Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.3s

Alternatives: 12

Speedup: 1.0×

• 34.5% 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: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -3 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* (- y z) t)))
   (if (<= z -3e+186)
     t_1
     (if (<= z -3.3e-187)
       t_2
       (if (<= z 1.3e-270) (* x (- 1.0 y)) (if (<= z 3.6e+25) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -3e+186) {
		tmp = t_1;
	} else if (z <= -3.3e-187) {
		tmp = t_2;
	} else if (z <= 1.3e-270) {
		tmp = x * (1.0 - y);
	} else if (z <= 3.6e+25) {
		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 = z * (x - t)
    t_2 = (y - z) * t
    if (z <= (-3d+186)) then
        tmp = t_1
    else if (z <= (-3.3d-187)) then
        tmp = t_2
    else if (z <= 1.3d-270) then
        tmp = x * (1.0d0 - y)
    else if (z <= 3.6d+25) 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 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -3e+186) {
		tmp = t_1;
	} else if (z <= -3.3e-187) {
		tmp = t_2;
	} else if (z <= 1.3e-270) {
		tmp = x * (1.0 - y);
	} else if (z <= 3.6e+25) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = (y - z) * t
	tmp = 0
	if z <= -3e+186:
		tmp = t_1
	elif z <= -3.3e-187:
		tmp = t_2
	elif z <= 1.3e-270:
		tmp = x * (1.0 - y)
	elif z <= 3.6e+25:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -3e+186)
		tmp = t_1;
	elseif (z <= -3.3e-187)
		tmp = t_2;
	elseif (z <= 1.3e-270)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 3.6e+25)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (z <= -3e+186)
		tmp = t_1;
	elseif (z <= -3.3e-187)
		tmp = t_2;
	elseif (z <= 1.3e-270)
		tmp = x * (1.0 - y);
	elseif (z <= 3.6e+25)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -3e+186], t$95$1, If[LessEqual[z, -3.3e-187], t$95$2, If[LessEqual[z, 1.3e-270], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+25], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999982e186 or 3.60000000000000015e25 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in x around 0 72.8%

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

      1. sub-neg 72.8%

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

      2. neg-mul-1 72.8%

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

      3. remove-double-neg 72.8%

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

      4. +-commutative 72.8%

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

   8. Simplified 72.8%

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

   9. Taylor expanded in z around inf 79.5%

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

   if -2.99999999999999982e186 < z < -3.3e-187 or 1.3000000000000001e-270 < z < 3.60000000000000015e25

   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 74.6%

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

      1. *-commutative 74.6%

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

      2. sub-neg 74.6%

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

      3. distribute-rgt-in 72.3%

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

   5. Applied egg-rr 72.3%

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

      1. associate-+r+ 72.3%

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

      2. distribute-lft-neg-out 72.3%

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

      3. unsub-neg 72.3%

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

      4. +-commutative 72.3%

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

      5. *-commutative 72.3%

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

   7. Applied egg-rr 72.3%

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

   8. Taylor expanded in t around inf 63.3%

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

   if -3.3e-187 < z < 1.3000000000000001e-270

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 74.5%

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

      1. neg-mul-1 74.5%

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

      2. unsub-neg 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-187}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+25}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -4.5e-30)
     t_1
     (if (<= t -1.55e-286)
       (* x (- 1.0 y))
       (if (<= t 1.35e-41) (* x (+ z 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -4.5e-30) {
		tmp = t_1;
	} else if (t <= -1.55e-286) {
		tmp = x * (1.0 - y);
	} else if (t <= 1.35e-41) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-4.5d-30)) then
        tmp = t_1
    else if (t <= (-1.55d-286)) then
        tmp = x * (1.0d0 - y)
    else if (t <= 1.35d-41) then
        tmp = x * (z + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -4.5e-30) {
		tmp = t_1;
	} else if (t <= -1.55e-286) {
		tmp = x * (1.0 - y);
	} else if (t <= 1.35e-41) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -4.5e-30:
		tmp = t_1
	elif t <= -1.55e-286:
		tmp = x * (1.0 - y)
	elif t <= 1.35e-41:
		tmp = x * (z + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -4.5e-30)
		tmp = t_1;
	elseif (t <= -1.55e-286)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (t <= 1.35e-41)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -4.5e-30)
		tmp = t_1;
	elseif (t <= -1.55e-286)
		tmp = x * (1.0 - y);
	elseif (t <= 1.35e-41)
		tmp = x * (z + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.5e-30], t$95$1, If[LessEqual[t, -1.55e-286], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-41], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999967e-30 or 1.35e-41 < 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 86.8%

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

      1. *-commutative 86.8%

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

      2. sub-neg 86.8%

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

      3. distribute-rgt-in 80.9%

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

   5. Applied egg-rr 80.9%

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

      1. associate-+r+ 80.9%

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

      2. distribute-lft-neg-out 80.9%

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

      3. unsub-neg 80.9%

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

      4. +-commutative 80.9%

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

      5. *-commutative 80.9%

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

   7. Applied egg-rr 80.9%

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

   8. Taylor expanded in t around inf 76.0%

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

   if -4.49999999999999967e-30 < t < -1.54999999999999991e-286

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in x around inf 53.5%

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

      1. neg-mul-1 53.5%

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

      2. unsub-neg 53.5%

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

   8. Simplified 53.5%

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

   if -1.54999999999999991e-286 < t < 1.35e-41

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.9%

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

      1. mul-1-neg 70.9%

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

      2. unsub-neg 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in x around inf 59.1%

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

      1. sub-neg 59.1%

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

      2. neg-mul-1 59.1%

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

      3. remove-double-neg 59.1%

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

      4. +-commutative 59.1%

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

   8. Simplified 59.1%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-146}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.85e-115)
     t_1
     (if (<= t -6.8e-286) (* y (- x)) (if (<= t 5.2e-146) (* x z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.85e-115) {
		tmp = t_1;
	} else if (t <= -6.8e-286) {
		tmp = y * -x;
	} else if (t <= 5.2e-146) {
		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 = (y - z) * t
    if (t <= (-1.85d-115)) then
        tmp = t_1
    else if (t <= (-6.8d-286)) then
        tmp = y * -x
    else if (t <= 5.2d-146) 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 = (y - z) * t;
	double tmp;
	if (t <= -1.85e-115) {
		tmp = t_1;
	} else if (t <= -6.8e-286) {
		tmp = y * -x;
	} else if (t <= 5.2e-146) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.85e-115:
		tmp = t_1
	elif t <= -6.8e-286:
		tmp = y * -x
	elif t <= 5.2e-146:
		tmp = x * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.85e-115)
		tmp = t_1;
	elseif (t <= -6.8e-286)
		tmp = Float64(y * Float64(-x));
	elseif (t <= 5.2e-146)
		tmp = Float64(x * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.85e-115)
		tmp = t_1;
	elseif (t <= -6.8e-286)
		tmp = y * -x;
	elseif (t <= 5.2e-146)
		tmp = x * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.85e-115], t$95$1, If[LessEqual[t, -6.8e-286], N[(y * (-x)), $MachinePrecision], If[LessEqual[t, 5.2e-146], N[(x * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.85e-115 or 5.19999999999999974e-146 < 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 80.8%

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

      1. *-commutative 80.8%

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

      2. sub-neg 80.8%

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

      3. distribute-rgt-in 76.0%

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

   5. Applied egg-rr 76.0%

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

      1. associate-+r+ 76.0%

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

      2. distribute-lft-neg-out 76.0%

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

      3. unsub-neg 76.0%

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

      4. +-commutative 76.0%

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

      5. *-commutative 76.0%

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

   7. Applied egg-rr 76.0%

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

   8. Taylor expanded in t around inf 69.3%

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

   if -1.85e-115 < t < -6.8000000000000002e-286

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 67.5%

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

      1. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in x around inf 61.3%

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

      1. neg-mul-1 61.3%

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

      2. unsub-neg 61.3%

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

   8. Simplified 61.3%

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

   9. Taylor expanded in y around inf 51.6%

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

       1. mul-1-neg 51.6%

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

       2. *-commutative 51.6%

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

       3. distribute-rgt-neg-in 51.6%

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

   11. Simplified 51.6%

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

   if -6.8000000000000002e-286 < t < 5.19999999999999974e-146

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in x around inf 64.8%

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

      1. sub-neg 64.8%

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

      2. neg-mul-1 64.8%

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

      3. remove-double-neg 64.8%

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

      4. +-commutative 64.8%

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

   8. Simplified 64.8%

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

   9. Taylor expanded in z around inf 42.9%

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

       1. *-commutative 42.9%

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

   11. Simplified 42.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-115}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-146}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{+62}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.72e+62)
   (* y t)
   (if (<= y 1.45e-136) (* t (- z)) (if (<= y 3e-39) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.72e+62) {
		tmp = y * t;
	} else if (y <= 1.45e-136) {
		tmp = t * -z;
	} else if (y <= 3e-39) {
		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 <= (-1.72d+62)) then
        tmp = y * t
    else if (y <= 1.45d-136) then
        tmp = t * -z
    else if (y <= 3d-39) 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 <= -1.72e+62) {
		tmp = y * t;
	} else if (y <= 1.45e-136) {
		tmp = t * -z;
	} else if (y <= 3e-39) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.72e+62:
		tmp = y * t
	elif y <= 1.45e-136:
		tmp = t * -z
	elif y <= 3e-39:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.72e+62)
		tmp = Float64(y * t);
	elseif (y <= 1.45e-136)
		tmp = Float64(t * Float64(-z));
	elseif (y <= 3e-39)
		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 <= -1.72e+62)
		tmp = y * t;
	elseif (y <= 1.45e-136)
		tmp = t * -z;
	elseif (y <= 3e-39)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.72e+62], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.45e-136], N[(t * (-z)), $MachinePrecision], If[LessEqual[y, 3e-39], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7200000000000001e62 or 3.00000000000000028e-39 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. sub-neg 61.4%

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

      3. distribute-rgt-in 54.3%

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

   5. Applied egg-rr 54.3%

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

      1. associate-+r+ 54.3%

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

      2. distribute-lft-neg-out 54.3%

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

      3. unsub-neg 54.3%

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

      4. +-commutative 54.3%

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

      5. *-commutative 54.3%

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

   7. Applied egg-rr 54.3%

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

   8. Taylor expanded in y around inf 51.3%

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

   if -1.7200000000000001e62 < y < 1.44999999999999997e-136

   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 70.6%

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

      1. *-commutative 70.6%

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

      2. sub-neg 70.6%

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

      3. distribute-rgt-in 70.6%

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

   5. Applied egg-rr 70.6%

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

      1. associate-+r+ 70.6%

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

      2. distribute-lft-neg-out 70.6%

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

      3. unsub-neg 70.6%

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

      4. +-commutative 70.6%

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

      5. *-commutative 70.6%

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

   7. Applied egg-rr 70.6%

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

   8. Taylor expanded in z around inf 43.0%

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

      1. associate-*r* 43.0%

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

      2. neg-mul-1 43.0%

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

   10. Simplified 43.0%

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

   if 1.44999999999999997e-136 < y < 3.00000000000000028e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y around 0 50.9%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{+62}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+65}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-255}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.32e+65)
   (* y t)
   (if (<= y 3.1e-255) (* x z) (if (<= y 1.05e-40) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.32e+65) {
		tmp = y * t;
	} else if (y <= 3.1e-255) {
		tmp = x * z;
	} else if (y <= 1.05e-40) {
		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 <= (-1.32d+65)) then
        tmp = y * t
    else if (y <= 3.1d-255) then
        tmp = x * z
    else if (y <= 1.05d-40) 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 <= -1.32e+65) {
		tmp = y * t;
	} else if (y <= 3.1e-255) {
		tmp = x * z;
	} else if (y <= 1.05e-40) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.32e+65:
		tmp = y * t
	elif y <= 3.1e-255:
		tmp = x * z
	elif y <= 1.05e-40:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.32e+65)
		tmp = Float64(y * t);
	elseif (y <= 3.1e-255)
		tmp = Float64(x * z);
	elseif (y <= 1.05e-40)
		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 <= -1.32e+65)
		tmp = y * t;
	elseif (y <= 3.1e-255)
		tmp = x * z;
	elseif (y <= 1.05e-40)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.32e+65], N[(y * t), $MachinePrecision], If[LessEqual[y, 3.1e-255], N[(x * z), $MachinePrecision], If[LessEqual[y, 1.05e-40], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.31999999999999995e65 or 1.05000000000000009e-40 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. sub-neg 61.4%

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

      3. distribute-rgt-in 54.3%

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

   5. Applied egg-rr 54.3%

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

      1. associate-+r+ 54.3%

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

      2. distribute-lft-neg-out 54.3%

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

      3. unsub-neg 54.3%

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

      4. +-commutative 54.3%

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

      5. *-commutative 54.3%

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

   7. Applied egg-rr 54.3%

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

   8. Taylor expanded in y around inf 51.3%

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

   if -1.31999999999999995e65 < y < 3.09999999999999997e-255

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. unsub-neg 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in x around inf 51.3%

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

      1. sub-neg 51.3%

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

      2. neg-mul-1 51.3%

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

      3. remove-double-neg 51.3%

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

      4. +-commutative 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in z around inf 35.9%

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

       1. *-commutative 35.9%

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

   11. Simplified 35.9%

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

   if 3.09999999999999997e-255 < y < 1.05000000000000009e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 47.1%

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

      1. *-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in y around 0 43.1%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+65}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-255}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+52} \lor \neg \left(y \leq 2.1 \cdot 10^{+39}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6e+52) (not (<= y 2.1e+39)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e+52) || !(y <= 2.1e+39)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - 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 <= (-6d+52)) .or. (.not. (y <= 2.1d+39))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e+52) || !(y <= 2.1e+39)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6e+52) or not (y <= 2.1e+39):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6e+52) || !(y <= 2.1e+39))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6e+52) || ~((y <= 2.1e+39)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6e+52], N[Not[LessEqual[y, 2.1e+39]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e52 or 2.0999999999999999e39 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.5%

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

      1. *-commutative 87.5%

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

   5. Simplified 87.5%

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

   if -6e52 < y < 2.0999999999999999e39

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

   5. Simplified 88.3%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+52} \lor \neg \left(y \leq 2.1 \cdot 10^{+39}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+28} \lor \neg \left(z \leq 3.6 \cdot 10^{+30}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.3e+28) (not (<= z 3.6e+30)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e+28) || !(z <= 3.6e+30)) {
		tmp = 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 <= (-3.3d+28)) .or. (.not. (z <= 3.6d+30))) then
        tmp = 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 <= -3.3e+28) || !(z <= 3.6e+30)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.3e+28) or not (z <= 3.6e+30):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.3e+28) || !(z <= 3.6e+30))
		tmp = 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 <= -3.3e+28) || ~((z <= 3.6e+30)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.3e+28], N[Not[LessEqual[z, 3.6e+30]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e28 or 3.6000000000000002e30 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in x around 0 71.5%

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

      1. sub-neg 71.5%

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

      2. neg-mul-1 71.5%

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

      3. remove-double-neg 71.5%

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

      4. +-commutative 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in z around inf 76.4%

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

   if -3.3e28 < z < 3.6000000000000002e30

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.0%

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

      1. *-commutative 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+28} \lor \neg \left(z \leq 3.6 \cdot 10^{+30}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+17} \lor \neg \left(z \leq 650000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.3e+17) (not (<= z 650000000000.0)))
   (* z (- x t))
   (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e+17) || !(z <= 650000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.3d+17)) .or. (.not. (z <= 650000000000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e+17) || !(z <= 650000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.3e+17) or not (z <= 650000000000.0):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.3e+17) || !(z <= 650000000000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.3e+17) || ~((z <= 650000000000.0)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.3e+17], N[Not[LessEqual[z, 650000000000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3e17 or 6.5e11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in x around 0 69.5%

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

      1. sub-neg 69.5%

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

      2. neg-mul-1 69.5%

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

      3. remove-double-neg 69.5%

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

      4. +-commutative 69.5%

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

   8. Simplified 69.5%

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

   9. Taylor expanded in z around inf 74.1%

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

   if -5.3e17 < z < 6.5e11

   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 77.6%

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

   4. Taylor expanded in y around inf 67.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+17} \lor \neg \left(z \leq 650000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-91} \lor \neg \left(t \leq 4.5 \cdot 10^{-42}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.7e-91) (not (<= t 4.5e-42))) (* (- y z) t) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.7e-91) || !(t <= 4.5e-42)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.7d-91)) .or. (.not. (t <= 4.5d-42))) then
        tmp = (y - z) * t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.7e-91) || !(t <= 4.5e-42)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.7e-91) or not (t <= 4.5e-42):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.7e-91) || !(t <= 4.5e-42))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.7e-91) || ~((t <= 4.5e-42)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.7e-91], N[Not[LessEqual[t, 4.5e-42]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.70000000000000006e-91 or 4.5e-42 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 84.1%

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

      1. *-commutative 84.1%

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

      2. sub-neg 84.1%

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

      3. distribute-rgt-in 78.7%

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

   5. Applied egg-rr 78.7%

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

      1. associate-+r+ 78.7%

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

      2. distribute-lft-neg-out 78.7%

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

      3. unsub-neg 78.7%

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

      4. +-commutative 78.7%

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

      5. *-commutative 78.7%

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

   7. Applied egg-rr 78.7%

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

   8. Taylor expanded in t around inf 73.5%

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

   if -4.70000000000000006e-91 < t < 4.5e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. unsub-neg 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in x around inf 52.7%

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

      1. sub-neg 52.7%

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

      2. neg-mul-1 52.7%

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

      3. remove-double-neg 52.7%

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

      4. +-commutative 52.7%

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

   8. Simplified 52.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-91} \lor \neg \left(t \leq 4.5 \cdot 10^{-42}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-104} \lor \neg \left(y \leq 1.55 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.5e-104) (not (<= y 1.55e-40))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5e-104) || !(y <= 1.55e-40)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.5d-104)) .or. (.not. (y <= 1.55d-40))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5e-104) || !(y <= 1.55e-40)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.5e-104) or not (y <= 1.55e-40):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.5e-104) || !(y <= 1.55e-40))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.5e-104) || ~((y <= 1.55e-40)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.5e-104], N[Not[LessEqual[y, 1.55e-40]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000001e-104 or 1.55000000000000005e-40 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 61.5%

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

      1. *-commutative 61.5%

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

      2. sub-neg 61.5%

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

      3. distribute-rgt-in 55.8%

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

   5. Applied egg-rr 55.8%

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

      1. associate-+r+ 55.8%

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

      2. distribute-lft-neg-out 55.8%

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

      3. unsub-neg 55.8%

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

      4. +-commutative 55.8%

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

      5. *-commutative 55.8%

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

   7. Applied egg-rr 55.8%

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

   8. Taylor expanded in y around inf 46.0%

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

   if -1.5000000000000001e-104 < y < 1.55000000000000005e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 37.9%

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

      1. *-commutative 37.9%

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

   5. Simplified 37.9%

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

   6. Taylor expanded in y around 0 33.0%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-104} \lor \neg \left(y \leq 1.55 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 18.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 60.5%

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

   1. *-commutative 60.5%

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

5. Simplified 60.5%

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

6. Taylor expanded in y around 0 15.6%

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

Developer Target 1: 96.7% 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 2024163 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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