Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 67.8% → 90.8%

Time: 17.1s

Alternatives: 22

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a}\\ t_2 := \frac{z}{a - z} + 1\\ \mathbf{if}\;x \leq -1 \cdot 10^{-26} \lor \neg \left(x \leq 5.5 \cdot 10^{-72}\right):\\ \;\;\;\;x \cdot \left(t\_2 + \left(t\_1 - \frac{t}{x} \cdot \frac{y - z}{z - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{y - z}{a - z} + \frac{x \cdot \left(t\_2 + t\_1\right)}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- z a))) (t_2 (+ (/ z (- a z)) 1.0)))
   (if (or (<= x -1e-26) (not (<= x 5.5e-72)))
     (* x (+ t_2 (- t_1 (* (/ t x) (/ (- y z) (- z a))))))
     (* t (+ (/ (- y z) (- a z)) (/ (* x (+ t_2 t_1)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - a);
	double t_2 = (z / (a - z)) + 1.0;
	double tmp;
	if ((x <= -1e-26) || !(x <= 5.5e-72)) {
		tmp = x * (t_2 + (t_1 - ((t / x) * ((y - z) / (z - a)))));
	} else {
		tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + t_1)) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y / (z - a)
    t_2 = (z / (a - z)) + 1.0d0
    if ((x <= (-1d-26)) .or. (.not. (x <= 5.5d-72))) then
        tmp = x * (t_2 + (t_1 - ((t / x) * ((y - z) / (z - a)))))
    else
        tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + t_1)) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - a);
	double t_2 = (z / (a - z)) + 1.0;
	double tmp;
	if ((x <= -1e-26) || !(x <= 5.5e-72)) {
		tmp = x * (t_2 + (t_1 - ((t / x) * ((y - z) / (z - a)))));
	} else {
		tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + t_1)) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z - a)
	t_2 = (z / (a - z)) + 1.0
	tmp = 0
	if (x <= -1e-26) or not (x <= 5.5e-72):
		tmp = x * (t_2 + (t_1 - ((t / x) * ((y - z) / (z - a)))))
	else:
		tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + t_1)) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z - a))
	t_2 = Float64(Float64(z / Float64(a - z)) + 1.0)
	tmp = 0.0
	if ((x <= -1e-26) || !(x <= 5.5e-72))
		tmp = Float64(x * Float64(t_2 + Float64(t_1 - Float64(Float64(t / x) * Float64(Float64(y - z) / Float64(z - a))))));
	else
		tmp = Float64(t * Float64(Float64(Float64(y - z) / Float64(a - z)) + Float64(Float64(x * Float64(t_2 + t_1)) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z - a);
	t_2 = (z / (a - z)) + 1.0;
	tmp = 0.0;
	if ((x <= -1e-26) || ~((x <= 5.5e-72)))
		tmp = x * (t_2 + (t_1 - ((t / x) * ((y - z) / (z - a)))));
	else
		tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + t_1)) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, If[Or[LessEqual[x, -1e-26], N[Not[LessEqual[x, 5.5e-72]], $MachinePrecision]], N[(x * N[(t$95$2 + N[(t$95$1 - N[(N[(t / x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(t$95$2 + t$95$1), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1e-26 or 5.49999999999999994e-72 < x

   1. Initial program 57.9%

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

      1. +-commutative 57.9%

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

      2. *-commutative 57.9%

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

      3. associate-/l* 74.7%

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

      4. fma-define 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in x around -inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. *-commutative 66.8%

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

      3. distribute-rgt-neg-in 66.8%

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

      4. +-commutative 66.8%

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

      5. mul-1-neg 66.8%

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

      6. unsub-neg 66.8%

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

      7. times-frac 87.1%

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

      8. +-commutative 87.1%

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

   7. Simplified 87.1%

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

   if -1e-26 < x < 5.49999999999999994e-72

   1. Initial program 78.6%

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

      1. +-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-/l* 90.8%

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

      4. fma-define 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x around -inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

      4. +-commutative 67.4%

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

      5. mul-1-neg 67.4%

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

      6. unsub-neg 67.4%

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

      7. times-frac 66.7%

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

      8. +-commutative 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in t around -inf 92.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-26} \lor \neg \left(x \leq 5.5 \cdot 10^{-72}\right):\\ \;\;\;\;x \cdot \left(\left(\frac{z}{a - z} + 1\right) + \left(\frac{y}{z - a} - \frac{t}{x} \cdot \frac{y - z}{z - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{y - z}{a - z} + \frac{x \cdot \left(\left(\frac{z}{a - z} + 1\right) + \frac{y}{z - a}\right)}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + x \cdot \frac{\left(y + \frac{a \cdot t}{x}\right) - \left(a + t \cdot \frac{y}{x}\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+275}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-241)
       t_2
       (if (<= t_2 0.0)
         (+ t (* x (/ (- (+ y (/ (* a t) x)) (+ a (* t (/ y x)))) z)))
         (if (<= t_2 2e+275) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * (((y + ((a * t) / x)) - (a + (t * (y / x)))) / z));
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * (((y + ((a * t) / x)) - (a + (t * (y / x)))) / z));
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-241:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (x * (((y + ((a * t) / x)) - (a + (t * (y / x)))) / z))
	elif t_2 <= 2e+275:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(Float64(y + Float64(Float64(a * t) / x)) - Float64(a + Float64(t * Float64(y / x)))) / z)));
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (x * (((y + ((a * t) / x)) - (a + (t * (y / x)))) / z));
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-241], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(x * N[(N[(N[(y + N[(N[(a * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(a + N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+275], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 1.99999999999999992e275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 42.6%

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

      1. associate-/l* 79.7%

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

   3. Simplified 79.7%

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

      1. clear-num 79.8%

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

      2. un-div-inv 80.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 80.0%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.9999999999999999e-241 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.99999999999999992e275

   1. Initial program 94.5%

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

   if -1.9999999999999999e-241 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.0%

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

      1. +-commutative 4.0%

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

      2. *-commutative 4.0%

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

      3. associate-/l* 4.0%

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

      4. fma-define 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in x around -inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. *-commutative 50.4%

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

      3. distribute-rgt-neg-in 50.4%

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

      4. +-commutative 50.4%

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

      5. mul-1-neg 50.4%

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

      6. unsub-neg 50.4%

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

      7. times-frac 52.3%

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

      8. +-commutative 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in z around -inf 98.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.8%

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

   10. Simplified 99.8%

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

Alternative 3: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\left(y - a\right) \cdot \frac{-1}{z}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+275}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-241)
       t_2
       (if (<= t_2 0.0)
         (+ t (* (- t x) (* (- y a) (/ -1.0 z))))
         (if (<= t_2 2e+275) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-241:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)))
	elif t_2 <= 2e+275:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(y - a) * Float64(-1.0 / z))));
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-241], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+275], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 1.99999999999999992e275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 42.6%

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

      1. associate-/l* 79.7%

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

   3. Simplified 79.7%

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

      1. clear-num 79.8%

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

      2. un-div-inv 80.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 80.0%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.9999999999999999e-241 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.99999999999999992e275

   1. Initial program 94.5%

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

   if -1.9999999999999999e-241 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.0%

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

      1. +-commutative 4.0%

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

      2. *-commutative 4.0%

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

      3. associate-/l* 4.0%

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

      4. fma-define 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. associate--l+ 98.8%

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

      2. associate-*r/ 98.8%

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

      3. associate-*r/ 98.8%

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

      4. mul-1-neg 98.8%

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

      5. div-sub 98.8%

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

      6. mul-1-neg 98.8%

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

      7. distribute-lft-out-- 98.8%

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

      8. associate-*r/ 98.8%

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

      9. mul-1-neg 98.8%

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

      10. unsub-neg 98.8%

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

      11. distribute-rgt-out-- 98.8%

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

   7. Simplified 98.8%

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

      1. div-inv 98.7%

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

   9. Applied egg-rr 98.7%

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

       1. associate-*l* 99.6%

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

   11. Simplified 99.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-241}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\left(y - a\right) \cdot \frac{-1}{z}\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+275}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+275}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-241)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 2e+275) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-241:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 2e+275:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-241], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+275], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 1.99999999999999992e275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 42.6%

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

      1. associate-/l* 79.7%

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

   3. Simplified 79.7%

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

      1. clear-num 79.8%

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

      2. un-div-inv 80.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 80.0%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.9999999999999999e-241 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.99999999999999992e275

   1. Initial program 94.5%

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

   if -1.9999999999999999e-241 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.0%

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

      1. +-commutative 4.0%

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

      2. *-commutative 4.0%

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

      3. associate-/l* 4.0%

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

      4. fma-define 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. associate--l+ 98.8%

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

      2. associate-*r/ 98.8%

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

      3. associate-*r/ 98.8%

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

      4. mul-1-neg 98.8%

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

      5. div-sub 98.8%

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

      6. mul-1-neg 98.8%

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

      7. distribute-lft-out-- 98.8%

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

      8. associate-*r/ 98.8%

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

      9. mul-1-neg 98.8%

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

      10. unsub-neg 98.8%

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

      11. distribute-rgt-out-- 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-241}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+275}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+275}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-241)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 2e+275) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-241:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 2e+275:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-241], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+275], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 1.99999999999999992e275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 42.6%

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

      1. associate-/l* 79.7%

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

   3. Simplified 79.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.9999999999999999e-241 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.99999999999999992e275

   1. Initial program 94.5%

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

   if -1.9999999999999999e-241 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.0%

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

      1. +-commutative 4.0%

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

      2. *-commutative 4.0%

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

      3. associate-/l* 4.0%

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

      4. fma-define 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. associate--l+ 98.8%

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

      2. associate-*r/ 98.8%

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

      3. associate-*r/ 98.8%

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

      4. mul-1-neg 98.8%

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

      5. div-sub 98.8%

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

      6. mul-1-neg 98.8%

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

      7. distribute-lft-out-- 98.8%

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

      8. associate-*r/ 98.8%

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

      9. mul-1-neg 98.8%

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

      10. unsub-neg 98.8%

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

      11. distribute-rgt-out-- 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-241}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+275}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(\frac{z}{a - z} + 1\right) + \left(\frac{y}{z - a} - \frac{t}{x} \cdot \frac{y - z}{z - a}\right)\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-278}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-72}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1
         (*
          x
          (+
           (+ (/ z (- a z)) 1.0)
           (- (/ y (- z a)) (* (/ t x) (/ (- y z) (- z a))))))))
   (if (<= x -1.25e-59)
     t_1
     (if (<= x -4.1e-278)
       (+ x (* (- y z) (/ (- t x) (- a z))))
       (if (<= x 7.8e-72) (+ x (* t (/ (- y z) (- a z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z / (a - z)) + 1.0) + ((y / (z - a)) - ((t / x) * ((y - z) / (z - a)))));
	double tmp;
	if (x <= -1.25e-59) {
		tmp = t_1;
	} else if (x <= -4.1e-278) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else if (x <= 7.8e-72) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (((z / (a - z)) + 1.0d0) + ((y / (z - a)) - ((t / x) * ((y - z) / (z - a)))))
    if (x <= (-1.25d-59)) then
        tmp = t_1
    else if (x <= (-4.1d-278)) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else if (x <= 7.8d-72) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z / (a - z)) + 1.0) + ((y / (z - a)) - ((t / x) * ((y - z) / (z - a)))));
	double tmp;
	if (x <= -1.25e-59) {
		tmp = t_1;
	} else if (x <= -4.1e-278) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else if (x <= 7.8e-72) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (((z / (a - z)) + 1.0) + ((y / (z - a)) - ((t / x) * ((y - z) / (z - a)))))
	tmp = 0
	if x <= -1.25e-59:
		tmp = t_1
	elif x <= -4.1e-278:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	elif x <= 7.8e-72:
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) + Float64(Float64(y / Float64(z - a)) - Float64(Float64(t / x) * Float64(Float64(y - z) / Float64(z - a))))))
	tmp = 0.0
	if (x <= -1.25e-59)
		tmp = t_1;
	elseif (x <= -4.1e-278)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	elseif (x <= 7.8e-72)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (((z / (a - z)) + 1.0) + ((y / (z - a)) - ((t / x) * ((y - z) / (z - a)))));
	tmp = 0.0;
	if (x <= -1.25e-59)
		tmp = t_1;
	elseif (x <= -4.1e-278)
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	elseif (x <= 7.8e-72)
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] - N[(N[(t / x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e-59], t$95$1, If[LessEqual[x, -4.1e-278], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-72], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e-59 or 7.8e-72 < x

   1. Initial program 58.5%

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

      1. +-commutative 58.5%

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

      2. *-commutative 58.5%

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

      3. associate-/l* 75.1%

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

      4. fma-define 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in x around -inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

      4. +-commutative 67.7%

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

      5. mul-1-neg 67.7%

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

      6. unsub-neg 67.7%

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

      7. times-frac 87.2%

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

      8. +-commutative 87.2%

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

   7. Simplified 87.2%

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

   if -1.25e-59 < x < -4.10000000000000001e-278

   1. Initial program 73.8%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   if -4.10000000000000001e-278 < x < 7.8e-72

   1. Initial program 83.5%

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

      1. associate-/l* 77.6%

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

   3. Simplified 77.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.1%

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

      1. associate-/l* 88.2%

         \[\leadsto x + \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 88.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(\left(\frac{z}{a - z} + 1\right) + \left(\frac{y}{z - a} - \frac{t}{x} \cdot \frac{y - z}{z - a}\right)\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-278}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-72}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(\frac{z}{a - z} + 1\right) + \left(\frac{y}{z - a} - \frac{t}{x} \cdot \frac{y - z}{z - a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-182} \lor \neg \left(a \leq 1.25 \cdot 10^{-164}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.8e-182) (not (<= a 1.25e-164)))
   (+ x (* (- y z) (/ (- t x) (- a z))))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.8e-182) || !(a <= 1.25e-164)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.8d-182)) .or. (.not. (a <= 1.25d-164))) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.8e-182) || !(a <= 1.25e-164)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.8e-182) or not (a <= 1.25e-164):
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.8e-182) || !(a <= 1.25e-164))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.8e-182) || ~((a <= 1.25e-164)))
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.8e-182], N[Not[LessEqual[a, 1.25e-164]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.79999999999999974e-182 or 1.2499999999999999e-164 < a

   1. Initial program 69.8%

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

      1. associate-/l* 81.0%

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

   3. Simplified 81.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   if -5.79999999999999974e-182 < a < 1.2499999999999999e-164

   1. Initial program 50.9%

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

      1. +-commutative 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-/l* 63.4%

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

      4. fma-define 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in z around inf 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. mul-1-neg 77.9%

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

      5. div-sub 77.9%

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

      6. mul-1-neg 77.9%

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

      7. distribute-lft-out-- 77.9%

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

      8. associate-*r/ 77.9%

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

      9. mul-1-neg 77.9%

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

      10. unsub-neg 77.9%

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

      11. distribute-rgt-out-- 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in y around inf 75.0%

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

      1. associate-/l* 83.7%

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

   10. Simplified 83.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-182} \lor \neg \left(a \leq 1.25 \cdot 10^{-164}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-44} \lor \neg \left(a \leq 3.3 \cdot 10^{-50}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.4e-44) (not (<= a 3.3e-50)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.4e-44) || !(a <= 3.3e-50)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.4d-44)) .or. (.not. (a <= 3.3d-50))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.4e-44) || !(a <= 3.3e-50)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.4e-44) or not (a <= 3.3e-50):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.4e-44) || !(a <= 3.3e-50))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.4e-44) || ~((a <= 3.3e-50)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.4e-44], N[Not[LessEqual[a, 3.3e-50]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.40000000000000016e-44 or 3.2999999999999998e-50 < a

   1. Initial program 72.4%

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

      1. associate-/l* 84.2%

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

   3. Simplified 84.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 66.0%

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

      1. associate-/l* 77.6%

         \[\leadsto x + \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 77.6%

      \[\leadsto x + \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -3.40000000000000016e-44 < a < 3.2999999999999998e-50

   1. Initial program 56.1%

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

      1. +-commutative 56.1%

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

      2. *-commutative 56.1%

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

      3. associate-/l* 71.4%

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

      4. fma-define 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in z around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. associate-*r/ 68.5%

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

      3. associate-*r/ 68.5%

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

      4. mul-1-neg 68.5%

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

      5. div-sub 69.4%

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

      6. mul-1-neg 69.4%

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

      7. distribute-lft-out-- 69.4%

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

      8. associate-*r/ 69.4%

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

      9. mul-1-neg 69.4%

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

      10. unsub-neg 69.4%

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

      11. distribute-rgt-out-- 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in y around inf 65.4%

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

      1. associate-/l* 73.6%

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

   10. Simplified 73.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-44} \lor \neg \left(a \leq 3.3 \cdot 10^{-50}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+50} \lor \neg \left(z \leq 1.15 \cdot 10^{+83}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e+50) (not (<= z 1.15e+83)))
   (+ t (* y (/ (- x t) z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e+50) || !(z <= 1.15e+83)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.2d+50)) .or. (.not. (z <= 1.15d+83))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e+50) || !(z <= 1.15e+83)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.2e+50) or not (z <= 1.15e+83):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2e+50) || !(z <= 1.15e+83))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.2e+50) || ~((z <= 1.15e+83)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2e+50], N[Not[LessEqual[z, 1.15e+83]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999987e50 or 1.14999999999999997e83 < z

   1. Initial program 39.1%

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

      1. +-commutative 39.1%

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

      2. *-commutative 39.1%

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

      3. associate-/l* 67.4%

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

      4. fma-define 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in z around inf 56.8%

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

      1. associate--l+ 56.8%

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

      2. associate-*r/ 56.8%

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

      3. associate-*r/ 56.8%

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

      4. mul-1-neg 56.8%

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

      5. div-sub 56.8%

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

      6. mul-1-neg 56.8%

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

      7. distribute-lft-out-- 56.8%

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

      8. associate-*r/ 56.8%

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

      9. mul-1-neg 56.8%

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

      10. unsub-neg 56.8%

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

      11. distribute-rgt-out-- 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in y around inf 54.0%

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

      1. associate-/l* 65.7%

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

   10. Simplified 65.7%

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

   if -9.19999999999999987e50 < z < 1.14999999999999997e83

   1. Initial program 83.3%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

      1. clear-num 85.0%

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

      2. un-div-inv 85.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 85.0%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. *-lft-identity 67.2%

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

      3. times-frac 72.2%

         \[\leadsto x + \color{blue}{\frac{t - x}{1} \cdot \frac{y}{a}} \]

      4. /-rgt-identity 72.2%

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

   9. Simplified 72.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+50} \lor \neg \left(z \leq 1.15 \cdot 10^{+83}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-44} \lor \neg \left(a \leq 1.15 \cdot 10^{-44}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.05e-44) (not (<= a 1.15e-44)))
   (+ x (* t (/ (- y z) a)))
   (* t (/ (- z y) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e-44) || !(a <= 1.15e-44)) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.05d-44)) .or. (.not. (a <= 1.15d-44))) then
        tmp = x + (t * ((y - z) / a))
    else
        tmp = t * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e-44) || !(a <= 1.15e-44)) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.05e-44) or not (a <= 1.15e-44):
		tmp = x + (t * ((y - z) / a))
	else:
		tmp = t * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.05e-44) || !(a <= 1.15e-44))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.05e-44) || ~((a <= 1.15e-44)))
		tmp = x + (t * ((y - z) / a));
	else
		tmp = t * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.05e-44], N[Not[LessEqual[a, 1.15e-44]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05000000000000001e-44 or 1.14999999999999999e-44 < a

   1. Initial program 72.4%

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

      1. associate-/l* 84.2%

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

   3. Simplified 84.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.7%

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

   6. Taylor expanded in a around inf 58.5%

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

      1. associate-/l* 63.8%

         \[\leadsto x + \color{blue}{t \cdot \frac{y - z}{a}} \]

   8. Simplified 63.8%

      \[\leadsto x + \color{blue}{t \cdot \frac{y - z}{a}} \]

   if -1.05000000000000001e-44 < a < 1.14999999999999999e-44

   1. Initial program 56.1%

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

      1. +-commutative 56.1%

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

      2. *-commutative 56.1%

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

      3. associate-/l* 71.4%

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

      4. fma-define 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in x around -inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. *-commutative 63.7%

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

      3. distribute-rgt-neg-in 63.7%

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

      4. +-commutative 63.7%

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

      5. mul-1-neg 63.7%

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

      6. unsub-neg 63.7%

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

      7. times-frac 82.6%

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

      8. +-commutative 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in a around 0 47.1%

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

      1. associate-*r* 47.1%

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

      2. neg-mul-1 47.1%

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

      3. distribute-lft-out-- 47.1%

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

      4. associate-/l* 50.8%

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

   10. Simplified 50.8%

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

   11. Taylor expanded in x around 0 36.3%

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

       1. mul-1-neg 36.3%

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

       2. associate-/l* 53.3%

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

   13. Simplified 53.3%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-44} \lor \neg \left(a \leq 1.15 \cdot 10^{-44}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-28}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-46}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e-28)
   (+ x (* z (/ t (- z a))))
   (if (<= a 5.5e-46) (+ t (* y (/ (- x t) z))) (+ x (* t (/ (- y z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e-28) {
		tmp = x + (z * (t / (z - a)));
	} else if (a <= 5.5e-46) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (t * ((y - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.8d-28)) then
        tmp = x + (z * (t / (z - a)))
    else if (a <= 5.5d-46) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (t * ((y - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e-28) {
		tmp = x + (z * (t / (z - a)));
	} else if (a <= 5.5e-46) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (t * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e-28:
		tmp = x + (z * (t / (z - a)))
	elif a <= 5.5e-46:
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (t * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e-28)
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	elseif (a <= 5.5e-46)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.8e-28)
		tmp = x + (z * (t / (z - a)));
	elseif (a <= 5.5e-46)
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (t * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e-28], N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-46], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.8000000000000001e-28

   1. Initial program 75.8%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 71.7%

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

   6. Taylor expanded in y around 0 65.7%

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

      1. neg-mul-1 65.7%

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

   8. Simplified 65.7%

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

   if -6.8000000000000001e-28 < a < 5.49999999999999983e-46

   1. Initial program 56.5%

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

      1. +-commutative 56.5%

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

      2. *-commutative 56.5%

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

      3. associate-/l* 72.2%

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

      4. fma-define 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in z around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. associate-*r/ 68.5%

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

      3. associate-*r/ 68.5%

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

      4. mul-1-neg 68.5%

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

      5. div-sub 69.3%

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

      6. mul-1-neg 69.3%

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

      7. distribute-lft-out-- 69.3%

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

      8. associate-*r/ 69.3%

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

      9. mul-1-neg 69.3%

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

      10. unsub-neg 69.3%

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

      11. distribute-rgt-out-- 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in y around inf 65.4%

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

      1. associate-/l* 73.4%

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

   10. Simplified 73.4%

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

   if 5.49999999999999983e-46 < a

   1. Initial program 69.1%

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

      1. associate-/l* 82.7%

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

   3. Simplified 82.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 75.9%

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

   6. Taylor expanded in a around inf 58.6%

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

      1. associate-/l* 68.1%

         \[\leadsto x + \color{blue}{t \cdot \frac{y - z}{a}} \]

   8. Simplified 68.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-28}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-46}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+81}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+83}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+81)
   (- t (/ (* x a) z))
   (if (<= z 2.1e+83) (+ x (* (- t x) (/ y a))) (* t (/ (- z y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+81) {
		tmp = t - ((x * a) / z);
	} else if (z <= 2.1e+83) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.9d+81)) then
        tmp = t - ((x * a) / z)
    else if (z <= 2.1d+83) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+81) {
		tmp = t - ((x * a) / z);
	} else if (z <= 2.1e+83) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+81:
		tmp = t - ((x * a) / z)
	elif z <= 2.1e+83:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+81)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 2.1e+83)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+81)
		tmp = t - ((x * a) / z);
	elseif (z <= 2.1e+83)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+81], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+83], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e81

   1. Initial program 39.1%

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

      1. +-commutative 39.1%

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

      2. *-commutative 39.1%

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

      3. associate-/l* 64.5%

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

      4. fma-define 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in z around inf 54.0%

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

      1. associate--l+ 54.0%

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

      2. associate-*r/ 54.0%

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

      3. associate-*r/ 54.0%

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

      4. mul-1-neg 54.0%

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

      5. div-sub 54.0%

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

      6. mul-1-neg 54.0%

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

      7. distribute-lft-out-- 54.0%

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

      8. associate-*r/ 54.0%

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

      9. mul-1-neg 54.0%

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

      10. unsub-neg 54.0%

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

      11. distribute-rgt-out-- 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in y around 0 38.3%

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

      1. neg-mul-1 38.3%

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

   10. Simplified 38.3%

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

   11. Taylor expanded in t around 0 44.3%

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

       1. *-commutative 44.3%

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

   13. Simplified 44.3%

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

   if -2.9e81 < z < 2.10000000000000002e83

   1. Initial program 80.9%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

      1. clear-num 84.2%

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

      2. un-div-inv 84.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 84.2%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in z around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. *-lft-identity 65.4%

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

      3. times-frac 70.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{1} \cdot \frac{y}{a}} \]

      4. /-rgt-identity 70.6%

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

   9. Simplified 70.6%

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

   if 2.10000000000000002e83 < z

   1. Initial program 36.7%

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

      1. +-commutative 36.7%

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

      2. *-commutative 36.7%

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

      3. associate-/l* 66.8%

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

      4. fma-define 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in x around -inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

      4. +-commutative 44.4%

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

      5. mul-1-neg 44.4%

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

      6. unsub-neg 44.4%

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

      7. times-frac 71.6%

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

      8. +-commutative 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 32.9%

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

      1. associate-*r* 32.9%

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

      2. neg-mul-1 32.9%

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

      3. distribute-lft-out-- 32.9%

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

      4. associate-/l* 38.4%

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

   10. Simplified 38.4%

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

   11. Taylor expanded in x around 0 33.3%

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

       1. mul-1-neg 33.3%

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

       2. associate-/l* 61.8%

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

   13. Simplified 61.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+81}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+83}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+81)
   (- t (/ (* x a) z))
   (if (<= z 1.35e+83) (+ x (* y (/ (- t x) a))) (* t (/ (- z y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+81) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.35e+83) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d+81)) then
        tmp = t - ((x * a) / z)
    else if (z <= 1.35d+83) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+81) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.35e+83) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+81:
		tmp = t - ((x * a) / z)
	elif z <= 1.35e+83:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+81)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 1.35e+83)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+81)
		tmp = t - ((x * a) / z);
	elseif (z <= 1.35e+83)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+81], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+83], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e81

   1. Initial program 39.1%

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

      1. +-commutative 39.1%

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

      2. *-commutative 39.1%

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

      3. associate-/l* 64.5%

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

      4. fma-define 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in z around inf 54.0%

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

      1. associate--l+ 54.0%

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

      2. associate-*r/ 54.0%

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

      3. associate-*r/ 54.0%

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

      4. mul-1-neg 54.0%

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

      5. div-sub 54.0%

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

      6. mul-1-neg 54.0%

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

      7. distribute-lft-out-- 54.0%

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

      8. associate-*r/ 54.0%

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

      9. mul-1-neg 54.0%

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

      10. unsub-neg 54.0%

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

      11. distribute-rgt-out-- 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in y around 0 38.3%

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

      1. neg-mul-1 38.3%

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

   10. Simplified 38.3%

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

   11. Taylor expanded in t around 0 44.3%

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

       1. *-commutative 44.3%

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

   13. Simplified 44.3%

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

   if -3.2e81 < z < 1.35000000000000003e83

   1. Initial program 80.9%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 65.4%

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

      1. associate-/l* 66.9%

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

   7. Simplified 66.9%

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

   if 1.35000000000000003e83 < z

   1. Initial program 36.7%

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

      1. +-commutative 36.7%

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

      2. *-commutative 36.7%

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

      3. associate-/l* 66.8%

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

      4. fma-define 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in x around -inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

      4. +-commutative 44.4%

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

      5. mul-1-neg 44.4%

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

      6. unsub-neg 44.4%

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

      7. times-frac 71.6%

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

      8. +-commutative 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 32.9%

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

      1. associate-*r* 32.9%

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

      2. neg-mul-1 32.9%

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

      3. distribute-lft-out-- 32.9%

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

      4. associate-/l* 38.4%

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

   10. Simplified 38.4%

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

   11. Taylor expanded in x around 0 33.3%

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

       1. mul-1-neg 33.3%

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

       2. associate-/l* 61.8%

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

   13. Simplified 61.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+90}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+90)
   (- t (/ (* x a) z))
   (if (<= z 1.75e+83) (+ x (* (/ y (- a z)) t)) (* t (/ (- z y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+90) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.75e+83) {
		tmp = x + ((y / (a - z)) * t);
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3d+90)) then
        tmp = t - ((x * a) / z)
    else if (z <= 1.75d+83) then
        tmp = x + ((y / (a - z)) * t)
    else
        tmp = t * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+90) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.75e+83) {
		tmp = x + ((y / (a - z)) * t);
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+90:
		tmp = t - ((x * a) / z)
	elif z <= 1.75e+83:
		tmp = x + ((y / (a - z)) * t)
	else:
		tmp = t * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+90)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 1.75e+83)
		tmp = Float64(x + Float64(Float64(y / Float64(a - z)) * t));
	else
		tmp = Float64(t * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+90)
		tmp = t - ((x * a) / z);
	elseif (z <= 1.75e+83)
		tmp = x + ((y / (a - z)) * t);
	else
		tmp = t * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+90], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+83], N[(x + N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999979e90

   1. Initial program 38.7%

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

      1. +-commutative 38.7%

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

      2. *-commutative 38.7%

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

      3. associate-/l* 65.1%

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

      4. fma-define 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in z around inf 52.1%

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

      1. associate--l+ 52.1%

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

      2. associate-*r/ 52.1%

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

      3. associate-*r/ 52.1%

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

      4. mul-1-neg 52.1%

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

      5. div-sub 52.1%

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

      6. mul-1-neg 52.1%

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

      7. distribute-lft-out-- 52.1%

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

      8. associate-*r/ 52.1%

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

      9. mul-1-neg 52.1%

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

      10. unsub-neg 52.1%

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

      11. distribute-rgt-out-- 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in y around 0 39.8%

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

      1. neg-mul-1 39.8%

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

   10. Simplified 39.8%

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

   11. Taylor expanded in t around 0 46.0%

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

       1. *-commutative 46.0%

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

   13. Simplified 46.0%

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

   if -2.99999999999999979e90 < z < 1.74999999999999989e83

   1. Initial program 80.5%

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

      1. associate-/l* 84.4%

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

   3. Simplified 84.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 66.4%

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

   6. Taylor expanded in y around inf 56.6%

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

      1. associate-/l* 61.0%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 61.0%

      \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

   if 1.74999999999999989e83 < z

   1. Initial program 36.7%

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

      1. +-commutative 36.7%

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

      2. *-commutative 36.7%

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

      3. associate-/l* 66.8%

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

      4. fma-define 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in x around -inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

      4. +-commutative 44.4%

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

      5. mul-1-neg 44.4%

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

      6. unsub-neg 44.4%

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

      7. times-frac 71.6%

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

      8. +-commutative 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 32.9%

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

      1. associate-*r* 32.9%

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

      2. neg-mul-1 32.9%

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

      3. distribute-lft-out-- 32.9%

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

      4. associate-/l* 38.4%

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

   10. Simplified 38.4%

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

   11. Taylor expanded in x around 0 33.3%

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

       1. mul-1-neg 33.3%

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

       2. associate-/l* 61.8%

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

   13. Simplified 61.8%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+90}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-57} \lor \neg \left(z \leq 4 \cdot 10^{+77}\right):\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e-57) (not (<= z 4e+77)))
   (- t (/ (* x a) z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e-57) || !(z <= 4e+77)) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.35d-57)) .or. (.not. (z <= 4d+77))) then
        tmp = t - ((x * a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e-57) || !(z <= 4e+77)) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e-57) or not (z <= 4e+77):
		tmp = t - ((x * a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e-57) || !(z <= 4e+77))
		tmp = Float64(t - Float64(Float64(x * a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e-57) || ~((z <= 4e+77)))
		tmp = t - ((x * a) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e-57], N[Not[LessEqual[z, 4e+77]], $MachinePrecision]], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e-57 or 3.99999999999999993e77 < z

   1. Initial program 42.2%

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

      1. +-commutative 42.2%

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

      2. *-commutative 42.2%

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

      3. associate-/l* 67.3%

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

      4. fma-define 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in z around inf 55.6%

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

      1. associate--l+ 55.6%

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

      2. associate-*r/ 55.6%

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

      3. associate-*r/ 55.6%

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

      4. mul-1-neg 55.6%

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

      5. div-sub 55.5%

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

      6. mul-1-neg 55.5%

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

      7. distribute-lft-out-- 55.5%

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

      8. associate-*r/ 55.5%

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

      9. mul-1-neg 55.5%

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

      10. unsub-neg 55.5%

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

      11. distribute-rgt-out-- 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in y around 0 42.7%

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

      1. neg-mul-1 42.7%

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

   10. Simplified 42.7%

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

   11. Taylor expanded in t around 0 45.8%

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

       1. *-commutative 45.8%

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

   13. Simplified 45.8%

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

   if -1.3500000000000001e-57 < z < 3.99999999999999993e77

   1. Initial program 90.0%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.0%

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

   6. Taylor expanded in z around 0 60.7%

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

      1. associate-/l* 62.9%

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

   8. Simplified 62.9%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-57} \lor \neg \left(z \leq 4 \cdot 10^{+77}\right):\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-57}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+83}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-57)
   (- t (/ (* x a) z))
   (if (<= z 1.6e+83) (+ x (* t (/ y a))) (* t (/ (- z y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-57) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.6e+83) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d-57)) then
        tmp = t - ((x * a) / z)
    else if (z <= 1.6d+83) then
        tmp = x + (t * (y / a))
    else
        tmp = t * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-57) {
		tmp = t - ((x * a) / z);
	} else if (z <= 1.6e+83) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-57:
		tmp = t - ((x * a) / z)
	elif z <= 1.6e+83:
		tmp = x + (t * (y / a))
	else:
		tmp = t * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-57)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (z <= 1.6e+83)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e-57)
		tmp = t - ((x * a) / z);
	elseif (z <= 1.6e+83)
		tmp = x + (t * (y / a));
	else
		tmp = t * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-57], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+83], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e-57

   1. Initial program 44.7%

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

      1. +-commutative 44.7%

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

      2. *-commutative 44.7%

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

      3. associate-/l* 67.9%

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

      4. fma-define 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in z around inf 52.3%

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

      1. associate--l+ 52.3%

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

      2. associate-*r/ 52.3%

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

      3. associate-*r/ 52.3%

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

      4. mul-1-neg 52.3%

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

      5. div-sub 52.3%

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

      6. mul-1-neg 52.3%

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

      7. distribute-lft-out-- 52.3%

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

      8. associate-*r/ 52.3%

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

      9. mul-1-neg 52.3%

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

      10. unsub-neg 52.3%

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

      11. distribute-rgt-out-- 52.4%

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

   7. Simplified 52.4%

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

   8. Taylor expanded in y around 0 36.6%

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

      1. neg-mul-1 36.6%

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

   10. Simplified 36.6%

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

   11. Taylor expanded in t around 0 41.2%

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

       1. *-commutative 41.2%

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

   13. Simplified 41.2%

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

   if -1.3500000000000001e-57 < z < 1.5999999999999999e83

   1. Initial program 89.4%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 71.6%

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

   6. Taylor expanded in z around 0 60.6%

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

      1. associate-/l* 62.7%

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

   8. Simplified 62.7%

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

   if 1.5999999999999999e83 < z

   1. Initial program 36.7%

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

      1. +-commutative 36.7%

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

      2. *-commutative 36.7%

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

      3. associate-/l* 66.8%

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

      4. fma-define 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in x around -inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

      4. +-commutative 44.4%

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

      5. mul-1-neg 44.4%

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

      6. unsub-neg 44.4%

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

      7. times-frac 71.6%

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

      8. +-commutative 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 32.9%

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

      1. associate-*r* 32.9%

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

      2. neg-mul-1 32.9%

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

      3. distribute-lft-out-- 32.9%

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

      4. associate-/l* 38.4%

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

   10. Simplified 38.4%

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

   11. Taylor expanded in x around 0 33.3%

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

       1. mul-1-neg 33.3%

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

       2. associate-/l* 61.8%

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

   13. Simplified 61.8%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-57}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+83}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+83}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+81) t (if (<= z 2.35e+83) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+81) {
		tmp = t;
	} else if (z <= 2.35e+83) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d+81)) then
        tmp = t
    else if (z <= 2.35d+83) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+81) {
		tmp = t;
	} else if (z <= 2.35e+83) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+81:
		tmp = t
	elif z <= 2.35e+83:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+81)
		tmp = t;
	elseif (z <= 2.35e+83)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+81)
		tmp = t;
	elseif (z <= 2.35e+83)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+81], t, If[LessEqual[z, 2.35e+83], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e81 or 2.3499999999999999e83 < z

   1. Initial program 38.0%

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

      1. +-commutative 38.0%

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

      2. *-commutative 38.0%

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

      3. associate-/l* 65.6%

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

      4. fma-define 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in x around -inf 49.0%

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

      1. mul-1-neg 49.0%

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

      2. *-commutative 49.0%

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

      3. distribute-rgt-neg-in 49.0%

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

      4. +-commutative 49.0%

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

      5. mul-1-neg 49.0%

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

      6. unsub-neg 49.0%

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

      7. times-frac 73.4%

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

      8. +-commutative 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in z around inf 45.6%

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

   if -3.2e81 < z < 2.3499999999999999e83

   1. Initial program 80.9%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 66.6%

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

   6. Taylor expanded in z around 0 52.5%

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

      1. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

Alternative 18: 39.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-39}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+99) x (if (<= a 6.2e-39) (+ t (* a (/ t z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+99) {
		tmp = x;
	} else if (a <= 6.2e-39) {
		tmp = t + (a * (t / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d+99)) then
        tmp = x
    else if (a <= 6.2d-39) then
        tmp = t + (a * (t / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+99) {
		tmp = x;
	} else if (a <= 6.2e-39) {
		tmp = t + (a * (t / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+99:
		tmp = x
	elif a <= 6.2e-39:
		tmp = t + (a * (t / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+99)
		tmp = x;
	elseif (a <= 6.2e-39)
		tmp = Float64(t + Float64(a * Float64(t / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+99)
		tmp = x;
	elseif (a <= 6.2e-39)
		tmp = t + (a * (t / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+99], x, If[LessEqual[a, 6.2e-39], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.50000000000000004e99 or 6.1999999999999994e-39 < a

   1. Initial program 71.0%

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

      1. +-commutative 71.0%

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

      2. *-commutative 71.0%

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

      3. associate-/l* 86.6%

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

      4. fma-define 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in a around inf 44.1%

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

   if -2.50000000000000004e99 < a < 6.1999999999999994e-39

   1. Initial program 60.7%

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

      1. +-commutative 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-/l* 75.4%

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

      4. fma-define 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. associate-*r/ 62.9%

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

      3. associate-*r/ 62.9%

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

      4. mul-1-neg 62.9%

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

      5. div-sub 63.6%

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

      6. mul-1-neg 63.6%

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

      7. distribute-lft-out-- 63.6%

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

      8. associate-*r/ 63.6%

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

      9. mul-1-neg 63.6%

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

      10. unsub-neg 63.6%

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

      11. distribute-rgt-out-- 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in y around 0 38.4%

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

      1. neg-mul-1 38.4%

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

   10. Simplified 38.4%

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

   11. Taylor expanded in x around 0 34.1%

       \[\leadsto \color{blue}{t - -1 \cdot \frac{a \cdot t}{z}} \]
   12. Step-by-step derivation

       1. sub-neg 34.1%

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

       2. mul-1-neg 34.1%

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

       3. remove-double-neg 34.1%

          \[\leadsto t + \color{blue}{\frac{a \cdot t}{z}} \]

       4. associate-/l* 37.9%

          \[\leadsto t + \color{blue}{a \cdot \frac{t}{z}} \]

   13. Simplified 37.9%

       \[\leadsto \color{blue}{t + a \cdot \frac{t}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 38.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+86)
   t
   (if (<= z -7.2e-58) (* x (/ (- y a) z)) (if (<= z 1.85e+83) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+86) {
		tmp = t;
	} else if (z <= -7.2e-58) {
		tmp = x * ((y - a) / z);
	} else if (z <= 1.85e+83) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+86)) then
        tmp = t
    else if (z <= (-7.2d-58)) then
        tmp = x * ((y - a) / z)
    else if (z <= 1.85d+83) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+86) {
		tmp = t;
	} else if (z <= -7.2e-58) {
		tmp = x * ((y - a) / z);
	} else if (z <= 1.85e+83) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+86:
		tmp = t
	elif z <= -7.2e-58:
		tmp = x * ((y - a) / z)
	elif z <= 1.85e+83:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+86)
		tmp = t;
	elseif (z <= -7.2e-58)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 1.85e+83)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+86)
		tmp = t;
	elseif (z <= -7.2e-58)
		tmp = x * ((y - a) / z);
	elseif (z <= 1.85e+83)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+86], t, If[LessEqual[z, -7.2e-58], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+83], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.49999999999999996e86 or 1.8500000000000001e83 < z

   1. Initial program 37.7%

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

      1. +-commutative 37.7%

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

      2. *-commutative 37.7%

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

      3. associate-/l* 65.9%

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

      4. fma-define 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in x around -inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. *-commutative 47.9%

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

      3. distribute-rgt-neg-in 47.9%

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

      4. +-commutative 47.9%

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

      5. mul-1-neg 47.9%

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

      6. unsub-neg 47.9%

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

      7. times-frac 72.8%

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

      8. +-commutative 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in z around inf 46.5%

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

   if -6.49999999999999996e86 < z < -7.20000000000000019e-58

   1. Initial program 53.2%

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

      1. +-commutative 53.2%

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

      2. *-commutative 53.2%

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

      3. associate-/l* 72.0%

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

      4. fma-define 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in z around inf 51.3%

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

      1. associate--l+ 51.3%

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

      2. associate-*r/ 51.3%

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

      3. associate-*r/ 51.3%

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

      4. mul-1-neg 51.3%

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

      5. div-sub 51.3%

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

      6. mul-1-neg 51.3%

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

      7. distribute-lft-out-- 51.3%

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

      8. associate-*r/ 51.3%

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

      9. mul-1-neg 51.3%

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

      10. unsub-neg 51.3%

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

      11. distribute-rgt-out-- 51.5%

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

   7. Simplified 51.5%

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

   8. Taylor expanded in t around 0 34.2%

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

      1. associate-/l* 36.6%

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

   10. Simplified 36.6%

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

   if -7.20000000000000019e-58 < z < 1.8500000000000001e83

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-/l* 93.8%

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

      4. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf 39.7%

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

Alternative 20: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+99) x (if (<= a 6.4e-40) (* t (+ 1.0 (/ a z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+99) {
		tmp = x;
	} else if (a <= 6.4e-40) {
		tmp = t * (1.0 + (a / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d+99)) then
        tmp = x
    else if (a <= 6.4d-40) then
        tmp = t * (1.0d0 + (a / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+99) {
		tmp = x;
	} else if (a <= 6.4e-40) {
		tmp = t * (1.0 + (a / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+99:
		tmp = x
	elif a <= 6.4e-40:
		tmp = t * (1.0 + (a / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+99)
		tmp = x;
	elseif (a <= 6.4e-40)
		tmp = Float64(t * Float64(1.0 + Float64(a / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+99)
		tmp = x;
	elseif (a <= 6.4e-40)
		tmp = t * (1.0 + (a / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+99], x, If[LessEqual[a, 6.4e-40], N[(t * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.50000000000000004e99 or 6.40000000000000004e-40 < a

   1. Initial program 71.0%

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

      1. +-commutative 71.0%

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

      2. *-commutative 71.0%

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

      3. associate-/l* 86.6%

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

      4. fma-define 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in a around inf 44.1%

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

   if -2.50000000000000004e99 < a < 6.40000000000000004e-40

   1. Initial program 60.7%

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

      1. +-commutative 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-/l* 75.4%

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

      4. fma-define 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. associate-*r/ 62.9%

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

      3. associate-*r/ 62.9%

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

      4. mul-1-neg 62.9%

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

      5. div-sub 63.6%

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

      6. mul-1-neg 63.6%

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

      7. distribute-lft-out-- 63.6%

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

      8. associate-*r/ 63.6%

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

      9. mul-1-neg 63.6%

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

      10. unsub-neg 63.6%

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

      11. distribute-rgt-out-- 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in y around 0 38.4%

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

      1. neg-mul-1 38.4%

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

   10. Simplified 38.4%

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

   11. Taylor expanded in t around inf 34.7%

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

       1. sub-neg 34.7%

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

       2. neg-mul-1 34.7%

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

       3. remove-double-neg 34.7%

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

   13. Simplified 34.7%

       \[\leadsto \color{blue}{t \cdot \left(1 + \frac{a}{z}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-57}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e-57) t (if (<= z 1.8e+83) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e-57) {
		tmp = t;
	} else if (z <= 1.8e+83) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.4d-57)) then
        tmp = t
    else if (z <= 1.8d+83) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e-57) {
		tmp = t;
	} else if (z <= 1.8e+83) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e-57:
		tmp = t
	elif z <= 1.8e+83:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e-57)
		tmp = t;
	elseif (z <= 1.8e+83)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e-57)
		tmp = t;
	elseif (z <= 1.8e+83)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e-57], t, If[LessEqual[z, 1.8e+83], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000016e-57 or 1.7999999999999999e83 < z

   1. Initial program 41.6%

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

      1. +-commutative 41.6%

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

      2. *-commutative 41.6%

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

      3. associate-/l* 67.3%

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

      4. fma-define 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in x around -inf 50.3%

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

      1. mul-1-neg 50.3%

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

      2. *-commutative 50.3%

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

      3. distribute-rgt-neg-in 50.3%

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

      4. +-commutative 50.3%

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

      5. mul-1-neg 50.3%

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

      6. unsub-neg 50.3%

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

      7. times-frac 72.7%

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

      8. +-commutative 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in z around inf 38.7%

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

   if -3.40000000000000016e-57 < z < 1.7999999999999999e83

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-/l* 93.8%

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

      4. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf 39.1%

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

Alternative 22: 25.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 65.3%

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

   1. +-commutative 65.3%

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

   2. *-commutative 65.3%

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

   3. associate-/l* 80.4%

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

   4. fma-define 80.4%

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

3. Simplified 80.4%

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

5. Taylor expanded in x around -inf 67.0%

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

   1. mul-1-neg 67.0%

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

   2. *-commutative 67.0%

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

   3. distribute-rgt-neg-in 67.0%

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

   4. +-commutative 67.0%

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

   5. mul-1-neg 67.0%

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

   6. unsub-neg 67.0%

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

   7. times-frac 79.8%

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

   8. +-commutative 79.8%

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

7. Simplified 79.8%

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

8. Taylor expanded in z around inf 23.5%

   \[\leadsto \color{blue}{t} \]
9. Add Preprocessing

Developer Target 1: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024132 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

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