Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.1% → 94.8%

Time: 16.6s

Alternatives: 18

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.1% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y + \left(\left(a \cdot \frac{t}{x} - t \cdot \frac{y}{x}\right) - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-290) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* x (/ (+ y (- (- (* a (/ t x)) (* t (/ y x))) a)) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-290) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	}
	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))))
	tmp = 0.0
	if ((t_1 <= -2e-290) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y + Float64(Float64(Float64(a * Float64(t / x)) - Float64(t * Float64(y / x))) - a)) / z)));
	end
	return 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]}, If[Or[LessEqual[t$95$1, -2e-290], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(x * N[(N[(y + N[(N[(N[(a * N[(t / x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-290 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. remove-double-neg 88.0%

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

      3. unsub-neg 88.0%

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

      4. *-commutative 88.0%

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

      5. associate-*l/ 76.2%

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

      6. associate-/l* 93.9%

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

      7. fma-neg 93.9%

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

      8. remove-double-neg 93.9%

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

   3. Simplified 93.9%

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

   if -2.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. remove-double-neg 3.5%

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

      3. unsub-neg 3.5%

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

      4. *-commutative 3.5%

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

      5. associate-*l/ 3.2%

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

      6. associate-/l* 3.5%

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

      7. fma-neg 3.5%

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

      8. remove-double-neg 3.5%

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

   3. Simplified 3.5%

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

   5. Taylor expanded in x around -inf 40.4%

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

      1. associate-*r* 40.4%

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

      2. neg-mul-1 40.4%

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

      3. fma-define 40.4%

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

      4. times-frac 57.1%

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

      5. +-commutative 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in z around -inf 69.3%

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

      1. associate-/l* 87.5%

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

      2. distribute-lft-out-- 87.5%

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

      3. associate--l+ 87.5%

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

      4. distribute-lft-out-- 87.5%

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

      5. mul-1-neg 87.5%

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

      6. associate-/l* 92.4%

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

      7. associate-/l* 97.4%

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

   10. Simplified 97.4%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-290} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y + \left(\left(a \cdot \frac{t}{x} - t \cdot \frac{y}{x}\right) - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := \frac{z}{a - z} + 1\\ t_3 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(t\_2 + t \cdot \left(\frac{\frac{y - z}{x}}{a - z} - \frac{\frac{y}{t}}{a - z}\right)\right)\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y + \left(\left(a \cdot \frac{t}{x} - t \cdot \frac{y}{x}\right) - a\right)}{z}\\ \mathbf{elif}\;t\_3 \leq 10^{-45}:\\ \;\;\;\;t \cdot \left(\frac{y - z}{a - z} + \frac{x \cdot \left(t\_2 + \frac{y}{z - a}\right)}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ (/ z (- a z)) 1.0))
        (t_3 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_3 (- INFINITY))
     (* x (+ t_2 (* t (- (/ (/ (- y z) x) (- a z)) (/ (/ y t) (- a z))))))
     (if (<= t_3 -2e-290)
       t_1
       (if (<= t_3 0.0)
         (+ t (* x (/ (+ y (- (- (* a (/ t x)) (* t (/ y x))) a)) z)))
         (if (<= t_3 1e-45)
           (* t (+ (/ (- y z) (- a z)) (/ (* x (+ t_2 (/ y (- z a)))) t)))
           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 = (z / (a - z)) + 1.0;
	double t_3 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * (t_2 + (t * ((((y - z) / x) / (a - z)) - ((y / t) / (a - z)))));
	} else if (t_3 <= -2e-290) {
		tmp = t_1;
	} else if (t_3 <= 0.0) {
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	} else if (t_3 <= 1e-45) {
		tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + (y / (z - a)))) / t));
	} 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 = (z / (a - z)) + 1.0;
	double t_3 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * (t_2 + (t * ((((y - z) / x) / (a - z)) - ((y / t) / (a - z)))));
	} else if (t_3 <= -2e-290) {
		tmp = t_1;
	} else if (t_3 <= 0.0) {
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	} else if (t_3 <= 1e-45) {
		tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + (y / (z - a)))) / t));
	} 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 = (z / (a - z)) + 1.0
	t_3 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * (t_2 + (t * ((((y - z) / x) / (a - z)) - ((y / t) / (a - z)))))
	elif t_3 <= -2e-290:
		tmp = t_1
	elif t_3 <= 0.0:
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z))
	elif t_3 <= 1e-45:
		tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + (y / (z - a)))) / t))
	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(Float64(z / Float64(a - z)) + 1.0)
	t_3 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(t_2 + Float64(t * Float64(Float64(Float64(Float64(y - z) / x) / Float64(a - z)) - Float64(Float64(y / t) / Float64(a - z))))));
	elseif (t_3 <= -2e-290)
		tmp = t_1;
	elseif (t_3 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y + Float64(Float64(Float64(a * Float64(t / x)) - Float64(t * Float64(y / x))) - a)) / z)));
	elseif (t_3 <= 1e-45)
		tmp = Float64(t * Float64(Float64(Float64(y - z) / Float64(a - z)) + Float64(Float64(x * Float64(t_2 + Float64(y / Float64(z - a)))) / t)));
	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 = (z / (a - z)) + 1.0;
	t_3 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * (t_2 + (t * ((((y - z) / x) / (a - z)) - ((y / t) / (a - z)))));
	elseif (t_3 <= -2e-290)
		tmp = t_1;
	elseif (t_3 <= 0.0)
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	elseif (t_3 <= 1e-45)
		tmp = t * (((y - z) / (a - z)) + ((x * (t_2 + (y / (z - a)))) / t));
	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[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(t$95$2 + N[(t * N[(N[(N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-290], t$95$1, If[LessEqual[t$95$3, 0.0], N[(t + N[(x * N[(N[(y + N[(N[(N[(a * N[(t / x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e-45], N[(t * N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(t$95$2 + N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. remove-double-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*l/ 95.7%

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

      6. associate-/l* 95.7%

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

      7. fma-neg 95.7%

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

      8. remove-double-neg 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around -inf 91.3%

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

      1. associate-*r* 91.3%

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

      2. neg-mul-1 91.3%

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

      3. fma-define 91.3%

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

      4. times-frac 95.5%

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

      5. +-commutative 95.5%

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

   7. Simplified 95.5%

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

   8. Taylor expanded in t around -inf 88.0%

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

      1. associate-*r* 88.0%

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

      2. neg-mul-1 88.0%

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

      3. associate--l+ 88.0%

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

      4. mul-1-neg 88.0%

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

      5. associate-/r* 96.0%

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

      6. div-sub 96.0%

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

      7. associate-/r* 100.0%

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

   10. Simplified 100.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-290 or 9.99999999999999984e-46 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

      1. clear-num 91.9%

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

      2. un-div-inv 92.1%

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

   4. Applied egg-rr 92.1%

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

   if -2.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. remove-double-neg 3.5%

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

      3. unsub-neg 3.5%

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

      4. *-commutative 3.5%

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

      5. associate-*l/ 3.2%

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

      6. associate-/l* 3.5%

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

      7. fma-neg 3.5%

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

      8. remove-double-neg 3.5%

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

   3. Simplified 3.5%

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

   5. Taylor expanded in x around -inf 40.4%

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

      1. associate-*r* 40.4%

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

      2. neg-mul-1 40.4%

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

      3. fma-define 40.4%

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

      4. times-frac 57.1%

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

      5. +-commutative 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in z around -inf 69.3%

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

      1. associate-/l* 87.5%

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

      2. distribute-lft-out-- 87.5%

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

      3. associate--l+ 87.5%

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

      4. distribute-lft-out-- 87.5%

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

      5. mul-1-neg 87.5%

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

      6. associate-/l* 92.4%

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

      7. associate-/l* 97.4%

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

   10. Simplified 97.4%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999984e-46

   1. Initial program 65.7%

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

      1. +-commutative 65.7%

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

      2. remove-double-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

      5. associate-*l/ 94.6%

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

      6. associate-/l* 90.7%

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

      7. fma-neg 90.7%

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

      8. remove-double-neg 90.7%

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

   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 99.9%

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

      1. associate-*r* 99.9%

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

      2. neg-mul-1 99.9%

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

      3. fma-define 99.9%

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

      4. times-frac 95.2%

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

      5. +-commutative 95.2%

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

   7. Simplified 95.2%

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

   8. Taylor expanded in t around inf 95.5%

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

      1. associate--l+ 95.5%

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

      2. associate-*r/ 95.5%

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

      3. associate-*r* 95.5%

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

      4. mul-1-neg 95.5%

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

      5. div-sub 95.5%

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

   10. Simplified 95.5%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x \cdot \left(\left(\frac{z}{a - z} + 1\right) + t \cdot \left(\frac{\frac{y - z}{x}}{a - z} - \frac{\frac{y}{t}}{a - z}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y + \left(\left(a \cdot \frac{t}{x} - t \cdot \frac{y}{x}\right) - a\right)}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-45}:\\ \;\;\;\;t \cdot \left(\frac{y - z}{a - z} + \frac{x \cdot \left(\left(\frac{z}{a - z} + 1\right) + \frac{y}{z - a}\right)}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y + \left(\left(a \cdot \frac{t}{x} - t \cdot \frac{y}{x}\right) - a\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{-45}:\\ \;\;\;\;t \cdot \left(\frac{y - z}{a - z} + \frac{x \cdot \left(\left(\frac{z}{a - z} + 1\right) + \frac{y}{z - a}\right)}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2e-290)
     t_1
     (if (<= t_2 0.0)
       (+ t (* x (/ (+ y (- (- (* a (/ t x)) (* t (/ y x))) a)) z)))
       (if (<= t_2 1e-45)
         (*
          t
          (+
           (/ (- y z) (- a z))
           (/ (* x (+ (+ (/ z (- a z)) 1.0) (/ y (- z a)))) t)))
         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 <= -2e-290) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	} else if (t_2 <= 1e-45) {
		tmp = t * (((y - z) / (a - z)) + ((x * (((z / (a - z)) + 1.0) + (y / (z - a)))) / t));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / (t - x)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-2d-290)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z))
    else if (t_2 <= 1d-45) then
        tmp = t * (((y - z) / (a - z)) + ((x * (((z / (a - z)) + 1.0d0) + (y / (z - a)))) / t))
    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 + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -2e-290) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	} else if (t_2 <= 1e-45) {
		tmp = t * (((y - z) / (a - z)) + ((x * (((z / (a - z)) + 1.0) + (y / (z - a)))) / t));
	} 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 <= -2e-290:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z))
	elif t_2 <= 1e-45:
		tmp = t * (((y - z) / (a - z)) + ((x * (((z / (a - z)) + 1.0) + (y / (z - a)))) / t))
	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(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -2e-290)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y + Float64(Float64(Float64(a * Float64(t / x)) - Float64(t * Float64(y / x))) - a)) / z)));
	elseif (t_2 <= 1e-45)
		tmp = Float64(t * Float64(Float64(Float64(y - z) / Float64(a - z)) + Float64(Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) + Float64(y / Float64(z - a)))) / t)));
	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 <= -2e-290)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	elseif (t_2 <= 1e-45)
		tmp = t * (((y - z) / (a - z)) + ((x * (((z / (a - z)) + 1.0) + (y / (z - a)))) / t));
	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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-290], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(x * N[(N[(y + N[(N[(N[(a * N[(t / x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-45], N[(t * N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-290 or 9.99999999999999984e-46 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.5%

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

      1. clear-num 90.5%

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

      2. un-div-inv 90.6%

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

   4. Applied egg-rr 90.6%

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

   if -2.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. remove-double-neg 3.5%

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

      3. unsub-neg 3.5%

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

      4. *-commutative 3.5%

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

      5. associate-*l/ 3.2%

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

      6. associate-/l* 3.5%

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

      7. fma-neg 3.5%

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

      8. remove-double-neg 3.5%

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

   3. Simplified 3.5%

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

   5. Taylor expanded in x around -inf 40.4%

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

      1. associate-*r* 40.4%

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

      2. neg-mul-1 40.4%

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

      3. fma-define 40.4%

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

      4. times-frac 57.1%

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

      5. +-commutative 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in z around -inf 69.3%

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

      1. associate-/l* 87.5%

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

      2. distribute-lft-out-- 87.5%

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

      3. associate--l+ 87.5%

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

      4. distribute-lft-out-- 87.5%

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

      5. mul-1-neg 87.5%

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

      6. associate-/l* 92.4%

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

      7. associate-/l* 97.4%

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

   10. Simplified 97.4%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999984e-46

   1. Initial program 65.7%

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

      1. +-commutative 65.7%

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

      2. remove-double-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

      5. associate-*l/ 94.6%

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

      6. associate-/l* 90.7%

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

      7. fma-neg 90.7%

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

      8. remove-double-neg 90.7%

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

   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 99.9%

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

      1. associate-*r* 99.9%

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

      2. neg-mul-1 99.9%

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

      3. fma-define 99.9%

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

      4. times-frac 95.2%

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

      5. +-commutative 95.2%

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

   7. Simplified 95.2%

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

   8. Taylor expanded in t around inf 95.5%

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

      1. associate--l+ 95.5%

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

      2. associate-*r/ 95.5%

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

      3. associate-*r* 95.5%

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

      4. mul-1-neg 95.5%

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

      5. div-sub 95.5%

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

   10. Simplified 95.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y + \left(\left(a \cdot \frac{t}{x} - t \cdot \frac{y}{x}\right) - a\right)}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-45}:\\ \;\;\;\;t \cdot \left(\frac{y - z}{a - z} + \frac{x \cdot \left(\left(\frac{z}{a - z} + 1\right) + \frac{y}{z - a}\right)}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-281}:\\ \;\;\;\;t + x \cdot \frac{y + \left(\left(a \cdot \frac{t}{x} - t \cdot \frac{y}{x}\right) - a\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{-45}:\\ \;\;\;\;x + \frac{-1}{\frac{a - z}{\left(y - z\right) \cdot \left(x - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2e-290)
     t_1
     (if (<= t_2 5e-281)
       (+ t (* x (/ (+ y (- (- (* a (/ t x)) (* t (/ y x))) a)) z)))
       (if (<= t_2 1e-45)
         (+ x (/ -1.0 (/ (- a z) (* (- y z) (- x t)))))
         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 <= -2e-290) {
		tmp = t_1;
	} else if (t_2 <= 5e-281) {
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	} else if (t_2 <= 1e-45) {
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / (t - x)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-2d-290)) then
        tmp = t_1
    else if (t_2 <= 5d-281) then
        tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z))
    else if (t_2 <= 1d-45) then
        tmp = x + ((-1.0d0) / ((a - z) / ((y - z) * (x - t))))
    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 + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -2e-290) {
		tmp = t_1;
	} else if (t_2 <= 5e-281) {
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	} else if (t_2 <= 1e-45) {
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))));
	} 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 <= -2e-290:
		tmp = t_1
	elif t_2 <= 5e-281:
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z))
	elif t_2 <= 1e-45:
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))))
	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(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -2e-290)
		tmp = t_1;
	elseif (t_2 <= 5e-281)
		tmp = Float64(t + Float64(x * Float64(Float64(y + Float64(Float64(Float64(a * Float64(t / x)) - Float64(t * Float64(y / x))) - a)) / z)));
	elseif (t_2 <= 1e-45)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - z) / Float64(Float64(y - z) * Float64(x - t)))));
	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 <= -2e-290)
		tmp = t_1;
	elseif (t_2 <= 5e-281)
		tmp = t + (x * ((y + (((a * (t / x)) - (t * (y / x))) - a)) / z));
	elseif (t_2 <= 1e-45)
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))));
	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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-290], t$95$1, If[LessEqual[t$95$2, 5e-281], N[(t + N[(x * N[(N[(y + N[(N[(N[(a * N[(t / x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-45], N[(x + N[(-1.0 / N[(N[(a - z), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-290 or 9.99999999999999984e-46 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.5%

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

      1. clear-num 90.5%

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

      2. un-div-inv 90.6%

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

   4. Applied egg-rr 90.6%

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

   if -2.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-281

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. remove-double-neg 3.5%

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

      3. unsub-neg 3.5%

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

      4. *-commutative 3.5%

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

      5. associate-*l/ 5.7%

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

      6. associate-/l* 6.0%

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

      7. fma-neg 6.0%

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

      8. remove-double-neg 6.0%

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

   3. Simplified 6.0%

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

   5. Taylor expanded in x around -inf 41.9%

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

      1. associate-*r* 41.9%

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

      2. neg-mul-1 41.9%

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

      3. fma-define 41.9%

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

      4. times-frac 58.2%

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

      5. +-commutative 58.2%

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

   7. Simplified 58.2%

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

   8. Taylor expanded in z around -inf 70.1%

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

      1. associate-/l* 87.8%

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

      2. distribute-lft-out-- 87.8%

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

      3. associate--l+ 87.8%

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

      4. distribute-lft-out-- 87.8%

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

      5. mul-1-neg 87.8%

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

      6. associate-/l* 92.5%

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

      7. associate-/l* 97.4%

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

   10. Simplified 97.4%

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

   if 4.9999999999999998e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999984e-46

   1. Initial program 68.6%

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

      1. associate-*r/ 94.4%

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

      2. clear-num 94.2%

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

   4. Applied egg-rr 94.2%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-281}:\\ \;\;\;\;t + x \cdot \frac{y + \left(\left(a \cdot \frac{t}{x} - t \cdot \frac{y}{x}\right) - a\right)}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-45}:\\ \;\;\;\;x + \frac{-1}{\frac{a - z}{\left(y - z\right) \cdot \left(x - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 10^{-246}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-290) (not (<= t_1 1e-246)))
     t_1
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-290) || !(t_1 <= 1e-246)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-290)) .or. (.not. (t_1 <= 1d-246))) then
        tmp = t_1
    else
        tmp = t + (((t - x) * (a - y)) / z)
    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 + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-290) || !(t_1 <= 1e-246)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-290) or not (t_1 <= 1e-246):
		tmp = t_1
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	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))))
	tmp = 0.0
	if ((t_1 <= -2e-290) || !(t_1 <= 1e-246))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-290) || ~((t_1 <= 1e-246)))
		tmp = t_1;
	else
		tmp = t + (((t - x) * (a - y)) / z);
	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]}, If[Or[LessEqual[t$95$1, -2e-290], N[Not[LessEqual[t$95$1, 1e-246]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-290 or 9.99999999999999956e-247 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.6%

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

   if -2.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999956e-247

   1. Initial program 3.7%

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

      1. +-commutative 3.7%

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

      2. remove-double-neg 3.7%

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

      3. unsub-neg 3.7%

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

      4. *-commutative 3.7%

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

      5. associate-*l/ 12.4%

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

      6. associate-/l* 12.7%

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

      7. fma-neg 12.7%

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

      8. remove-double-neg 12.7%

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

   3. Simplified 12.7%

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

   5. Taylor expanded in z around inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-*r/ 70.0%

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

      3. associate-*r/ 70.0%

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

      4. mul-1-neg 70.0%

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

      5. div-sub 69.9%

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

      6. mul-1-neg 69.9%

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

      7. distribute-lft-out-- 69.9%

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

      8. associate-*r/ 69.9%

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

      9. mul-1-neg 69.9%

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

      10. unsub-neg 69.9%

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

      11. distribute-rgt-out-- 70.0%

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

   7. Simplified 70.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-290} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-246}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;t\_1 \leq 10^{-246}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-290)
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (if (<= t_1 1e-246) (+ t (/ (* (- t x) (- a y)) z)) 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 tmp;
	if (t_1 <= -2e-290) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (t_1 <= 1e-246) {
		tmp = t + (((t - x) * (a - y)) / 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 + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-2d-290)) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else if (t_1 <= 1d-246) then
        tmp = t + (((t - x) * (a - y)) / 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 + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-290) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (t_1 <= 1e-246) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -2e-290:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	elif t_1 <= 1e-246:
		tmp = t + (((t - x) * (a - y)) / z)
	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))))
	tmp = 0.0
	if (t_1 <= -2e-290)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	elseif (t_1 <= 1e-246)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	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)));
	tmp = 0.0;
	if (t_1 <= -2e-290)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	elseif (t_1 <= 1e-246)
		tmp = t + (((t - x) * (a - y)) / 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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-290], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-246], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-290

   1. Initial program 91.1%

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

      1. clear-num 91.0%

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

      2. un-div-inv 91.2%

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

   4. Applied egg-rr 91.2%

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

   if -2.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999956e-247

   1. Initial program 3.7%

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

      1. +-commutative 3.7%

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

      2. remove-double-neg 3.7%

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

      3. unsub-neg 3.7%

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

      4. *-commutative 3.7%

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

      5. associate-*l/ 12.4%

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

      6. associate-/l* 12.7%

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

      7. fma-neg 12.7%

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

      8. remove-double-neg 12.7%

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

   3. Simplified 12.7%

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

   5. Taylor expanded in z around inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-*r/ 70.0%

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

      3. associate-*r/ 70.0%

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

      4. mul-1-neg 70.0%

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

      5. div-sub 69.9%

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

      6. mul-1-neg 69.9%

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

      7. distribute-lft-out-- 69.9%

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

      8. associate-*r/ 69.9%

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

      9. mul-1-neg 69.9%

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

      10. unsub-neg 69.9%

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

      11. distribute-rgt-out-- 70.0%

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

   7. Simplified 70.0%

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

   if 9.99999999999999956e-247 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 87.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-246}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{-190} \lor \neg \left(t \leq 1.65 \cdot 10^{-131}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.08e-190) (not (<= t 1.65e-131)))
   (+ x (* t (/ (- y z) (- a z))))
   (* x (+ (/ (- y z) (- z a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.08e-190) || !(t <= 1.65e-131)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	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 ((t <= (-1.08d-190)) .or. (.not. (t <= 1.65d-131))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.08e-190) || !(t <= 1.65e-131)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.08e-190) or not (t <= 1.65e-131):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.08e-190) || !(t <= 1.65e-131))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.08e-190) || ~((t <= 1.65e-131)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = x * (((y - z) / (z - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.08e-190], N[Not[LessEqual[t, 1.65e-131]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.08e-190 or 1.6500000000000001e-131 < t

   1. Initial program 81.9%

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

   3. Taylor expanded in t around inf 58.4%

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

      1. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

   if -1.08e-190 < t < 1.6500000000000001e-131

   1. Initial program 56.1%

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

      1. +-commutative 56.1%

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

      2. remove-double-neg 56.1%

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

      3. unsub-neg 56.1%

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

      4. *-commutative 56.1%

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

      5. associate-*l/ 62.5%

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

      6. associate-/l* 65.5%

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

      7. fma-neg 65.5%

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

      8. remove-double-neg 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in t around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-rgt-identity 58.7%

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

      3. associate-/l* 61.7%

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

      4. distribute-rgt-neg-in 61.7%

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

      5. mul-1-neg 61.7%

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

      6. distribute-lft-in 61.7%

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

      7. mul-1-neg 61.7%

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

      8. unsub-neg 61.7%

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

   7. Simplified 61.7%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{-190} \lor \neg \left(t \leq 1.65 \cdot 10^{-131}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+151}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+21)
   (+ x (* t (/ (- y z) (- a z))))
   (if (<= z 1.1e+151)
     (+ x (* (- t x) (/ y (- a z))))
     (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+21) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (z <= 1.1e+151) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else {
		tmp = t / ((a - 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 <= (-5.5d+21)) then
        tmp = x + (t * ((y - z) / (a - z)))
    else if (z <= 1.1d+151) then
        tmp = x + ((t - x) * (y / (a - z)))
    else
        tmp = t / ((a - 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 <= -5.5e+21) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (z <= 1.1e+151) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+21:
		tmp = x + (t * ((y - z) / (a - z)))
	elif z <= 1.1e+151:
		tmp = x + ((t - x) * (y / (a - z)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+21)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	elseif (z <= 1.1e+151)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / Float64(a - z))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+21)
		tmp = x + (t * ((y - z) / (a - z)));
	elseif (z <= 1.1e+151)
		tmp = x + ((t - x) * (y / (a - z)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+21], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+151], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5e21

   1. Initial program 63.0%

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

   3. Taylor expanded in t around inf 37.4%

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

      1. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   if -5.5e21 < z < 1.10000000000000003e151

   1. Initial program 86.8%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. *-lft-identity 77.1%

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

      3. times-frac 83.3%

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

      4. /-rgt-identity 83.3%

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

   5. Simplified 83.3%

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

   if 1.10000000000000003e151 < z

   1. Initial program 53.1%

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

      1. +-commutative 53.1%

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

      2. remove-double-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. *-commutative 53.1%

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

      5. associate-*l/ 34.8%

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

      6. associate-/l* 62.7%

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

      7. fma-neg 62.7%

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

      8. remove-double-neg 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in x around -inf 43.6%

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

      1. associate-*r* 43.6%

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

      2. neg-mul-1 43.6%

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

      3. fma-define 43.6%

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

      4. times-frac 71.0%

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

      5. +-commutative 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in t around inf 78.9%

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

      1. associate--l+ 78.9%

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

      2. associate-*r/ 78.9%

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

      3. associate-*r* 78.9%

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

      4. mul-1-neg 78.9%

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

      5. div-sub 78.9%

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

   10. Simplified 78.9%

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

   11. Taylor expanded in t around inf 70.4%

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

       1. div-sub 70.4%

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

   13. Simplified 70.4%

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

       1. clear-num 70.4%

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

       2. un-div-inv 70.4%

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

   15. Applied egg-rr 70.4%

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

Alternative 9: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-64} \lor \neg \left(z \leq 1.9 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e-64) (not (<= z 1.9e+83)))
   (/ t (/ (- a z) (- y z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-64) || !(z <= 1.9e+83)) {
		tmp = t / ((a - z) / (y - 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 <= (-2.3d-64)) .or. (.not. (z <= 1.9d+83))) then
        tmp = t / ((a - z) / (y - 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 <= -2.3e-64) || !(z <= 1.9e+83)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e-64) or not (z <= 1.9e+83):
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e-64) || !(z <= 1.9e+83))
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - 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 <= -2.3e-64) || ~((z <= 1.9e+83)))
		tmp = t / ((a - z) / (y - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e-64], N[Not[LessEqual[z, 1.9e+83]], $MachinePrecision]], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - 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 < -2.3000000000000001e-64 or 1.9000000000000001e83 < z

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. remove-double-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. associate-*l/ 43.3%

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

      6. associate-/l* 68.2%

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

      7. fma-neg 68.2%

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

      8. remove-double-neg 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in x around -inf 51.8%

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

      1. associate-*r* 51.8%

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

      2. neg-mul-1 51.8%

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

      3. fma-define 51.8%

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

      4. times-frac 73.5%

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

      5. +-commutative 73.5%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in t around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. associate-*r/ 78.6%

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

      3. associate-*r* 78.6%

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

      4. mul-1-neg 78.6%

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

      5. div-sub 78.6%

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

   10. Simplified 78.6%

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

   11. Taylor expanded in t around inf 57.5%

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

       1. div-sub 57.5%

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

   13. Simplified 57.5%

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

       1. clear-num 57.5%

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

       2. un-div-inv 57.6%

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

   15. Applied egg-rr 57.6%

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

   if -2.3000000000000001e-64 < z < 1.9000000000000001e83

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 84.6%

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

      1. *-commutative 84.6%

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

      2. *-lft-identity 84.6%

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

      3. times-frac 89.1%

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

      4. /-rgt-identity 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in a around inf 78.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-64} \lor \neg \left(z \leq 1.9 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-69} \lor \neg \left(z \leq 2.35 \cdot 10^{+83}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e-69) (not (<= z 2.35e+83)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e-69) || !(z <= 2.35e+83)) {
		tmp = t * ((y - z) / (a - 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 <= (-1.8d-69)) .or. (.not. (z <= 2.35d+83))) then
        tmp = t * ((y - z) / (a - 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 <= -1.8e-69) || !(z <= 2.35e+83)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e-69) or not (z <= 2.35e+83):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e-69) || !(z <= 2.35e+83))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - 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 <= -1.8e-69) || ~((z <= 2.35e+83)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.8e-69], N[Not[LessEqual[z, 2.35e+83]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - 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 < -1.80000000000000009e-69 or 2.3499999999999999e83 < z

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. remove-double-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. associate-*l/ 43.3%

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

      6. associate-/l* 68.2%

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

      7. fma-neg 68.2%

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

      8. remove-double-neg 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in x around -inf 51.8%

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

      1. associate-*r* 51.8%

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

      2. neg-mul-1 51.8%

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

      3. fma-define 51.8%

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

      4. times-frac 73.5%

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

      5. +-commutative 73.5%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in t around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. associate-*r/ 78.6%

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

      3. associate-*r* 78.6%

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

      4. mul-1-neg 78.6%

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

      5. div-sub 78.6%

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

   10. Simplified 78.6%

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

   11. Taylor expanded in t around inf 57.5%

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

       1. div-sub 57.5%

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

   13. Simplified 57.5%

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

   if -1.80000000000000009e-69 < z < 2.3499999999999999e83

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 84.6%

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

      1. *-commutative 84.6%

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

      2. *-lft-identity 84.6%

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

      3. times-frac 89.1%

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

      4. /-rgt-identity 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in a around inf 78.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-69} \lor \neg \left(z \leq 2.35 \cdot 10^{+83}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-68} \lor \neg \left(z \leq 1.3 \cdot 10^{+83}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e-68) (not (<= z 1.3e+83)))
   (* t (/ (- y z) (- a z)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e-68) || !(z <= 1.3e+83)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / 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 <= (-5.8d-68)) .or. (.not. (z <= 1.3d+83))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y * ((t - x) / 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 <= -5.8e-68) || !(z <= 1.3e+83)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e-68) or not (z <= 1.3e+83):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e-68) || !(z <= 1.3e+83))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e-68) || ~((z <= 1.3e+83)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e-68], N[Not[LessEqual[z, 1.3e+83]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000001e-68 or 1.3000000000000001e83 < z

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. remove-double-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. associate-*l/ 43.3%

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

      6. associate-/l* 68.2%

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

      7. fma-neg 68.2%

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

      8. remove-double-neg 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in x around -inf 51.8%

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

      1. associate-*r* 51.8%

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

      2. neg-mul-1 51.8%

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

      3. fma-define 51.8%

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

      4. times-frac 73.5%

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

      5. +-commutative 73.5%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in t around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. associate-*r/ 78.6%

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

      3. associate-*r* 78.6%

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

      4. mul-1-neg 78.6%

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

      5. div-sub 78.6%

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

   10. Simplified 78.6%

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

   11. Taylor expanded in t around inf 57.5%

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

       1. div-sub 57.5%

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

   13. Simplified 57.5%

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

   if -5.8000000000000001e-68 < z < 1.3000000000000001e83

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 75.0%

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

      1. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-68} \lor \neg \left(z \leq 1.3 \cdot 10^{+83}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-58} \lor \neg \left(z \leq 1.02 \cdot 10^{+151}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.9e-58) (not (<= z 1.02e+151)))
   (* t (/ (- y z) (- a z)))
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.9e-58) || !(z <= 1.02e+151)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * (t / (a - 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 <= (-4.9d-58)) .or. (.not. (z <= 1.02d+151))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y * (t / (a - 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 <= -4.9e-58) || !(z <= 1.02e+151)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.9e-58) or not (z <= 1.02e+151):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.9e-58) || !(z <= 1.02e+151))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.9e-58) || ~((z <= 1.02e+151)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.9e-58], N[Not[LessEqual[z, 1.02e+151]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9000000000000003e-58 or 1.02000000000000002e151 < z

   1. Initial program 60.9%

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

      1. +-commutative 60.9%

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

      2. remove-double-neg 60.9%

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

      3. unsub-neg 60.9%

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

      4. *-commutative 60.9%

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

      5. associate-*l/ 42.2%

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

      6. associate-/l* 66.6%

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

      7. fma-neg 66.6%

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

      8. remove-double-neg 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in x around -inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. neg-mul-1 51.2%

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

      3. fma-define 51.2%

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

      4. times-frac 73.0%

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

      5. +-commutative 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in t around inf 79.2%

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

      1. associate--l+ 79.2%

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

      2. associate-*r/ 79.2%

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

      3. associate-*r* 79.2%

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

      4. mul-1-neg 79.2%

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

      5. div-sub 79.2%

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

   10. Simplified 79.2%

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

   11. Taylor expanded in t around inf 57.6%

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

       1. div-sub 57.6%

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

   13. Simplified 57.6%

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

   if -4.9000000000000003e-58 < z < 1.02000000000000002e151

   1. Initial program 89.1%

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

   3. Taylor expanded in t around inf 71.4%

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

   4. Taylor expanded in y around inf 66.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-58} \lor \neg \left(z \leq 1.02 \cdot 10^{+151}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-38} \lor \neg \left(t \leq 6.5 \cdot 10^{-125}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e-38) (not (<= t 6.5e-125)))
   (* t (/ (- y z) (- a z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e-38) || !(t <= 6.5e-125)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (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 ((t <= (-2.7d-38)) .or. (.not. (t <= 6.5d-125))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (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 ((t <= -2.7e-38) || !(t <= 6.5e-125)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e-38) or not (t <= 6.5e-125):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e-38) || !(t <= 6.5e-125))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.7e-38) || ~((t <= 6.5e-125)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e-38], N[Not[LessEqual[t, 6.5e-125]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000005e-38 or 6.4999999999999999e-125 < t

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. remove-double-neg 84.5%

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

      3. unsub-neg 84.5%

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

      4. *-commutative 84.5%

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

      5. associate-*l/ 64.4%

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

      6. associate-/l* 89.0%

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

      7. fma-neg 89.0%

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

      8. remove-double-neg 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around -inf 59.1%

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

      1. associate-*r* 59.1%

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

      2. neg-mul-1 59.1%

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

      3. fma-define 59.1%

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

      4. times-frac 80.2%

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

      5. +-commutative 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in t around inf 93.5%

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

      1. associate--l+ 93.5%

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

      2. associate-*r/ 93.5%

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

      3. associate-*r* 93.5%

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

      4. mul-1-neg 93.5%

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

      5. div-sub 93.5%

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

   10. Simplified 93.5%

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

   11. Taylor expanded in t around inf 69.4%

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

       1. div-sub 69.4%

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

   13. Simplified 69.4%

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

   if -2.70000000000000005e-38 < t < 6.4999999999999999e-125

   1. Initial program 63.0%

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

   3. Taylor expanded in z around 0 54.2%

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

      1. associate-/l* 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in x around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   8. Simplified 51.3%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-38} \lor \neg \left(t \leq 6.5 \cdot 10^{-125}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+90} \lor \neg \left(z \leq 1.02 \cdot 10^{+151}\right):\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+90) (not (<= z 1.02e+151)))
   (* t (/ z (- z a)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+90) || !(z <= 1.02e+151)) {
		tmp = t * (z / (z - a));
	} else {
		tmp = x * (1.0 - (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 <= (-1.2d+90)) .or. (.not. (z <= 1.02d+151))) then
        tmp = t * (z / (z - a))
    else
        tmp = x * (1.0d0 - (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 <= -1.2e+90) || !(z <= 1.02e+151)) {
		tmp = t * (z / (z - a));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+90) or not (z <= 1.02e+151):
		tmp = t * (z / (z - a))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+90) || !(z <= 1.02e+151))
		tmp = Float64(t * Float64(z / Float64(z - a)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+90) || ~((z <= 1.02e+151)))
		tmp = t * (z / (z - a));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+90], N[Not[LessEqual[z, 1.02e+151]], $MachinePrecision]], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000005e90 or 1.02000000000000002e151 < z

   1. Initial program 56.8%

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

      1. +-commutative 56.8%

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

      2. remove-double-neg 56.8%

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

      3. unsub-neg 56.8%

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

      4. *-commutative 56.8%

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

      5. associate-*l/ 37.0%

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

      6. associate-/l* 64.0%

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

      7. fma-neg 64.0%

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

      8. remove-double-neg 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in x around -inf 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. associate-*r* 47.9%

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

      2. neg-mul-1 47.9%

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

      3. fma-define 47.9%

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

      4. times-frac 72.7%

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

      5. +-commutative 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. associate-*r/ 79.5%

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

      3. associate-*r* 79.5%

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

      4. mul-1-neg 79.5%

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

      5. div-sub 79.5%

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

   10. Simplified 79.5%

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

   11. Taylor expanded in t around inf 60.8%

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

       1. div-sub 60.8%

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

   13. Simplified 60.8%

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

   14. Taylor expanded in y around 0 57.8%

       \[\leadsto t \cdot \frac{\color{blue}{-1 \cdot z}}{a - z} \]
   15. Step-by-step derivation

       1. neg-mul-1 57.8%

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

   16. Simplified 57.8%

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

   if -1.20000000000000005e90 < z < 1.02000000000000002e151

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 62.7%

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

      1. associate-/l* 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in x around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

   8. Simplified 53.9%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+90} \lor \neg \left(z \leq 1.02 \cdot 10^{+151}\right):\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+89) t (if (<= z 1.02e+151) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+89) {
		tmp = t;
	} else if (z <= 1.02e+151) {
		tmp = x * (1.0 - (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 <= (-3.6d+89)) then
        tmp = t
    else if (z <= 1.02d+151) then
        tmp = x * (1.0d0 - (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 <= -3.6e+89) {
		tmp = t;
	} else if (z <= 1.02e+151) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+89:
		tmp = t
	elif z <= 1.02e+151:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+89)
		tmp = t;
	elseif (z <= 1.02e+151)
		tmp = Float64(x * Float64(1.0 - 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 <= -3.6e+89)
		tmp = t;
	elseif (z <= 1.02e+151)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+89], t, If[LessEqual[z, 1.02e+151], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e89 or 1.02000000000000002e151 < z

   1. Initial program 56.8%

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

      1. +-commutative 56.8%

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

      2. remove-double-neg 56.8%

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

      3. unsub-neg 56.8%

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

      4. *-commutative 56.8%

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

      5. associate-*l/ 37.0%

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

      6. associate-/l* 64.0%

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

      7. fma-neg 64.0%

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

      8. remove-double-neg 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in x around -inf 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. associate-*r* 47.9%

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

      2. neg-mul-1 47.9%

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

      3. fma-define 47.9%

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

      4. times-frac 72.7%

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

      5. +-commutative 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in z around inf 48.9%

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

   if -3.6e89 < z < 1.02000000000000002e151

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 62.7%

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

      1. associate-/l* 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in x around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

   8. Simplified 53.9%

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

Alternative 16: 39.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+75)
   t
   (if (<= z -6.5e+15) (* t (/ (- y z) a)) (if (<= z 1.95e+83) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+75) {
		tmp = t;
	} else if (z <= -6.5e+15) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.95e+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 <= (-3.8d+75)) then
        tmp = t
    else if (z <= (-6.5d+15)) then
        tmp = t * ((y - z) / a)
    else if (z <= 1.95d+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 <= -3.8e+75) {
		tmp = t;
	} else if (z <= -6.5e+15) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.95e+83) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+75:
		tmp = t
	elif z <= -6.5e+15:
		tmp = t * ((y - z) / a)
	elif z <= 1.95e+83:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+75)
		tmp = t;
	elseif (z <= -6.5e+15)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 1.95e+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 <= -3.8e+75)
		tmp = t;
	elseif (z <= -6.5e+15)
		tmp = t * ((y - z) / a);
	elseif (z <= 1.95e+83)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+75], t, If[LessEqual[z, -6.5e+15], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+83], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e75 or 1.9500000000000001e83 < z

   1. Initial program 59.9%

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

      1. +-commutative 59.9%

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

      2. remove-double-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

      5. associate-*l/ 39.3%

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

      6. associate-/l* 66.3%

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

      7. fma-neg 66.3%

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

      8. remove-double-neg 66.3%

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

   3. Simplified 66.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   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. associate-*r* 49.0%

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

      2. neg-mul-1 49.0%

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

      3. fma-define 49.0%

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

      4. times-frac 74.0%

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

      5. +-commutative 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in z around inf 44.7%

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

   if -3.8000000000000002e75 < z < -6.5e15

   1. Initial program 72.0%

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

      1. +-commutative 72.0%

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

      2. remove-double-neg 72.0%

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

      3. unsub-neg 72.0%

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

      4. *-commutative 72.0%

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

      5. associate-*l/ 41.5%

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

      6. associate-/l* 76.9%

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

      7. fma-neg 76.9%

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

      8. remove-double-neg 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in x around -inf 36.2%

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

      1. associate-*r* 36.2%

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

      2. neg-mul-1 36.2%

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

      3. fma-define 36.2%

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

      4. times-frac 58.9%

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

      5. +-commutative 58.9%

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

   7. Simplified 58.9%

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

   8. Taylor expanded in t around inf 86.1%

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

      1. associate--l+ 86.1%

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

      2. associate-*r/ 86.1%

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

      3. associate-*r* 86.1%

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

      4. mul-1-neg 86.1%

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

      5. div-sub 86.1%

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

   10. Simplified 86.1%

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

   11. Taylor expanded in t around inf 63.0%

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

       1. div-sub 63.0%

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

   13. Simplified 63.0%

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

   14. Taylor expanded in a around inf 25.1%

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

       1. associate-/l* 43.1%

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

   16. Simplified 43.1%

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

   if -6.5e15 < z < 1.9500000000000001e83

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. remove-double-neg 86.5%

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

      3. unsub-neg 86.5%

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

      4. *-commutative 86.5%

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

      5. associate-*l/ 86.6%

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

      6. associate-/l* 90.6%

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

      7. fma-neg 90.5%

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

      8. remove-double-neg 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in a around inf 37.3%

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

Alternative 17: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-57}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e-57) t (if (<= z 2e+83) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e-57) {
		tmp = t;
	} else if (z <= 2e+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 <= (-3.8d-57)) then
        tmp = t
    else if (z <= 2d+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 <= -3.8e-57) {
		tmp = t;
	} else if (z <= 2e+83) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e-57:
		tmp = t
	elif z <= 2e+83:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e-57)
		tmp = t;
	elseif (z <= 2e+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 <= -3.8e-57)
		tmp = t;
	elseif (z <= 2e+83)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e-57], t, If[LessEqual[z, 2e+83], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999997e-57 or 2.00000000000000006e83 < z

   1. Initial program 61.8%

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

      1. +-commutative 61.8%

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

      2. remove-double-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. *-commutative 61.8%

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

      5. associate-*l/ 41.6%

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

      6. associate-/l* 67.3%

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

      7. fma-neg 67.2%

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

      8. remove-double-neg 67.2%

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

   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. associate-*r* 50.3%

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

      2. neg-mul-1 50.3%

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

      3. fma-define 50.3%

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

      4. times-frac 72.7%

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

      5. +-commutative 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in z around inf 38.7%

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

   if -3.7999999999999997e-57 < z < 2.00000000000000006e83

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. remove-double-neg 89.4%

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

      3. unsub-neg 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-*l/ 89.4%

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

      6. associate-/l* 93.8%

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

      7. fma-neg 93.8%

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

      8. remove-double-neg 93.8%

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

   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 18: 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 75.5%

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

   1. +-commutative 75.5%

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

   2. remove-double-neg 75.5%

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

   3. unsub-neg 75.5%

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

   4. *-commutative 75.5%

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

   5. associate-*l/ 65.3%

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

   6. associate-/l* 80.4%

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

   7. fma-neg 80.4%

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

   8. remove-double-neg 80.4%

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

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. associate-*r* 67.0%

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

   2. neg-mul-1 67.0%

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

   3. fma-define 67.0%

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

   4. times-frac 79.8%

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

   5. +-commutative 79.8%

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

7. Simplified 79.8%

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

8. Taylor expanded in z around inf 23.5%

   \[\leadsto \color{blue}{t} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024132 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))