Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 17

Speedup: 1.0×

• 34.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 0.0071 \lor \neg \left(t \leq 4 \cdot 10^{+65}\right) \land t \leq 1.9 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -5.1e+85)
     t_1
     (if (<= t -2.3e-9)
       (* z (- x t))
       (if (or (<= t 0.0071) (and (not (<= t 4e+65)) (<= t 1.9e+98)))
         (* x (- (+ z 1.0) y))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -5.1e+85) {
		tmp = t_1;
	} else if (t <= -2.3e-9) {
		tmp = z * (x - t);
	} else if ((t <= 0.0071) || (!(t <= 4e+65) && (t <= 1.9e+98))) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-5.1d+85)) then
        tmp = t_1
    else if (t <= (-2.3d-9)) then
        tmp = z * (x - t)
    else if ((t <= 0.0071d0) .or. (.not. (t <= 4d+65)) .and. (t <= 1.9d+98)) then
        tmp = x * ((z + 1.0d0) - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -5.1e+85) {
		tmp = t_1;
	} else if (t <= -2.3e-9) {
		tmp = z * (x - t);
	} else if ((t <= 0.0071) || (!(t <= 4e+65) && (t <= 1.9e+98))) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -5.1e+85:
		tmp = t_1
	elif t <= -2.3e-9:
		tmp = z * (x - t)
	elif (t <= 0.0071) or (not (t <= 4e+65) and (t <= 1.9e+98)):
		tmp = x * ((z + 1.0) - y)
	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 <= -5.1e+85)
		tmp = t_1;
	elseif (t <= -2.3e-9)
		tmp = Float64(z * Float64(x - t));
	elseif ((t <= 0.0071) || (!(t <= 4e+65) && (t <= 1.9e+98)))
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	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 <= -5.1e+85)
		tmp = t_1;
	elseif (t <= -2.3e-9)
		tmp = z * (x - t);
	elseif ((t <= 0.0071) || (~((t <= 4e+65)) && (t <= 1.9e+98)))
		tmp = x * ((z + 1.0) - y);
	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, -5.1e+85], t$95$1, If[LessEqual[t, -2.3e-9], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 0.0071], And[N[Not[LessEqual[t, 4e+65]], $MachinePrecision], LessEqual[t, 1.9e+98]]], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0999999999999998e85 or 0.0071000000000000004 < t < 4e65 or 1.89999999999999995e98 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 96.1%

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

      1. +-commutative 96.1%

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

      2. mul-1-neg 96.1%

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

      3. unsub-neg 96.1%

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

      4. sub-neg 96.1%

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

      5. +-commutative 96.1%

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

      6. distribute-neg-in 96.1%

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

      7. metadata-eval 96.1%

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

      8. associate-+l+ 96.1%

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

      9. +-commutative 96.1%

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

      10. sub-neg 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in t around inf 83.8%

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

   if -5.0999999999999998e85 < t < -2.2999999999999999e-9

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 75.6%

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

      1. cancel-sign-sub-inv 75.6%

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

      2. metadata-eval 75.6%

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

      3. *-lft-identity 75.6%

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

      4. +-commutative 75.6%

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

      5. mul-1-neg 75.6%

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

      6. sub-neg 75.6%

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

   7. Simplified 75.6%

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

   if -2.2999999999999999e-9 < t < 0.0071000000000000004 or 4e65 < t < 1.89999999999999995e98

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. sub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.2%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+85}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 0.0071 \lor \neg \left(t \leq 4 \cdot 10^{+65}\right) \land t \leq 1.9 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 3: 62.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -8 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 0.00096 \lor \neg \left(t \leq 3.15 \cdot 10^{+66}\right) \land t \leq 1.45 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -8e-68)
     t_1
     (if (<= t 1.9e-77)
       (* x (- 1.0 y))
       (if (or (<= t 0.00096) (and (not (<= t 3.15e+66)) (<= t 1.45e+98)))
         (* 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 <= -8e-68) {
		tmp = t_1;
	} else if (t <= 1.9e-77) {
		tmp = x * (1.0 - y);
	} else if ((t <= 0.00096) || (!(t <= 3.15e+66) && (t <= 1.45e+98))) {
		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 <= (-8d-68)) then
        tmp = t_1
    else if (t <= 1.9d-77) then
        tmp = x * (1.0d0 - y)
    else if ((t <= 0.00096d0) .or. (.not. (t <= 3.15d+66)) .and. (t <= 1.45d+98)) 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 <= -8e-68) {
		tmp = t_1;
	} else if (t <= 1.9e-77) {
		tmp = x * (1.0 - y);
	} else if ((t <= 0.00096) || (!(t <= 3.15e+66) && (t <= 1.45e+98))) {
		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 <= -8e-68:
		tmp = t_1
	elif t <= 1.9e-77:
		tmp = x * (1.0 - y)
	elif (t <= 0.00096) or (not (t <= 3.15e+66) and (t <= 1.45e+98)):
		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 <= -8e-68)
		tmp = t_1;
	elseif (t <= 1.9e-77)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((t <= 0.00096) || (!(t <= 3.15e+66) && (t <= 1.45e+98)))
		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 <= -8e-68)
		tmp = t_1;
	elseif (t <= 1.9e-77)
		tmp = x * (1.0 - y);
	elseif ((t <= 0.00096) || (~((t <= 3.15e+66)) && (t <= 1.45e+98)))
		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, -8e-68], t$95$1, If[LessEqual[t, 1.9e-77], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 0.00096], And[N[Not[LessEqual[t, 3.15e+66]], $MachinePrecision], LessEqual[t, 1.45e+98]]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000053e-68 or 9.60000000000000024e-4 < t < 3.1499999999999999e66 or 1.45000000000000005e98 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 96.9%

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

      1. +-commutative 96.9%

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

      2. mul-1-neg 96.9%

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

      3. unsub-neg 96.9%

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

      4. sub-neg 96.9%

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

      5. +-commutative 96.9%

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

      6. distribute-neg-in 96.9%

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

      7. metadata-eval 96.9%

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

      8. associate-+l+ 96.9%

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

      9. +-commutative 96.9%

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

      10. sub-neg 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in t around inf 75.8%

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

   if -8.00000000000000053e-68 < t < 1.8999999999999999e-77

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. sub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. *-commutative 71.3%

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

      2. sub-neg 71.3%

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

      3. metadata-eval 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in t around 0 66.2%

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

      1. mul-1-neg 66.2%

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

      2. sub-neg 66.2%

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

      3. metadata-eval 66.2%

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

      4. distribute-rgt-neg-in 66.2%

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

      5. neg-sub0 66.2%

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)} \]

      6. metadata-eval 66.2%

         \[\leadsto x \cdot \left(0 - \left(y + \color{blue}{\left(-1\right)}\right)\right) \]

      7. sub-neg 66.2%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(y - 1\right)}\right) \]

      8. associate-+l- 66.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(0 - y\right) + 1\right)} \]

      9. neg-sub0 66.2%

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

      10. +-commutative 66.2%

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

      11. sub-neg 66.2%

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

   10. Simplified 66.2%

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

   if 1.8999999999999999e-77 < t < 9.60000000000000024e-4 or 3.1499999999999999e66 < t < 1.45000000000000005e98

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

      4. +-commutative 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in y around 0 66.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-68}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 0.00096 \lor \neg \left(t \leq 3.15 \cdot 10^{+66}\right) \land t \leq 1.45 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 4: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -3450000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1100:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (* z (- x t))))
   (if (<= z -3450000000000.0)
     t_2
     (if (<= z -8.5e-26)
       (* y (- t x))
       (if (<= z 5e-220)
         t_1
         (if (<= z 1.4e-68) (* x (- 1.0 y)) (if (<= z 1100.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = z * (x - t);
	double tmp;
	if (z <= -3450000000000.0) {
		tmp = t_2;
	} else if (z <= -8.5e-26) {
		tmp = y * (t - x);
	} else if (z <= 5e-220) {
		tmp = t_1;
	} else if (z <= 1.4e-68) {
		tmp = x * (1.0 - y);
	} else if (z <= 1100.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * t)
    t_2 = z * (x - t)
    if (z <= (-3450000000000.0d0)) then
        tmp = t_2
    else if (z <= (-8.5d-26)) then
        tmp = y * (t - x)
    else if (z <= 5d-220) then
        tmp = t_1
    else if (z <= 1.4d-68) then
        tmp = x * (1.0d0 - y)
    else if (z <= 1100.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = z * (x - t);
	double tmp;
	if (z <= -3450000000000.0) {
		tmp = t_2;
	} else if (z <= -8.5e-26) {
		tmp = y * (t - x);
	} else if (z <= 5e-220) {
		tmp = t_1;
	} else if (z <= 1.4e-68) {
		tmp = x * (1.0 - y);
	} else if (z <= 1100.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = z * (x - t)
	tmp = 0
	if z <= -3450000000000.0:
		tmp = t_2
	elif z <= -8.5e-26:
		tmp = y * (t - x)
	elif z <= 5e-220:
		tmp = t_1
	elif z <= 1.4e-68:
		tmp = x * (1.0 - y)
	elif z <= 1100.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -3450000000000.0)
		tmp = t_2;
	elseif (z <= -8.5e-26)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 5e-220)
		tmp = t_1;
	elseif (z <= 1.4e-68)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 1100.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	t_2 = z * (x - t);
	tmp = 0.0;
	if (z <= -3450000000000.0)
		tmp = t_2;
	elseif (z <= -8.5e-26)
		tmp = y * (t - x);
	elseif (z <= 5e-220)
		tmp = t_1;
	elseif (z <= 1.4e-68)
		tmp = x * (1.0 - y);
	elseif (z <= 1100.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3450000000000.0], t$95$2, If[LessEqual[z, -8.5e-26], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-220], t$95$1, If[LessEqual[z, 1.4e-68], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1100.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.45e12 or 1100 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 97.5%

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

      1. +-commutative 97.5%

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

      2. mul-1-neg 97.5%

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

      3. unsub-neg 97.5%

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

      4. sub-neg 97.5%

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

      5. +-commutative 97.5%

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

      6. distribute-neg-in 97.5%

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

      7. metadata-eval 97.5%

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

      8. associate-+l+ 97.5%

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

      9. +-commutative 97.5%

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

      10. sub-neg 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in z around inf 79.0%

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

      1. cancel-sign-sub-inv 79.0%

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

      2. metadata-eval 79.0%

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

      3. *-lft-identity 79.0%

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

      4. +-commutative 79.0%

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

      5. mul-1-neg 79.0%

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

      6. sub-neg 79.0%

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

   7. Simplified 79.0%

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

   if -3.45e12 < z < -8.50000000000000004e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 89.3%

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

   if -8.50000000000000004e-26 < z < 5.0000000000000002e-220 or 1.4000000000000001e-68 < z < 1100

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.7%

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

   3. Taylor expanded in y around inf 73.2%

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

      1. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   if 5.0000000000000002e-220 < z < 1.4000000000000001e-68

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 88.7%

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

      1. *-commutative 88.7%

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

      2. sub-neg 88.7%

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

      3. metadata-eval 88.7%

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

   7. Simplified 88.7%

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

   8. Taylor expanded in t around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. sub-neg 75.7%

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

      3. metadata-eval 75.7%

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

      4. distribute-rgt-neg-in 75.7%

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

      5. neg-sub0 75.7%

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)} \]

      6. metadata-eval 75.7%

         \[\leadsto x \cdot \left(0 - \left(y + \color{blue}{\left(-1\right)}\right)\right) \]

      7. sub-neg 75.7%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(y - 1\right)}\right) \]

      8. associate-+l- 75.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(0 - y\right) + 1\right)} \]

      9. neg-sub0 75.7%

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

      10. +-commutative 75.7%

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

      11. sub-neg 75.7%

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

   10. Simplified 75.7%

       \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3450000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-220}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1100:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 5: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -7.1 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-36} \lor \neg \left(t \leq 0.0085\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))))
   (if (<= t -7.1e+84)
     t_1
     (if (<= t -1.2e+15)
       (* z (- x t))
       (if (or (<= t -2.95e-36) (not (<= t 0.0085)))
         t_1
         (* x (- (+ z 1.0) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (t <= -7.1e+84) {
		tmp = t_1;
	} else if (t <= -1.2e+15) {
		tmp = z * (x - t);
	} else if ((t <= -2.95e-36) || !(t <= 0.0085)) {
		tmp = t_1;
	} else {
		tmp = x * ((z + 1.0) - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * t)
    if (t <= (-7.1d+84)) then
        tmp = t_1
    else if (t <= (-1.2d+15)) then
        tmp = z * (x - t)
    else if ((t <= (-2.95d-36)) .or. (.not. (t <= 0.0085d0))) then
        tmp = t_1
    else
        tmp = x * ((z + 1.0d0) - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (t <= -7.1e+84) {
		tmp = t_1;
	} else if (t <= -1.2e+15) {
		tmp = z * (x - t);
	} else if ((t <= -2.95e-36) || !(t <= 0.0085)) {
		tmp = t_1;
	} else {
		tmp = x * ((z + 1.0) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	tmp = 0
	if t <= -7.1e+84:
		tmp = t_1
	elif t <= -1.2e+15:
		tmp = z * (x - t)
	elif (t <= -2.95e-36) or not (t <= 0.0085):
		tmp = t_1
	else:
		tmp = x * ((z + 1.0) - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t <= -7.1e+84)
		tmp = t_1;
	elseif (t <= -1.2e+15)
		tmp = Float64(z * Float64(x - t));
	elseif ((t <= -2.95e-36) || !(t <= 0.0085))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	tmp = 0.0;
	if (t <= -7.1e+84)
		tmp = t_1;
	elseif (t <= -1.2e+15)
		tmp = z * (x - t);
	elseif ((t <= -2.95e-36) || ~((t <= 0.0085)))
		tmp = t_1;
	else
		tmp = x * ((z + 1.0) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.1e+84], t$95$1, If[LessEqual[t, -1.2e+15], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.95e-36], N[Not[LessEqual[t, 0.0085]], $MachinePrecision]], t$95$1, N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0999999999999998e84 or -1.2e15 < t < -2.94999999999999998e-36 or 0.0085000000000000006 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 91.1%

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

   if -7.0999999999999998e84 < t < -1.2e15

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. cancel-sign-sub-inv 82.2%

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

      2. metadata-eval 82.2%

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

      3. *-lft-identity 82.2%

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

      4. +-commutative 82.2%

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

      5. mul-1-neg 82.2%

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

      6. sub-neg 82.2%

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

   7. Simplified 82.2%

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

   if -2.94999999999999998e-36 < t < 0.0085000000000000006

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. sub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around inf 87.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{+84}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-36} \lor \neg \left(t \leq 0.0085\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \]

Alternative 6: 81.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-41}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 0.038:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))))
   (if (<= t -7.2e+84)
     t_1
     (if (<= t -2.1e-41)
       (+ x (* z (- x t)))
       (if (<= t 0.038) (+ x (* x (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (t <= -7.2e+84) {
		tmp = t_1;
	} else if (t <= -2.1e-41) {
		tmp = x + (z * (x - t));
	} else if (t <= 0.038) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * t)
    if (t <= (-7.2d+84)) then
        tmp = t_1
    else if (t <= (-2.1d-41)) then
        tmp = x + (z * (x - t))
    else if (t <= 0.038d0) then
        tmp = x + (x * (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (t <= -7.2e+84) {
		tmp = t_1;
	} else if (t <= -2.1e-41) {
		tmp = x + (z * (x - t));
	} else if (t <= 0.038) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	tmp = 0
	if t <= -7.2e+84:
		tmp = t_1
	elif t <= -2.1e-41:
		tmp = x + (z * (x - t))
	elif t <= 0.038:
		tmp = x + (x * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t <= -7.2e+84)
		tmp = t_1;
	elseif (t <= -2.1e-41)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	elseif (t <= 0.038)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	tmp = 0.0;
	if (t <= -7.2e+84)
		tmp = t_1;
	elseif (t <= -2.1e-41)
		tmp = x + (z * (x - t));
	elseif (t <= 0.038)
		tmp = x + (x * (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+84], t$95$1, If[LessEqual[t, -2.1e-41], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.038], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.1999999999999999e84 or 0.0379999999999999991 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 92.1%

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

   if -7.1999999999999999e84 < t < -2.10000000000000013e-41

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

   4. Simplified 81.7%

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

   if -2.10000000000000013e-41 < t < 0.0379999999999999991

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. unsub-neg 87.1%

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

      3. distribute-lft-out-- 87.2%

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

      4. *-rgt-identity 87.2%

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

   4. Simplified 87.2%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+84}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-41}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 0.038:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 7: 37.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -255000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-269}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -255000.0)
   (* z x)
   (if (<= z 2.8e-269)
     (* y t)
     (if (<= z 9e-10) x (if (<= z 8.2e+108) (* y (- x)) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -255000.0) {
		tmp = z * x;
	} else if (z <= 2.8e-269) {
		tmp = y * t;
	} else if (z <= 9e-10) {
		tmp = x;
	} else if (z <= 8.2e+108) {
		tmp = y * -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 <= (-255000.0d0)) then
        tmp = z * x
    else if (z <= 2.8d-269) then
        tmp = y * t
    else if (z <= 9d-10) then
        tmp = x
    else if (z <= 8.2d+108) then
        tmp = y * -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 <= -255000.0) {
		tmp = z * x;
	} else if (z <= 2.8e-269) {
		tmp = y * t;
	} else if (z <= 9e-10) {
		tmp = x;
	} else if (z <= 8.2e+108) {
		tmp = y * -x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -255000.0:
		tmp = z * x
	elif z <= 2.8e-269:
		tmp = y * t
	elif z <= 9e-10:
		tmp = x
	elif z <= 8.2e+108:
		tmp = y * -x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -255000.0)
		tmp = Float64(z * x);
	elseif (z <= 2.8e-269)
		tmp = Float64(y * t);
	elseif (z <= 9e-10)
		tmp = x;
	elseif (z <= 8.2e+108)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -255000.0)
		tmp = z * x;
	elseif (z <= 2.8e-269)
		tmp = y * t;
	elseif (z <= 9e-10)
		tmp = x;
	elseif (z <= 8.2e+108)
		tmp = y * -x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -255000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.8e-269], N[(y * t), $MachinePrecision], If[LessEqual[z, 9e-10], x, If[LessEqual[z, 8.2e+108], N[(y * (-x)), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -255000 or 8.1999999999999998e108 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

      3. distribute-lft-out-- 61.7%

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

      4. *-rgt-identity 61.7%

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

   4. Simplified 61.7%

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

   5. Taylor expanded in z around inf 50.1%

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

   if -255000 < z < 2.79999999999999995e-269

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. unsub-neg 98.7%

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

      4. sub-neg 98.7%

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

      5. +-commutative 98.7%

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

      6. distribute-neg-in 98.7%

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

      7. metadata-eval 98.7%

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

      8. associate-+l+ 98.7%

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

      9. +-commutative 98.7%

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

      10. sub-neg 98.7%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in z around 0 93.1%

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

      1. *-commutative 93.1%

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

      2. sub-neg 93.1%

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

      3. metadata-eval 93.1%

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

   7. Simplified 93.1%

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

   8. Taylor expanded in t around inf 43.9%

      \[\leadsto \color{blue}{t \cdot y} \]
   9. Step-by-step derivation

      1. *-commutative 43.9%

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

   10. Simplified 43.9%

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

   if 2.79999999999999995e-269 < z < 8.9999999999999999e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.6%

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

   3. Taylor expanded in x around inf 46.8%

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

   if 8.9999999999999999e-10 < z < 8.1999999999999998e108

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unsub-neg 48.7%

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

      3. distribute-lft-out-- 48.7%

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

      4. *-rgt-identity 48.7%

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

   4. Simplified 48.7%

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

   5. Taylor expanded in y around inf 37.0%

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

      1. mul-1-neg 37.0%

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

      2. distribute-rgt-neg-in 37.0%

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

   7. Simplified 37.0%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -255000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-269}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 8: 37.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -510000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-268}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -510000.0)
   (* z x)
   (if (<= z 4.8e-268)
     (* y t)
     (if (<= z 1.1e-22) x (if (<= z 1.2e+105) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -510000.0) {
		tmp = z * x;
	} else if (z <= 4.8e-268) {
		tmp = y * t;
	} else if (z <= 1.1e-22) {
		tmp = x;
	} else if (z <= 1.2e+105) {
		tmp = y * t;
	} 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 <= (-510000.0d0)) then
        tmp = z * x
    else if (z <= 4.8d-268) then
        tmp = y * t
    else if (z <= 1.1d-22) then
        tmp = x
    else if (z <= 1.2d+105) then
        tmp = y * t
    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 <= -510000.0) {
		tmp = z * x;
	} else if (z <= 4.8e-268) {
		tmp = y * t;
	} else if (z <= 1.1e-22) {
		tmp = x;
	} else if (z <= 1.2e+105) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -510000.0:
		tmp = z * x
	elif z <= 4.8e-268:
		tmp = y * t
	elif z <= 1.1e-22:
		tmp = x
	elif z <= 1.2e+105:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -510000.0)
		tmp = Float64(z * x);
	elseif (z <= 4.8e-268)
		tmp = Float64(y * t);
	elseif (z <= 1.1e-22)
		tmp = x;
	elseif (z <= 1.2e+105)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -510000.0)
		tmp = z * x;
	elseif (z <= 4.8e-268)
		tmp = y * t;
	elseif (z <= 1.1e-22)
		tmp = x;
	elseif (z <= 1.2e+105)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -510000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, 4.8e-268], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.1e-22], x, If[LessEqual[z, 1.2e+105], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1e5 or 1.19999999999999987e105 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

      3. distribute-lft-out-- 61.4%

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

      4. *-rgt-identity 61.4%

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

   4. Simplified 61.4%

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

   5. Taylor expanded in z around inf 49.2%

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

   if -5.1e5 < z < 4.7999999999999998e-268 or 1.1e-22 < z < 1.19999999999999987e105

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 98.1%

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

      1. +-commutative 98.1%

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

      2. mul-1-neg 98.1%

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

      3. unsub-neg 98.1%

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

      4. sub-neg 98.1%

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

      5. +-commutative 98.1%

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

      6. distribute-neg-in 98.1%

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

      7. metadata-eval 98.1%

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

      8. associate-+l+ 98.1%

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

      9. +-commutative 98.1%

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

      10. sub-neg 98.1%

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

   4. Simplified 98.1%

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

   5. Taylor expanded in z around 0 82.8%

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

      1. *-commutative 82.8%

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

      2. sub-neg 82.8%

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

      3. metadata-eval 82.8%

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

   7. Simplified 82.8%

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

   8. Taylor expanded in t around inf 39.4%

      \[\leadsto \color{blue}{t \cdot y} \]
   9. Step-by-step derivation

      1. *-commutative 39.4%

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

   10. Simplified 39.4%

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

   if 4.7999999999999998e-268 < z < 1.1e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.8%

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

   3. Taylor expanded in x around inf 48.6%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -510000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-268}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 9: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1100000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1100000000000.0)
     t_1
     (if (<= z 1.3e-271)
       (* y (- t x))
       (if (<= z 1.8e+32) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1100000000000.0) {
		tmp = t_1;
	} else if (z <= 1.3e-271) {
		tmp = y * (t - x);
	} else if (z <= 1.8e+32) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-1100000000000.0d0)) then
        tmp = t_1
    else if (z <= 1.3d-271) then
        tmp = y * (t - x)
    else if (z <= 1.8d+32) then
        tmp = x * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1100000000000.0) {
		tmp = t_1;
	} else if (z <= 1.3e-271) {
		tmp = y * (t - x);
	} else if (z <= 1.8e+32) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1100000000000.0:
		tmp = t_1
	elif z <= 1.3e-271:
		tmp = y * (t - x)
	elif z <= 1.8e+32:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1100000000000.0)
		tmp = t_1;
	elseif (z <= 1.3e-271)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 1.8e+32)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1100000000000.0)
		tmp = t_1;
	elseif (z <= 1.3e-271)
		tmp = y * (t - x);
	elseif (z <= 1.8e+32)
		tmp = x * (1.0 - y);
	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]}, If[LessEqual[z, -1100000000000.0], t$95$1, If[LessEqual[z, 1.3e-271], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+32], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e12 or 1.7999999999999998e32 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 98.2%

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

      1. +-commutative 98.2%

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

      2. mul-1-neg 98.2%

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

      3. unsub-neg 98.2%

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

      4. sub-neg 98.2%

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

      5. +-commutative 98.2%

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

      6. distribute-neg-in 98.2%

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

      7. metadata-eval 98.2%

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

      8. associate-+l+ 98.2%

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

      9. +-commutative 98.2%

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

      10. sub-neg 98.2%

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

   4. Simplified 98.2%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. cancel-sign-sub-inv 81.0%

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

      2. metadata-eval 81.0%

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

      3. *-lft-identity 81.0%

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

      4. +-commutative 81.0%

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

      5. mul-1-neg 81.0%

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

      6. sub-neg 81.0%

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

   7. Simplified 81.0%

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

   if -1.1e12 < z < 1.3e-271

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. unsub-neg 98.7%

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

      4. sub-neg 98.7%

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

      5. +-commutative 98.7%

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

      6. distribute-neg-in 98.7%

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

      7. metadata-eval 98.7%

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

      8. associate-+l+ 98.7%

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

      9. +-commutative 98.7%

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

      10. sub-neg 98.7%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in y around inf 68.5%

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

   if 1.3e-271 < z < 1.7999999999999998e32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 98.4%

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

      1. +-commutative 98.4%

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

      2. mul-1-neg 98.4%

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

      3. unsub-neg 98.4%

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

      4. sub-neg 98.4%

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

      5. +-commutative 98.4%

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

      6. distribute-neg-in 98.4%

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

      7. metadata-eval 98.4%

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

      8. associate-+l+ 98.4%

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

      9. +-commutative 98.4%

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

      10. sub-neg 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in z around 0 84.6%

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

      1. *-commutative 84.6%

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

      2. sub-neg 84.6%

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

      3. metadata-eval 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in t around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. sub-neg 67.3%

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

      3. metadata-eval 67.3%

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

      4. distribute-rgt-neg-in 67.3%

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

      5. neg-sub0 67.3%

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)} \]

      6. metadata-eval 67.3%

         \[\leadsto x \cdot \left(0 - \left(y + \color{blue}{\left(-1\right)}\right)\right) \]

      7. sub-neg 67.3%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(y - 1\right)}\right) \]

      8. associate-+l- 67.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(0 - y\right) + 1\right)} \]

      9. neg-sub0 67.3%

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

      10. +-commutative 67.3%

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

      11. sub-neg 67.3%

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

   10. Simplified 67.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1100000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 10: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17000000000 \lor \neg \left(z \leq 2.45 \cdot 10^{+32}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -17000000000.0) (not (<= z 2.45e+32)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -17000000000.0) || !(z <= 2.45e+32)) {
		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 <= (-17000000000.0d0)) .or. (.not. (z <= 2.45d+32))) 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 <= -17000000000.0) || !(z <= 2.45e+32)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -17000000000.0) or not (z <= 2.45e+32):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -17000000000.0) || !(z <= 2.45e+32))
		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 <= -17000000000.0) || ~((z <= 2.45e+32)))
		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, -17000000000.0], N[Not[LessEqual[z, 2.45e+32]], $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 < -1.7e10 or 2.4500000000000001e32 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 98.2%

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

      1. +-commutative 98.2%

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

      2. mul-1-neg 98.2%

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

      3. unsub-neg 98.2%

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

      4. sub-neg 98.2%

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

      5. +-commutative 98.2%

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

      6. distribute-neg-in 98.2%

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

      7. metadata-eval 98.2%

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

      8. associate-+l+ 98.2%

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

      9. +-commutative 98.2%

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

      10. sub-neg 98.2%

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

   4. Simplified 98.2%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. cancel-sign-sub-inv 81.0%

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

      2. metadata-eval 81.0%

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

      3. *-lft-identity 81.0%

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

      4. +-commutative 81.0%

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

      5. mul-1-neg 81.0%

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

      6. sub-neg 81.0%

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

   7. Simplified 81.0%

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

   if -1.7e10 < z < 2.4500000000000001e32

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.9%

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

      1. *-commutative 89.9%

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

   4. Simplified 89.9%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000000000 \lor \neg \left(z \leq 2.45 \cdot 10^{+32}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 11: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-47} \lor \neg \left(t \leq 8.2 \cdot 10^{-78}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.1e-47) (not (<= t 8.2e-78))) (* (- y z) t) (* y (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e-47) || !(t <= 8.2e-78)) {
		tmp = (y - z) * t;
	} else {
		tmp = y * -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 ((t <= (-4.1d-47)) .or. (.not. (t <= 8.2d-78))) then
        tmp = (y - z) * t
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e-47) || !(t <= 8.2e-78)) {
		tmp = (y - z) * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.1e-47) or not (t <= 8.2e-78):
		tmp = (y - z) * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.1e-47) || !(t <= 8.2e-78))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.1e-47) || ~((t <= 8.2e-78)))
		tmp = (y - z) * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.1e-47], N[Not[LessEqual[t, 8.2e-78]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.10000000000000002e-47 or 8.1999999999999996e-78 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

      4. sub-neg 97.3%

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

      5. +-commutative 97.3%

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

      6. distribute-neg-in 97.3%

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

      7. metadata-eval 97.3%

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

      8. associate-+l+ 97.3%

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

      9. +-commutative 97.3%

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

      10. sub-neg 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in t around inf 68.5%

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

   if -4.10000000000000002e-47 < t < 8.1999999999999996e-78

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

      3. distribute-lft-out-- 89.6%

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

      4. *-rgt-identity 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in y around inf 43.0%

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

      1. mul-1-neg 43.0%

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

      2. distribute-rgt-neg-in 43.0%

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

   7. Simplified 43.0%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-47} \lor \neg \left(t \leq 8.2 \cdot 10^{-78}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 12: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+14} \lor \neg \left(x \leq 8.2 \cdot 10^{+102}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.5e+14) (not (<= x 8.2e+102))) (* x (+ z 1.0)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e+14) || !(x <= 8.2e+102)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.5d+14)) .or. (.not. (x <= 8.2d+102))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e+14) || !(x <= 8.2e+102)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.5e+14) or not (x <= 8.2e+102):
		tmp = x * (z + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.5e+14) || !(x <= 8.2e+102))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.5e+14) || ~((x <= 8.2e+102)))
		tmp = x * (z + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.5e+14], N[Not[LessEqual[x, 8.2e+102]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e14 or 8.1999999999999999e102 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 92.7%

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

      1. mul-1-neg 92.7%

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

      2. *-commutative 92.7%

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

      3. distribute-rgt-neg-in 92.7%

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

      4. +-commutative 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in y around 0 59.8%

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

   if -4.5e14 < x < 8.1999999999999999e102

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 99.3%

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

      1. +-commutative 99.3%

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

      2. mul-1-neg 99.3%

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

      3. unsub-neg 99.3%

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

      4. sub-neg 99.3%

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

      5. +-commutative 99.3%

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

      6. distribute-neg-in 99.3%

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

      7. metadata-eval 99.3%

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

      8. associate-+l+ 99.3%

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

      9. +-commutative 99.3%

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

      10. sub-neg 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in t around inf 65.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+14} \lor \neg \left(x \leq 8.2 \cdot 10^{+102}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 13: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -320000 \lor \neg \left(y \leq 2.8\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -320000.0) (not (<= y 2.8))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -320000.0) || !(y <= 2.8)) {
		tmp = y * (t - x);
	} 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 ((y <= (-320000.0d0)) .or. (.not. (y <= 2.8d0))) then
        tmp = y * (t - x)
    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 ((y <= -320000.0) || !(y <= 2.8)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -320000.0) or not (y <= 2.8):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -320000.0) || !(y <= 2.8))
		tmp = Float64(y * Float64(t - x));
	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 ((y <= -320000.0) || ~((y <= 2.8)))
		tmp = y * (t - x);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -320000.0], N[Not[LessEqual[y, 2.8]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e5 or 2.7999999999999998 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 97.7%

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

      1. +-commutative 97.7%

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

      2. mul-1-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. sub-neg 97.7%

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

      5. +-commutative 97.7%

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

      6. distribute-neg-in 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-+l+ 97.7%

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

      9. +-commutative 97.7%

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

      10. sub-neg 97.7%

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

   4. Simplified 97.7%

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

   5. Taylor expanded in y around inf 79.8%

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

   if -3.2e5 < y < 2.7999999999999998

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. *-commutative 62.6%

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

      3. distribute-rgt-neg-in 62.6%

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

      4. +-commutative 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in y around 0 61.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -320000 \lor \neg \left(y \leq 2.8\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 14: 71.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57} \lor \neg \left(y \leq 0.65\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e+57) (not (<= y 0.65))) (* y (- t x)) (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e+57) || !(y <= 0.65)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.2d+57)) .or. (.not. (y <= 0.65d0))) then
        tmp = y * (t - x)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e+57) || !(y <= 0.65)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e+57) or not (y <= 0.65):
		tmp = y * (t - x)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e+57) || !(y <= 0.65))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.2e+57) || ~((y <= 0.65)))
		tmp = y * (t - x);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e+57], N[Not[LessEqual[y, 0.65]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000029e57 or 0.650000000000000022 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 97.7%

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

      1. +-commutative 97.7%

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

      2. mul-1-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. sub-neg 97.7%

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

      5. +-commutative 97.7%

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

      6. distribute-neg-in 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-+l+ 97.7%

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

      9. +-commutative 97.7%

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

      10. sub-neg 97.7%

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

   4. Simplified 97.7%

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

   5. Taylor expanded in y around inf 81.6%

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

   if -3.20000000000000029e57 < y < 0.650000000000000022

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.4%

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

   3. Taylor expanded in y around 0 72.4%

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

   4. Taylor expanded in y around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unsub-neg 65.4%

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

   6. Simplified 65.4%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57} \lor \neg \left(y \leq 0.65\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 15: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 16: 37.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30500:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -30500.0) (* z x) (if (<= z 2.2e+18) x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -30500.0) {
		tmp = z * x;
	} else if (z <= 2.2e+18) {
		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 <= (-30500.0d0)) then
        tmp = z * x
    else if (z <= 2.2d+18) 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 <= -30500.0) {
		tmp = z * x;
	} else if (z <= 2.2e+18) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -30500.0:
		tmp = z * x
	elif z <= 2.2e+18:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -30500.0)
		tmp = Float64(z * x);
	elseif (z <= 2.2e+18)
		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 <= -30500.0)
		tmp = z * x;
	elseif (z <= 2.2e+18)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -30500.0], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.2e+18], x, N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -30500 or 2.2e18 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. unsub-neg 59.0%

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

      3. distribute-lft-out-- 59.0%

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

      4. *-rgt-identity 59.0%

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

   4. Simplified 59.0%

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

   5. Taylor expanded in z around inf 43.5%

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

   if -30500 < z < 2.2e18

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.8%

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

   3. Taylor expanded in x around inf 33.1%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30500:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 17: 17.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 61.7%

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

3. Taylor expanded in x around inf 18.8%

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

4. Final simplification 18.8%

   \[\leadsto x \]

Developer target: 96.4% 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 2023271 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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