.8e-243) {
		tmp = x;
	} else if (z <= 12200000000.0) {
		tmp = x * -y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-0.44d0)) then
        tmp = x * z
    else if (z <= 5.8d-243) then
        tmp = x
    else if (z <= 12200000000.0d0) then
        tmp = x * -y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.44) {
		tmp = x * z;
	} else if (z <= 5.8e-243) {
		tmp = x;
	} else if (z <= 12200000000.0) {
		tmp = x * -y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.44:
		tmp = x * z
	elif z <= 5.8e-243:
		tmp = x
	elif z <= 12200000000.0:
		tmp = x * -y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.44)
		tmp = Float64(x * z);
	elseif (z <= 5.8e-243)
		tmp = x;
	elseif (z <= 12200000000.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.44)
		tmp = x * z;
	elseif (z <= 5.8e-243)
		tmp = x;
	elseif (z <= 12200000000.0)
		tmp = x * -y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.44], N[(x * z), $MachinePrecision], If[LessEqual[z, 5.8e-243], x, If[LessEqual[z, 12200000000.0], N[(x * (-y)), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.440000000000000002 or 1.22e10 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 51.8%

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

      1. mul-1-neg 51.8%

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

      2. distribute-rgt-neg-in 51.8%

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

      3. sub-neg 51.8%

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

      4. +-commutative 51.8%

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

      5. distribute-neg-in 51.8%

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

      6. remove-double-neg 51.8%

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

      7. sub-neg 51.8%

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

   5. Simplified 51.8%

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

      1. sub-neg 51.8%

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

      2. distribute-rgt-in 47.9%

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

   7. Applied egg-rr 47.9%

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

      1. associate-+r+ 47.9%

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

      2. distribute-lft-neg-out 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-un-lft-identity 47.9%

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

      5. distribute-rgt-out 47.9%

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

   9. Applied egg-rr 47.9%

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

   10. Taylor expanded in z around inf 43.3%

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

       1. *-commutative 43.3%

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

   12. Simplified 43.3%

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

   if -0.440000000000000002 < z < 5.79999999999999953e-243

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.6%

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

   4. Taylor expanded in x around inf 37.0%

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

   if 5.79999999999999953e-243 < z < 1.22e10

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-rgt-neg-in 54.1%

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

      3. sub-neg 54.1%

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

      4. +-commutative 54.1%

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

      5. distribute-neg-in 54.1%

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

      6. remove-double-neg 54.1%

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

      7. sub-neg 54.1%

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

   5. Simplified 54.1%

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

      1. sub-neg 54.1%

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

      2. distribute-rgt-in 54.1%

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

   7. Applied egg-rr 54.1%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. unsub-neg 52.6%

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

      4. *-commutative 52.6%

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

   10. Simplified 52.6%

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

   11. Taylor expanded in y around inf 33.6%

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

       1. associate-*r* 33.6%

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

       2. neg-mul-1 33.6%

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

       3. *-commutative 33.6%

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

   13. Simplified 33.6%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.44:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 12200000000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-34} \lor \neg \left(t \leq 1.65 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.45e-34) (not (<= t 1.65e+37)))
   (+ x (* (- y z) t))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-34) || !(t <= 1.65e+37)) {
		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 ((t <= (-1.45d-34)) .or. (.not. (t <= 1.65d+37))) 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 ((t <= -1.45e-34) || !(t <= 1.65e+37)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.45e-34) or not (t <= 1.65e+37):
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.45e-34) || !(t <= 1.65e+37))
		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 ((t <= -1.45e-34) || ~((t <= 1.65e+37)))
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.45e-34], N[Not[LessEqual[t, 1.65e+37]], $MachinePrecision]], 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 2 regimes

2. if t < -1.4500000000000001e-34 or 1.65e37 < 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 95.6%

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

   if -1.4500000000000001e-34 < t < 1.65e37

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. distribute-rgt-neg-in 82.7%

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

      3. sub-neg 82.7%

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

      4. +-commutative 82.7%

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

      5. distribute-neg-in 82.7%

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

      6. remove-double-neg 82.7%

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

      7. sub-neg 82.7%

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

   5. Simplified 82.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-34} \lor \neg \left(t \leq 1.65 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.062 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.062) (not (<= z 1.0))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.062) || !(z <= 1.0)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.062d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.062) || !(z <= 1.0)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.062) or not (z <= 1.0):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.062) || !(z <= 1.0))
		tmp = Float64(x * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.062) || ~((z <= 1.0)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.062], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.062 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 52.5%

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

      1. mul-1-neg 52.5%

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

      2. distribute-rgt-neg-in 52.5%

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

      3. sub-neg 52.5%

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

      4. +-commutative 52.5%

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

      5. distribute-neg-in 52.5%

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

      6. remove-double-neg 52.5%

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

      7. sub-neg 52.5%

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

   5. Simplified 52.5%

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

      1. sub-neg 52.5%

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

      2. distribute-rgt-in 48.7%

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

   7. Applied egg-rr 48.7%

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

      1. associate-+r+ 48.7%

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

      2. distribute-lft-neg-out 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-un-lft-identity 48.7%

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

      5. distribute-rgt-out 48.7%

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

   9. Applied egg-rr 48.7%

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

   10. Taylor expanded in z around inf 43.1%

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

       1. *-commutative 43.1%

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

   12. Simplified 43.1%

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

   if -0.062 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 79.5%

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

   4. Taylor expanded in x around inf 30.1%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.062 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 17.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 68.1%

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

4. Taylor expanded in x around inf 16.0%

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

Developer target: 96.3% 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 2024085 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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