Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.3s

Alternatives: 13

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 35.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+45}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -1e+262)
     t_1
     (if (<= z -8e+45)
       (* z x)
       (if (<= z -1.35e-125)
         t_1
         (if (<= z 1.1e-157) x (if (<= z 1.96e+87) (* y (- x)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1e+262) {
		tmp = t_1;
	} else if (z <= -8e+45) {
		tmp = z * x;
	} else if (z <= -1.35e-125) {
		tmp = t_1;
	} else if (z <= 1.1e-157) {
		tmp = x;
	} else if (z <= 1.96e+87) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-1d+262)) then
        tmp = t_1
    else if (z <= (-8d+45)) then
        tmp = z * x
    else if (z <= (-1.35d-125)) then
        tmp = t_1
    else if (z <= 1.1d-157) then
        tmp = x
    else if (z <= 1.96d+87) then
        tmp = y * -x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1e+262) {
		tmp = t_1;
	} else if (z <= -8e+45) {
		tmp = z * x;
	} else if (z <= -1.35e-125) {
		tmp = t_1;
	} else if (z <= 1.1e-157) {
		tmp = x;
	} else if (z <= 1.96e+87) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -1e+262:
		tmp = t_1
	elif z <= -8e+45:
		tmp = z * x
	elif z <= -1.35e-125:
		tmp = t_1
	elif z <= 1.1e-157:
		tmp = x
	elif z <= 1.96e+87:
		tmp = y * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -1e+262)
		tmp = t_1;
	elseif (z <= -8e+45)
		tmp = Float64(z * x);
	elseif (z <= -1.35e-125)
		tmp = t_1;
	elseif (z <= 1.1e-157)
		tmp = x;
	elseif (z <= 1.96e+87)
		tmp = Float64(y * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -1e+262)
		tmp = t_1;
	elseif (z <= -8e+45)
		tmp = z * x;
	elseif (z <= -1.35e-125)
		tmp = t_1;
	elseif (z <= 1.1e-157)
		tmp = x;
	elseif (z <= 1.96e+87)
		tmp = y * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -1e+262], t$95$1, If[LessEqual[z, -8e+45], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.35e-125], t$95$1, If[LessEqual[z, 1.1e-157], x, If[LessEqual[z, 1.96e+87], N[(y * (-x)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1e262 or -7.9999999999999994e45 < z < -1.3499999999999999e-125 or 1.96e87 < z

   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 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in x around 0 47.6%

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

      1. associate-*r* 47.6%

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

      2. mul-1-neg 47.6%

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

   8. Simplified 47.6%

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

   if -1e262 < z < -7.9999999999999994e45

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in z around inf 54.6%

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

   if -1.3499999999999999e-125 < z < 1.10000000000000005e-157

   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 96.6%

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

      1. *-commutative 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in y around 0 42.6%

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

   if 1.10000000000000005e-157 < z < 1.96e87

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around inf 43.3%

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

      1. mul-1-neg 43.3%

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

   8. Simplified 43.3%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+262}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+45}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 0.00035:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* x (+ z 1.0))))
   (if (<= t -1.06e-112)
     t_1
     (if (<= t 1.55e-213)
       t_2
       (if (<= t 0.00035) (* x (- 1.0 y)) (if (<= t 3.4e+52) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (t <= -1.06e-112) {
		tmp = t_1;
	} else if (t <= 1.55e-213) {
		tmp = t_2;
	} else if (t <= 0.00035) {
		tmp = x * (1.0 - y);
	} else if (t <= 3.4e+52) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * t
    t_2 = x * (z + 1.0d0)
    if (t <= (-1.06d-112)) then
        tmp = t_1
    else if (t <= 1.55d-213) then
        tmp = t_2
    else if (t <= 0.00035d0) then
        tmp = x * (1.0d0 - y)
    else if (t <= 3.4d+52) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (t <= -1.06e-112) {
		tmp = t_1;
	} else if (t <= 1.55e-213) {
		tmp = t_2;
	} else if (t <= 0.00035) {
		tmp = x * (1.0 - y);
	} else if (t <= 3.4e+52) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = x * (z + 1.0)
	tmp = 0
	if t <= -1.06e-112:
		tmp = t_1
	elif t <= 1.55e-213:
		tmp = t_2
	elif t <= 0.00035:
		tmp = x * (1.0 - y)
	elif t <= 3.4e+52:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (t <= -1.06e-112)
		tmp = t_1;
	elseif (t <= 1.55e-213)
		tmp = t_2;
	elseif (t <= 0.00035)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (t <= 3.4e+52)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (t <= -1.06e-112)
		tmp = t_1;
	elseif (t <= 1.55e-213)
		tmp = t_2;
	elseif (t <= 0.00035)
		tmp = x * (1.0 - y);
	elseif (t <= 3.4e+52)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.06e-112], t$95$1, If[LessEqual[t, 1.55e-213], t$95$2, If[LessEqual[t, 0.00035], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+52], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0600000000000001e-112 or 3.4e52 < t

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 91.2%

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

   4. Applied egg-rr 91.2%

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

   5. Taylor expanded in y around inf 88.4%

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

      1. associate-*r* 88.4%

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

      2. mul-1-neg 88.4%

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

   7. Simplified 88.4%

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

      1. associate-+r+ 88.4%

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

      2. distribute-lft-neg-out 88.4%

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

      3. unsub-neg 88.4%

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

      4. +-commutative 88.4%

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

      5. *-commutative 88.4%

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

   9. Applied egg-rr 88.4%

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

   10. Taylor expanded in t around inf 73.9%

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

   if -1.0600000000000001e-112 < t < 1.5499999999999999e-213 or 3.49999999999999996e-4 < t < 3.4e52

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. unsub-neg 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in y around 0 70.8%

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

      1. +-commutative 70.8%

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

   8. Simplified 70.8%

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

   if 1.5499999999999999e-213 < t < 3.49999999999999996e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in z around 0 66.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{-112}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 0.00035:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-257}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -4.7e-8)
     t_1
     (if (<= y 1.62e-257)
       (- x (* z t))
       (if (<= y 5.8e+63) (* x (+ z 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -4.7e-8) {
		tmp = t_1;
	} else if (y <= 1.62e-257) {
		tmp = x - (z * t);
	} else if (y <= 5.8e+63) {
		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 * (t - x)
    if (y <= (-4.7d-8)) then
        tmp = t_1
    else if (y <= 1.62d-257) then
        tmp = x - (z * t)
    else if (y <= 5.8d+63) 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 * (t - x);
	double tmp;
	if (y <= -4.7e-8) {
		tmp = t_1;
	} else if (y <= 1.62e-257) {
		tmp = x - (z * t);
	} else if (y <= 5.8e+63) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -4.7e-8:
		tmp = t_1
	elif y <= 1.62e-257:
		tmp = x - (z * t)
	elif y <= 5.8e+63:
		tmp = x * (z + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -4.7e-8)
		tmp = t_1;
	elseif (y <= 1.62e-257)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 5.8e+63)
		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 * (t - x);
	tmp = 0.0;
	if (y <= -4.7e-8)
		tmp = t_1;
	elseif (y <= 1.62e-257)
		tmp = x - (z * t);
	elseif (y <= 5.8e+63)
		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[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e-8], t$95$1, If[LessEqual[y, 1.62e-257], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+63], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6999999999999997e-8 or 5.7999999999999999e63 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 94.9%

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in y around inf 86.5%

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

      1. associate-*r* 86.5%

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

      2. mul-1-neg 86.5%

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

   7. Simplified 86.5%

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

      1. associate-+r+ 86.5%

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

      2. distribute-lft-neg-out 86.5%

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

      3. unsub-neg 86.5%

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

      4. +-commutative 86.5%

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

      5. *-commutative 86.5%

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

   9. Applied egg-rr 86.5%

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

   10. Taylor expanded in y around inf 77.6%

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

   if -4.6999999999999997e-8 < y < 1.6200000000000001e-257

   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 96.6%

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

      1. mul-1-neg 96.6%

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

      2. unsub-neg 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in t around inf 80.2%

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

   if 1.6200000000000001e-257 < y < 5.7999999999999999e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. unsub-neg 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in y around 0 63.4%

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

      1. +-commutative 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-257}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-8} \lor \neg \left(y - z \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -5e-8) (not (<= (- y z) 2e-15))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -5e-8) || !((y - z) <= 2e-15)) {
		tmp = (y - z) * 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 - z) <= (-5d-8)) .or. (.not. ((y - z) <= 2d-15))) then
        tmp = (y - z) * 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 - z) <= -5e-8) || !((y - z) <= 2e-15)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -5e-8) or not ((y - z) <= 2e-15):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -5e-8) || !(Float64(y - z) <= 2e-15))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -5e-8) || ~(((y - z) <= 2e-15)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -5e-8], N[Not[LessEqual[N[(y - z), $MachinePrecision], 2e-15]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -4.9999999999999998e-8 or 2.0000000000000002e-15 < (-.f64 y z)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 93.9%

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

   4. Applied egg-rr 93.9%

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

   5. Taylor expanded in y around inf 73.5%

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

      1. associate-*r* 73.5%

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

      2. mul-1-neg 73.5%

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

   7. Simplified 73.5%

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

      1. associate-+r+ 73.5%

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

      2. distribute-lft-neg-out 73.5%

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

      3. unsub-neg 73.5%

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

      4. +-commutative 73.5%

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

      5. *-commutative 73.5%

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

   9. Applied egg-rr 73.5%

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

   10. Taylor expanded in t around inf 52.0%

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

   if -4.9999999999999998e-8 < (-.f64 y z) < 2.0000000000000002e-15

   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 84.2%

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

      1. *-commutative 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in y around 0 71.9%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-8} \lor \neg \left(y - z \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -63000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -63000.0)
   (* z x)
   (if (<= z -5.2e-99) (* y (- x)) (if (<= z 1.6e-15) x (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -63000.0) {
		tmp = z * x;
	} else if (z <= -5.2e-99) {
		tmp = y * -x;
	} else if (z <= 1.6e-15) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-63000.0d0)) then
        tmp = z * x
    else if (z <= (-5.2d-99)) then
        tmp = y * -x
    else if (z <= 1.6d-15) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -63000.0) {
		tmp = z * x;
	} else if (z <= -5.2e-99) {
		tmp = y * -x;
	} else if (z <= 1.6e-15) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -63000.0:
		tmp = z * x
	elif z <= -5.2e-99:
		tmp = y * -x
	elif z <= 1.6e-15:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -63000.0)
		tmp = Float64(z * x);
	elseif (z <= -5.2e-99)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.6e-15)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -63000.0)
		tmp = z * x;
	elseif (z <= -5.2e-99)
		tmp = y * -x;
	elseif (z <= 1.6e-15)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -63000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -5.2e-99], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.6e-15], x, N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -63000 or 1.6e-15 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. unsub-neg 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in z around inf 44.3%

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

   if -63000 < z < -5.2000000000000001e-99

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in y around inf 43.2%

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

      1. mul-1-neg 43.2%

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

   8. Simplified 43.2%

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

   if -5.2000000000000001e-99 < z < 1.6e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 93.8%

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

      1. *-commutative 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in y around 0 40.5%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -63000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-50} \lor \neg \left(t \leq 1.05 \cdot 10^{+62}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.5e-50) (not (<= t 1.05e+62)))
   (* (- y z) t)
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.5e-50) || !(t <= 1.05e+62)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.5d-50)) .or. (.not. (t <= 1.05d+62))) then
        tmp = (y - z) * t
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.5e-50) || !(t <= 1.05e+62)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.5e-50) or not (t <= 1.05e+62):
		tmp = (y - z) * t
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.5e-50) || !(t <= 1.05e+62))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.5e-50) || ~((t <= 1.05e+62)))
		tmp = (y - z) * t;
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.5e-50], N[Not[LessEqual[t, 1.05e+62]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.49999999999999984e-50 or 1.05e62 < t

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in y around inf 89.8%

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

      1. associate-*r* 89.8%

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

      2. mul-1-neg 89.8%

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

   7. Simplified 89.8%

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

      1. associate-+r+ 89.8%

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

      2. distribute-lft-neg-out 89.8%

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

      3. unsub-neg 89.8%

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

      4. +-commutative 89.8%

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

      5. *-commutative 89.8%

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

   9. Applied egg-rr 89.8%

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

   10. Taylor expanded in t around inf 78.9%

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

   if -2.49999999999999984e-50 < t < 1.05e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.1%

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

      1. mul-1-neg 83.1%

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

      2. unsub-neg 83.1%

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

   5. Simplified 83.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-50} \lor \neg \left(t \leq 1.05 \cdot 10^{+62}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-51} \lor \neg \left(t \leq 1.7 \cdot 10^{+54}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4e-51) (not (<= t 1.7e+54)))
   (- x (* t (- z y)))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4e-51) || !(t <= 1.7e+54)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4d-51)) .or. (.not. (t <= 1.7d+54))) then
        tmp = x - (t * (z - y))
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4e-51) || !(t <= 1.7e+54)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4e-51) or not (t <= 1.7e+54):
		tmp = x - (t * (z - y))
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4e-51) || !(t <= 1.7e+54))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4e-51) || ~((t <= 1.7e+54)))
		tmp = x - (t * (z - y));
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4e-51], N[Not[LessEqual[t, 1.7e+54]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4e-51 or 1.7e54 < 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 84.6%

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

   if -4e-51 < t < 1.7e54

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. unsub-neg 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-51} \lor \neg \left(t \leq 1.7 \cdot 10^{+54}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 3.9 \cdot 10^{+20}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.175) (not (<= z 3.9e+20)))
   (- x (* z (- t x)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.175) || !(z <= 3.9e+20)) {
		tmp = x - (z * (t - x));
	} 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 <= (-0.175d0)) .or. (.not. (z <= 3.9d+20))) then
        tmp = x - (z * (t - x))
    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 <= -0.175) || !(z <= 3.9e+20)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.175) or not (z <= 3.9e+20):
		tmp = x - (z * (t - x))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.175) || !(z <= 3.9e+20))
		tmp = Float64(x - Float64(z * Float64(t - x)));
	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 <= -0.175) || ~((z <= 3.9e+20)))
		tmp = x - (z * (t - x));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.175], N[Not[LessEqual[z, 3.9e+20]], $MachinePrecision]], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.17499999999999999 or 3.9e20 < 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 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

   5. Simplified 83.2%

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

   if -0.17499999999999999 < z < 3.9e20

   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 91.1%

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

      1. *-commutative 91.1%

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

   5. Simplified 91.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 3.9 \cdot 10^{+20}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.48 \cdot 10^{-111} \lor \neg \left(t \leq 9.2 \cdot 10^{+51}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.48e-111) (not (<= t 9.2e+51)))
   (* (- y z) t)
   (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.48e-111) || !(t <= 9.2e+51)) {
		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 <= (-1.48d-111)) .or. (.not. (t <= 9.2d+51))) 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 <= -1.48e-111) || !(t <= 9.2e+51)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.48e-111) or not (t <= 9.2e+51):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.48e-111) || !(t <= 9.2e+51))
		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 <= -1.48e-111) || ~((t <= 9.2e+51)))
		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, -1.48e-111], N[Not[LessEqual[t, 9.2e+51]], $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 < -1.4799999999999999e-111 or 9.2000000000000002e51 < t

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 91.2%

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

   4. Applied egg-rr 91.2%

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

   5. Taylor expanded in y around inf 88.4%

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

      1. associate-*r* 88.4%

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

      2. mul-1-neg 88.4%

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

   7. Simplified 88.4%

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

      1. associate-+r+ 88.4%

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

      2. distribute-lft-neg-out 88.4%

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

      3. unsub-neg 88.4%

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

      4. +-commutative 88.4%

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

      5. *-commutative 88.4%

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

   9. Applied egg-rr 88.4%

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

   10. Taylor expanded in t around inf 73.9%

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

   if -1.4799999999999999e-111 < t < 9.2000000000000002e51

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in y around 0 64.7%

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

      1. +-commutative 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.48 \cdot 10^{-111} \lor \neg \left(t \leq 9.2 \cdot 10^{+51}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.6 \cdot 10^{-15}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.6e-15))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.6e-15)) {
		tmp = z * x;
	} 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 <= (-1.0d0)) .or. (.not. (z <= 1.6d-15))) then
        tmp = z * x
    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 <= -1.0) || !(z <= 1.6e-15)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.6e-15):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.6e-15))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.6e-15)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.6e-15]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.6e-15 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. unsub-neg 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in z around inf 44.3%

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

   if -1 < z < 1.6e-15

   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 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in y around 0 37.0%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.6 \cdot 10^{-15}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 13: 17.5% 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 58.2%

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

   1. *-commutative 58.2%

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

5. Simplified 58.2%

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

6. Taylor expanded in y around 0 18.8%

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

7. Final simplification 18.8%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.0% 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 2024130 
(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))))