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

Percentage Accurate: 67.5% → 89.8%

Time: 18.2s

Alternatives: 25

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-240}:\\ \;\;\;\;\mathsf{fma}\left(t_1, t - x, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z))) (t_2 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_2 -2e-240)
     (fma t_1 (- t x) x)
     (if (<= t_2 0.0) (+ t (/ (* x (- y a)) z)) (+ x (* (- t x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -2e-240) {
		tmp = fma(t_1, (t - x), x);
	} else if (t_2 <= 0.0) {
		tmp = t + ((x * (y - a)) / z);
	} else {
		tmp = x + ((t - x) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(a - z))
	t_2 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -2e-240)
		tmp = fma(t_1, Float64(t - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-240], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.9999999999999999e-240

   1. Initial program 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-*l/ 91.5%

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

      3. fma-def 91.5%

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

   3. Simplified 91.5%

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

   if -1.9999999999999999e-240 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 6.0%

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

      1. +-commutative 6.0%

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

      2. associate-*l/ 6.2%

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

      3. fma-def 6.2%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in z around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 92.4%

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

      3. distribute-lft-out-- 92.4%

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

      4. mul-1-neg 92.4%

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

      5. distribute-neg-frac 92.4%

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

      6. associate-/l* 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. unsub-neg 99.8%

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

      10. distribute-rgt-out-- 99.8%

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

      11. *-commutative 99.8%

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

      12. associate-/l* 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. neg-mul-1 99.8%

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

   9. Simplified 99.8%

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

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

   1. Initial program 77.4%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -2 \cdot 10^{-240}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 2: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-240} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -2e-240) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (* x (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-240) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x * (y - 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) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if ((t_1 <= (-2d-240)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + ((x * (y - a)) / 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) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-240) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if (t_1 <= -2e-240) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + ((x * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -2e-240) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -2e-240) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + ((x * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-240], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.9999999999999999e-240 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 78.3%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   if -1.9999999999999999e-240 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 6.0%

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

      1. +-commutative 6.0%

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

      2. associate-*l/ 6.2%

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

      3. fma-def 6.2%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in z around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 92.4%

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

      3. distribute-lft-out-- 92.4%

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

      4. mul-1-neg 92.4%

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

      5. distribute-neg-frac 92.4%

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

      6. associate-/l* 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. unsub-neg 99.8%

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

      10. distribute-rgt-out-- 99.8%

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

      11. *-commutative 99.8%

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

      12. associate-/l* 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. neg-mul-1 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -2 \cdot 10^{-240} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \]

Alternative 3: 57.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.42 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-117}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-259}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-190}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.42e-43)
     t_2
     (if (<= t -1.7e-116)
       t_1
       (if (<= t -4.8e-117)
         t
         (if (<= t -2.5e-259)
           (* (- t x) (/ y (- a z)))
           (if (<= t 5.5e-237)
             t_1
             (if (<= t 6.5e-190)
               (/ (* x (- y a)) z)
               (if (<= t 2.35e+36) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.42e-43) {
		tmp = t_2;
	} else if (t <= -1.7e-116) {
		tmp = t_1;
	} else if (t <= -4.8e-117) {
		tmp = t;
	} else if (t <= -2.5e-259) {
		tmp = (t - x) * (y / (a - z));
	} else if (t <= 5.5e-237) {
		tmp = t_1;
	} else if (t <= 6.5e-190) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 2.35e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-1.42d-43)) then
        tmp = t_2
    else if (t <= (-1.7d-116)) then
        tmp = t_1
    else if (t <= (-4.8d-117)) then
        tmp = t
    else if (t <= (-2.5d-259)) then
        tmp = (t - x) * (y / (a - z))
    else if (t <= 5.5d-237) then
        tmp = t_1
    else if (t <= 6.5d-190) then
        tmp = (x * (y - a)) / z
    else if (t <= 2.35d+36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.42e-43) {
		tmp = t_2;
	} else if (t <= -1.7e-116) {
		tmp = t_1;
	} else if (t <= -4.8e-117) {
		tmp = t;
	} else if (t <= -2.5e-259) {
		tmp = (t - x) * (y / (a - z));
	} else if (t <= 5.5e-237) {
		tmp = t_1;
	} else if (t <= 6.5e-190) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 2.35e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.42e-43:
		tmp = t_2
	elif t <= -1.7e-116:
		tmp = t_1
	elif t <= -4.8e-117:
		tmp = t
	elif t <= -2.5e-259:
		tmp = (t - x) * (y / (a - z))
	elif t <= 5.5e-237:
		tmp = t_1
	elif t <= 6.5e-190:
		tmp = (x * (y - a)) / z
	elif t <= 2.35e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.42e-43)
		tmp = t_2;
	elseif (t <= -1.7e-116)
		tmp = t_1;
	elseif (t <= -4.8e-117)
		tmp = t;
	elseif (t <= -2.5e-259)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (t <= 5.5e-237)
		tmp = t_1;
	elseif (t <= 6.5e-190)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (t <= 2.35e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.42e-43)
		tmp = t_2;
	elseif (t <= -1.7e-116)
		tmp = t_1;
	elseif (t <= -4.8e-117)
		tmp = t;
	elseif (t <= -2.5e-259)
		tmp = (t - x) * (y / (a - z));
	elseif (t <= 5.5e-237)
		tmp = t_1;
	elseif (t <= 6.5e-190)
		tmp = (x * (y - a)) / z;
	elseif (t <= 2.35e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.42e-43], t$95$2, If[LessEqual[t, -1.7e-116], t$95$1, If[LessEqual[t, -4.8e-117], t, If[LessEqual[t, -2.5e-259], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-237], t$95$1, If[LessEqual[t, 6.5e-190], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 2.35e+36], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.41999999999999993e-43 or 2.34999999999999994e36 < t

   1. Initial program 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-*l/ 94.6%

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

      3. fma-def 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 77.0%

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

      1. div-sub 77.0%

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

   6. Simplified 77.0%

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

   if -1.41999999999999993e-43 < t < -1.69999999999999996e-116 or -2.49999999999999989e-259 < t < 5.49999999999999981e-237 or 6.4999999999999997e-190 < t < 2.34999999999999994e36

   1. Initial program 79.2%

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

      1. +-commutative 79.2%

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

      2. associate-*l/ 89.5%

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

      3. fma-def 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in t around 0 56.0%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 56.0%

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

      2. associate-*l/ 62.1%

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

      3. *-commutative 62.1%

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

      4. distribute-rgt-neg-in 62.1%

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

   9. Simplified 62.1%

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

   10. Taylor expanded in x around 0 62.1%

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

       1. mul-1-neg 62.1%

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

       2. sub-neg 62.1%

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

       3. *-commutative 62.1%

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

   12. Simplified 62.1%

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

   if -1.69999999999999996e-116 < t < -4.80000000000000028e-117

   1. Initial program 4.2%

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

      1. +-commutative 4.2%

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

      2. associate-*l/ 4.2%

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

      3. fma-def 4.2%

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

   3. Simplified 4.2%

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

   4. Taylor expanded in z around inf 100.0%

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

   if -4.80000000000000028e-117 < t < -2.49999999999999989e-259

   1. Initial program 59.5%

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

      1. +-commutative 59.5%

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

      2. associate-*l/ 64.3%

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

      3. fma-def 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in y around -inf 49.0%

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

      1. expm1-log1p-u 44.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a - z}\right)\right)} \]

      2. expm1-udef 24.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a - z}\right)} - 1} \]

   6. Applied egg-rr 24.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a - z}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 44.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - x\right)}{a - z}\right)\right)} \]

      2. expm1-log1p 49.0%

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

      3. *-commutative 49.0%

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

      4. associate-*r/ 56.6%

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

   8. Simplified 56.6%

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

   if 5.49999999999999981e-237 < t < 6.4999999999999997e-190

   1. Initial program 51.2%

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

      1. +-commutative 51.2%

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

      2. associate-*l/ 51.5%

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

      3. fma-def 51.5%

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

   3. Simplified 51.5%

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

   4. Taylor expanded in z around inf 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-/l* 57.0%

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

      3. distribute-lft-out-- 57.0%

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

      4. mul-1-neg 57.0%

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

      5. distribute-neg-frac 57.0%

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

      6. associate-/l* 78.2%

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

      7. *-commutative 78.2%

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

      8. distribute-rgt-out-- 78.2%

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

      9. unsub-neg 78.2%

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

      10. distribute-rgt-out-- 78.2%

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

      11. *-commutative 78.2%

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

      12. associate-/l* 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in t around 0 66.8%

      \[\leadsto \color{blue}{\frac{\left(y - a\right) \cdot x}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-117}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-259}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-190}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 4: 70.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{a - y}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+67}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.027:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-33} \lor \neg \left(z \leq 2.4 \cdot 10^{-22}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t)))))
   (if (<= z -4.5e+134)
     (+ t (/ (- a y) (- (/ z x))))
     (if (<= z -3.6e+67)
       (- x (* (- y z) (/ t z)))
       (if (<= z -1.9e+14)
         t_1
         (if (<= z -0.027)
           (- x (/ (- z y) (/ a t)))
           (if (or (<= z -1.8e-33) (not (<= z 2.4e-22)))
             t_1
             (- x (/ (- z y) (/ a (- t x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -4.5e+134) {
		tmp = t + ((a - y) / -(z / x));
	} else if (z <= -3.6e+67) {
		tmp = x - ((y - z) * (t / z));
	} else if (z <= -1.9e+14) {
		tmp = t_1;
	} else if (z <= -0.027) {
		tmp = x - ((z - y) / (a / t));
	} else if ((z <= -1.8e-33) || !(z <= 2.4e-22)) {
		tmp = t_1;
	} else {
		tmp = x - ((z - y) / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    if (z <= (-4.5d+134)) then
        tmp = t + ((a - y) / -(z / x))
    else if (z <= (-3.6d+67)) then
        tmp = x - ((y - z) * (t / z))
    else if (z <= (-1.9d+14)) then
        tmp = t_1
    else if (z <= (-0.027d0)) then
        tmp = x - ((z - y) / (a / t))
    else if ((z <= (-1.8d-33)) .or. (.not. (z <= 2.4d-22))) then
        tmp = t_1
    else
        tmp = x - ((z - y) / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -4.5e+134) {
		tmp = t + ((a - y) / -(z / x));
	} else if (z <= -3.6e+67) {
		tmp = x - ((y - z) * (t / z));
	} else if (z <= -1.9e+14) {
		tmp = t_1;
	} else if (z <= -0.027) {
		tmp = x - ((z - y) / (a / t));
	} else if ((z <= -1.8e-33) || !(z <= 2.4e-22)) {
		tmp = t_1;
	} else {
		tmp = x - ((z - y) / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	tmp = 0
	if z <= -4.5e+134:
		tmp = t + ((a - y) / -(z / x))
	elif z <= -3.6e+67:
		tmp = x - ((y - z) * (t / z))
	elif z <= -1.9e+14:
		tmp = t_1
	elif z <= -0.027:
		tmp = x - ((z - y) / (a / t))
	elif (z <= -1.8e-33) or not (z <= 2.4e-22):
		tmp = t_1
	else:
		tmp = x - ((z - y) / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -4.5e+134)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(-Float64(z / x))));
	elseif (z <= -3.6e+67)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(t / z)));
	elseif (z <= -1.9e+14)
		tmp = t_1;
	elseif (z <= -0.027)
		tmp = Float64(x - Float64(Float64(z - y) / Float64(a / t)));
	elseif ((z <= -1.8e-33) || !(z <= 2.4e-22))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z - y) / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y / z) * (x - t));
	tmp = 0.0;
	if (z <= -4.5e+134)
		tmp = t + ((a - y) / -(z / x));
	elseif (z <= -3.6e+67)
		tmp = x - ((y - z) * (t / z));
	elseif (z <= -1.9e+14)
		tmp = t_1;
	elseif (z <= -0.027)
		tmp = x - ((z - y) / (a / t));
	elseif ((z <= -1.8e-33) || ~((z <= 2.4e-22)))
		tmp = t_1;
	else
		tmp = x - ((z - y) / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+134], N[(t + N[(N[(a - y), $MachinePrecision] / (-N[(z / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e+67], N[(x - N[(N[(y - z), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e+14], t$95$1, If[LessEqual[z, -0.027], N[(x - N[(N[(z - y), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.8e-33], N[Not[LessEqual[z, 2.4e-22]], $MachinePrecision]], t$95$1, N[(x - N[(N[(z - y), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.4999999999999997e134

   1. Initial program 24.8%

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

      1. +-commutative 24.8%

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

      2. associate-*l/ 60.0%

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

      3. fma-def 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in z around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-/l* 86.3%

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

      3. distribute-lft-out-- 86.3%

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

      4. mul-1-neg 86.3%

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

      5. distribute-neg-frac 86.3%

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

      6. associate-/l* 72.8%

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

      7. *-commutative 72.8%

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

      8. distribute-rgt-out-- 72.5%

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

      9. unsub-neg 72.5%

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

      10. distribute-rgt-out-- 72.8%

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

      11. *-commutative 72.8%

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

      12. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in t around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-neg-frac 85.9%

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

   9. Simplified 85.9%

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

   if -4.4999999999999997e134 < z < -3.5999999999999999e67

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-*l/ 93.9%

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

      3. fma-def 93.9%

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

   3. Simplified 93.9%

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

      1. fma-udef 93.9%

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

      2. associate-*l/ 75.5%

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

      3. associate-*r/ 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in t around inf 83.0%

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

   7. Taylor expanded in a around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

   9. Simplified 77.1%

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

   if -3.5999999999999999e67 < z < -1.9e14 or -0.0269999999999999997 < z < -1.80000000000000017e-33 or 2.40000000000000002e-22 < z

   1. Initial program 65.1%

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

      1. +-commutative 65.1%

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

      2. associate-*l/ 83.5%

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

      3. fma-def 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in z around inf 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 73.3%

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

      3. distribute-lft-out-- 73.3%

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

      4. mul-1-neg 73.3%

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

      5. distribute-neg-frac 73.3%

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

      6. associate-/l* 68.4%

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

      7. *-commutative 68.4%

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

      8. distribute-rgt-out-- 68.3%

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

      9. unsub-neg 68.3%

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

      10. distribute-rgt-out-- 68.4%

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

      11. *-commutative 68.4%

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

      12. associate-/l* 73.3%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in y around inf 68.7%

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

      1. associate-*l/ 74.4%

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

   9. Simplified 74.4%

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

   if -1.9e14 < z < -0.0269999999999999997

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 96.3%

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

      1. +-commutative 96.3%

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

      2. associate-/l* 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in t around inf 96.3%

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

   if -1.80000000000000017e-33 < z < 2.40000000000000002e-22

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-*l/ 96.0%

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

      3. fma-def 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in a around inf 77.2%

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

      1. +-commutative 77.2%

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

      2. associate-/l* 80.6%

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

   6. Simplified 80.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a}{t - x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{a - y}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+67}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+14}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -0.027:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-33} \lor \neg \left(z \leq 2.4 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 5: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{a - y}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+65}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-33} \lor \neg \left(z \leq 2.8 \cdot 10^{-22}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t)))))
   (if (<= z -2.2e+134)
     (+ t (/ (- a y) (- (/ z x))))
     (if (<= z -4e+65)
       (- x (* (- y z) (/ t z)))
       (if (<= z -8e+16)
         t_1
         (if (<= z -5.5e-8)
           (- x (/ (- z y) (/ a t)))
           (if (or (<= z -4.5e-33) (not (<= z 2.8e-22)))
             t_1
             (+ x (* (- t x) (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -2.2e+134) {
		tmp = t + ((a - y) / -(z / x));
	} else if (z <= -4e+65) {
		tmp = x - ((y - z) * (t / z));
	} else if (z <= -8e+16) {
		tmp = t_1;
	} else if (z <= -5.5e-8) {
		tmp = x - ((z - y) / (a / t));
	} else if ((z <= -4.5e-33) || !(z <= 2.8e-22)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    if (z <= (-2.2d+134)) then
        tmp = t + ((a - y) / -(z / x))
    else if (z <= (-4d+65)) then
        tmp = x - ((y - z) * (t / z))
    else if (z <= (-8d+16)) then
        tmp = t_1
    else if (z <= (-5.5d-8)) then
        tmp = x - ((z - y) / (a / t))
    else if ((z <= (-4.5d-33)) .or. (.not. (z <= 2.8d-22))) then
        tmp = t_1
    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 t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -2.2e+134) {
		tmp = t + ((a - y) / -(z / x));
	} else if (z <= -4e+65) {
		tmp = x - ((y - z) * (t / z));
	} else if (z <= -8e+16) {
		tmp = t_1;
	} else if (z <= -5.5e-8) {
		tmp = x - ((z - y) / (a / t));
	} else if ((z <= -4.5e-33) || !(z <= 2.8e-22)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	tmp = 0
	if z <= -2.2e+134:
		tmp = t + ((a - y) / -(z / x))
	elif z <= -4e+65:
		tmp = x - ((y - z) * (t / z))
	elif z <= -8e+16:
		tmp = t_1
	elif z <= -5.5e-8:
		tmp = x - ((z - y) / (a / t))
	elif (z <= -4.5e-33) or not (z <= 2.8e-22):
		tmp = t_1
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -2.2e+134)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(-Float64(z / x))));
	elseif (z <= -4e+65)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(t / z)));
	elseif (z <= -8e+16)
		tmp = t_1;
	elseif (z <= -5.5e-8)
		tmp = Float64(x - Float64(Float64(z - y) / Float64(a / t)));
	elseif ((z <= -4.5e-33) || !(z <= 2.8e-22))
		tmp = t_1;
	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)
	t_1 = t + ((y / z) * (x - t));
	tmp = 0.0;
	if (z <= -2.2e+134)
		tmp = t + ((a - y) / -(z / x));
	elseif (z <= -4e+65)
		tmp = x - ((y - z) * (t / z));
	elseif (z <= -8e+16)
		tmp = t_1;
	elseif (z <= -5.5e-8)
		tmp = x - ((z - y) / (a / t));
	elseif ((z <= -4.5e-33) || ~((z <= 2.8e-22)))
		tmp = t_1;
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+134], N[(t + N[(N[(a - y), $MachinePrecision] / (-N[(z / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e+65], N[(x - N[(N[(y - z), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e+16], t$95$1, If[LessEqual[z, -5.5e-8], N[(x - N[(N[(z - y), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.5e-33], N[Not[LessEqual[z, 2.8e-22]], $MachinePrecision]], t$95$1, N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2e134

   1. Initial program 24.8%

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

      1. +-commutative 24.8%

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

      2. associate-*l/ 60.0%

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

      3. fma-def 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in z around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-/l* 86.3%

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

      3. distribute-lft-out-- 86.3%

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

      4. mul-1-neg 86.3%

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

      5. distribute-neg-frac 86.3%

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

      6. associate-/l* 72.8%

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

      7. *-commutative 72.8%

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

      8. distribute-rgt-out-- 72.5%

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

      9. unsub-neg 72.5%

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

      10. distribute-rgt-out-- 72.8%

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

      11. *-commutative 72.8%

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

      12. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in t around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-neg-frac 85.9%

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

   9. Simplified 85.9%

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

   if -2.2e134 < z < -4e65

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-*l/ 93.9%

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

      3. fma-def 93.9%

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

   3. Simplified 93.9%

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

      1. fma-udef 93.9%

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

      2. associate-*l/ 75.5%

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

      3. associate-*r/ 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in t around inf 83.0%

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

   7. Taylor expanded in a around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

   9. Simplified 77.1%

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

   if -4e65 < z < -8e16 or -5.5000000000000003e-8 < z < -4.49999999999999991e-33 or 2.79999999999999995e-22 < z

   1. Initial program 65.1%

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

      1. +-commutative 65.1%

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

      2. associate-*l/ 83.5%

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

      3. fma-def 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in z around inf 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 73.3%

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

      3. distribute-lft-out-- 73.3%

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

      4. mul-1-neg 73.3%

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

      5. distribute-neg-frac 73.3%

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

      6. associate-/l* 68.4%

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

      7. *-commutative 68.4%

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

      8. distribute-rgt-out-- 68.3%

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

      9. unsub-neg 68.3%

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

      10. distribute-rgt-out-- 68.4%

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

      11. *-commutative 68.4%

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

      12. associate-/l* 73.3%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in y around inf 68.7%

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

      1. associate-*l/ 74.4%

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

   9. Simplified 74.4%

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

   if -8e16 < z < -5.5000000000000003e-8

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 96.3%

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

      1. +-commutative 96.3%

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

      2. associate-/l* 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in t around inf 96.3%

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

   if -4.49999999999999991e-33 < z < 2.79999999999999995e-22

   1. Initial program 90.7%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around 0 79.0%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{a - y}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+65}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+16}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-33} \lor \neg \left(z \leq 2.8 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 57.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;x \leq -30500:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 2.7:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+95}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -1.4e+156)
     t_2
     (if (<= x -1.3e+39)
       (/ (- y) (/ z (- t x)))
       (if (<= x -30500.0)
         (+ x (* t (/ y a)))
         (if (<= x 2.7)
           t_1
           (if (<= x 1.8e+95) (+ x t) (if (<= x 4e+100) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.4e+156) {
		tmp = t_2;
	} else if (x <= -1.3e+39) {
		tmp = -y / (z / (t - x));
	} else if (x <= -30500.0) {
		tmp = x + (t * (y / a));
	} else if (x <= 2.7) {
		tmp = t_1;
	} else if (x <= 1.8e+95) {
		tmp = x + t;
	} else if (x <= 4e+100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-1.4d+156)) then
        tmp = t_2
    else if (x <= (-1.3d+39)) then
        tmp = -y / (z / (t - x))
    else if (x <= (-30500.0d0)) then
        tmp = x + (t * (y / a))
    else if (x <= 2.7d0) then
        tmp = t_1
    else if (x <= 1.8d+95) then
        tmp = x + t
    else if (x <= 4d+100) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.4e+156) {
		tmp = t_2;
	} else if (x <= -1.3e+39) {
		tmp = -y / (z / (t - x));
	} else if (x <= -30500.0) {
		tmp = x + (t * (y / a));
	} else if (x <= 2.7) {
		tmp = t_1;
	} else if (x <= 1.8e+95) {
		tmp = x + t;
	} else if (x <= 4e+100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -1.4e+156:
		tmp = t_2
	elif x <= -1.3e+39:
		tmp = -y / (z / (t - x))
	elif x <= -30500.0:
		tmp = x + (t * (y / a))
	elif x <= 2.7:
		tmp = t_1
	elif x <= 1.8e+95:
		tmp = x + t
	elif x <= 4e+100:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -1.4e+156)
		tmp = t_2;
	elseif (x <= -1.3e+39)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (x <= -30500.0)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (x <= 2.7)
		tmp = t_1;
	elseif (x <= 1.8e+95)
		tmp = Float64(x + t);
	elseif (x <= 4e+100)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -1.4e+156)
		tmp = t_2;
	elseif (x <= -1.3e+39)
		tmp = -y / (z / (t - x));
	elseif (x <= -30500.0)
		tmp = x + (t * (y / a));
	elseif (x <= 2.7)
		tmp = t_1;
	elseif (x <= 1.8e+95)
		tmp = x + t;
	elseif (x <= 4e+100)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+156], t$95$2, If[LessEqual[x, -1.3e+39], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -30500.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7], t$95$1, If[LessEqual[x, 1.8e+95], N[(x + t), $MachinePrecision], If[LessEqual[x, 4e+100], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.39999999999999994e156 or 4.00000000000000006e100 < x

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. associate-*l/ 84.5%

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

      3. fma-def 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in z around 0 51.7%

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

      1. +-commutative 51.7%

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

      2. associate-/l* 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in t around 0 51.7%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 51.7%

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

      2. associate-*l/ 61.6%

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

      3. *-commutative 61.6%

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

      4. distribute-rgt-neg-in 61.6%

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

   9. Simplified 61.6%

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

   10. Taylor expanded in x around 0 61.6%

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

       1. mul-1-neg 61.6%

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

       2. sub-neg 61.6%

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

       3. *-commutative 61.6%

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

   12. Simplified 61.6%

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

   if -1.39999999999999994e156 < x < -1.3e39

   1. Initial program 39.8%

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

      1. +-commutative 39.8%

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

      2. associate-*l/ 70.6%

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

      3. fma-def 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in y around -inf 47.1%

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

   5. Taylor expanded in a around 0 42.8%

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

      1. mul-1-neg 42.8%

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

      2. associate-/l* 51.5%

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

      3. distribute-neg-frac 51.5%

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

   7. Simplified 51.5%

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

   if -1.3e39 < x < -30500

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. associate-/l* 69.5%

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

   6. Simplified 69.5%

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

   7. Taylor expanded in t around inf 69.5%

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

      1. associate-*l/ 69.5%

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

      2. *-commutative 69.5%

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

   9. Simplified 69.5%

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

   if -30500 < x < 2.7000000000000002 or 1.79999999999999989e95 < x < 4.00000000000000006e100

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-*l/ 89.9%

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

      3. fma-def 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in t around inf 70.9%

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

      1. div-sub 71.0%

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

   6. Simplified 71.0%

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

   if 2.7000000000000002 < x < 1.79999999999999989e95

   1. Initial program 67.2%

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

      1. +-commutative 67.2%

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

      2. associate-*l/ 85.5%

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

      3. fma-def 85.5%

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

   3. Simplified 85.5%

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

      1. fma-udef 85.5%

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

      2. associate-*l/ 67.2%

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

      3. associate-*r/ 76.5%

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

   5. Applied egg-rr 76.5%

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

   6. Taylor expanded in t around inf 65.1%

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

   7. Taylor expanded in z around inf 69.5%

      \[\leadsto \color{blue}{t} + x \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;x \leq -30500:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 2.7:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+95}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 7: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -45000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 230:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+93}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -7.5e+164)
     t_2
     (if (<= x -8.5e+36)
       (* y (/ (- t x) (- a z)))
       (if (<= x -45000.0)
         (+ x (* t (/ y a)))
         (if (<= x 230.0)
           t_1
           (if (<= x 5.3e+93) (+ x t) (if (<= x 4.5e+101) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -7.5e+164) {
		tmp = t_2;
	} else if (x <= -8.5e+36) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= -45000.0) {
		tmp = x + (t * (y / a));
	} else if (x <= 230.0) {
		tmp = t_1;
	} else if (x <= 5.3e+93) {
		tmp = x + t;
	} else if (x <= 4.5e+101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-7.5d+164)) then
        tmp = t_2
    else if (x <= (-8.5d+36)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= (-45000.0d0)) then
        tmp = x + (t * (y / a))
    else if (x <= 230.0d0) then
        tmp = t_1
    else if (x <= 5.3d+93) then
        tmp = x + t
    else if (x <= 4.5d+101) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -7.5e+164) {
		tmp = t_2;
	} else if (x <= -8.5e+36) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= -45000.0) {
		tmp = x + (t * (y / a));
	} else if (x <= 230.0) {
		tmp = t_1;
	} else if (x <= 5.3e+93) {
		tmp = x + t;
	} else if (x <= 4.5e+101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -7.5e+164:
		tmp = t_2
	elif x <= -8.5e+36:
		tmp = y * ((t - x) / (a - z))
	elif x <= -45000.0:
		tmp = x + (t * (y / a))
	elif x <= 230.0:
		tmp = t_1
	elif x <= 5.3e+93:
		tmp = x + t
	elif x <= 4.5e+101:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -7.5e+164)
		tmp = t_2;
	elseif (x <= -8.5e+36)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= -45000.0)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (x <= 230.0)
		tmp = t_1;
	elseif (x <= 5.3e+93)
		tmp = Float64(x + t);
	elseif (x <= 4.5e+101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -7.5e+164)
		tmp = t_2;
	elseif (x <= -8.5e+36)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= -45000.0)
		tmp = x + (t * (y / a));
	elseif (x <= 230.0)
		tmp = t_1;
	elseif (x <= 5.3e+93)
		tmp = x + t;
	elseif (x <= 4.5e+101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e+164], t$95$2, If[LessEqual[x, -8.5e+36], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -45000.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 230.0], t$95$1, If[LessEqual[x, 5.3e+93], N[(x + t), $MachinePrecision], If[LessEqual[x, 4.5e+101], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.49999999999999976e164 or 4.5000000000000002e101 < x

   1. Initial program 62.7%

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

      1. +-commutative 62.7%

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

      2. associate-*l/ 84.3%

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

      3. fma-def 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around 0 51.0%

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

      1. +-commutative 51.0%

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

      2. associate-/l* 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in t around 0 50.9%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 50.9%

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

      2. associate-*l/ 61.0%

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

      3. *-commutative 61.0%

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

      4. distribute-rgt-neg-in 61.0%

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

   9. Simplified 61.0%

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

   10. Taylor expanded in x around 0 61.0%

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

       1. mul-1-neg 61.0%

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

       2. sub-neg 61.0%

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

       3. *-commutative 61.0%

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

   12. Simplified 61.0%

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

   if -7.49999999999999976e164 < x < -8.50000000000000014e36

   1. Initial program 42.2%

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

      1. +-commutative 42.2%

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

      2. associate-*l/ 71.8%

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

      3. fma-def 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in y around inf 57.7%

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

      1. div-sub 57.7%

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

      2. *-commutative 57.7%

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

   6. Simplified 57.7%

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

   if -8.50000000000000014e36 < x < -45000

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. associate-/l* 69.5%

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

   6. Simplified 69.5%

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

   7. Taylor expanded in t around inf 69.5%

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

      1. associate-*l/ 69.5%

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

      2. *-commutative 69.5%

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

   9. Simplified 69.5%

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

   if -45000 < x < 230 or 5.3000000000000004e93 < x < 4.5000000000000002e101

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-*l/ 89.9%

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

      3. fma-def 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in t around inf 70.9%

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

      1. div-sub 71.0%

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

   6. Simplified 71.0%

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

   if 230 < x < 5.3000000000000004e93

   1. Initial program 67.2%

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

      1. +-commutative 67.2%

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

      2. associate-*l/ 85.5%

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

      3. fma-def 85.5%

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

   3. Simplified 85.5%

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

      1. fma-udef 85.5%

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

      2. associate-*l/ 67.2%

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

      3. associate-*r/ 76.5%

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

   5. Applied egg-rr 76.5%

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

   6. Taylor expanded in t around inf 65.1%

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

   7. Taylor expanded in z around inf 69.5%

      \[\leadsto \color{blue}{t} + x \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -45000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 230:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+93}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 8: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+135}:\\ \;\;\;\;t + \frac{a - y}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= z -2e+135)
     (+ t (/ (- a y) (- (/ z x))))
     (if (<= z -7.4e-85)
       t_1
       (if (<= z 1.1e-129)
         (+ x (* (- t x) (/ y a)))
         (if (<= z 4.7e+33) t_1 (+ t (* (/ y z) (- x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (z <= -2e+135) {
		tmp = t + ((a - y) / -(z / x));
	} else if (z <= -7.4e-85) {
		tmp = t_1;
	} else if (z <= 1.1e-129) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 4.7e+33) {
		tmp = t_1;
	} else {
		tmp = t + ((y / z) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / (a - z)))
    if (z <= (-2d+135)) then
        tmp = t + ((a - y) / -(z / x))
    else if (z <= (-7.4d-85)) then
        tmp = t_1
    else if (z <= 1.1d-129) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 4.7d+33) then
        tmp = t_1
    else
        tmp = t + ((y / z) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (z <= -2e+135) {
		tmp = t + ((a - y) / -(z / x));
	} else if (z <= -7.4e-85) {
		tmp = t_1;
	} else if (z <= 1.1e-129) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 4.7e+33) {
		tmp = t_1;
	} else {
		tmp = t + ((y / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if z <= -2e+135:
		tmp = t + ((a - y) / -(z / x))
	elif z <= -7.4e-85:
		tmp = t_1
	elif z <= 1.1e-129:
		tmp = x + ((t - x) * (y / a))
	elif z <= 4.7e+33:
		tmp = t_1
	else:
		tmp = t + ((y / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (z <= -2e+135)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(-Float64(z / x))));
	elseif (z <= -7.4e-85)
		tmp = t_1;
	elseif (z <= 1.1e-129)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 4.7e+33)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (z <= -2e+135)
		tmp = t + ((a - y) / -(z / x));
	elseif (z <= -7.4e-85)
		tmp = t_1;
	elseif (z <= 1.1e-129)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 4.7e+33)
		tmp = t_1;
	else
		tmp = t + ((y / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+135], N[(t + N[(N[(a - y), $MachinePrecision] / (-N[(z / x), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.4e-85], t$95$1, If[LessEqual[z, 1.1e-129], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+33], t$95$1, N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.99999999999999992e135

   1. Initial program 24.8%

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

      1. +-commutative 24.8%

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

      2. associate-*l/ 60.0%

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

      3. fma-def 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in z around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-/l* 86.3%

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

      3. distribute-lft-out-- 86.3%

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

      4. mul-1-neg 86.3%

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

      5. distribute-neg-frac 86.3%

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

      6. associate-/l* 72.8%

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

      7. *-commutative 72.8%

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

      8. distribute-rgt-out-- 72.5%

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

      9. unsub-neg 72.5%

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

      10. distribute-rgt-out-- 72.8%

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

      11. *-commutative 72.8%

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

      12. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in t around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-neg-frac 85.9%

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

   9. Simplified 85.9%

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

   if -1.99999999999999992e135 < z < -7.39999999999999966e-85 or 1.10000000000000001e-129 < z < 4.6999999999999998e33

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-*l/ 92.8%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

      1. fma-udef 92.8%

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

      2. associate-*l/ 86.1%

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

      3. associate-*r/ 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in t around inf 72.6%

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

   if -7.39999999999999966e-85 < z < 1.10000000000000001e-129

   1. Initial program 92.7%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 88.7%

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

   if 4.6999999999999998e33 < z

   1. Initial program 54.2%

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

      1. +-commutative 54.2%

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

      2. associate-*l/ 81.0%

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

      3. fma-def 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-/l* 77.4%

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

      3. distribute-lft-out-- 77.4%

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

      4. mul-1-neg 77.4%

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

      5. distribute-neg-frac 77.4%

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

      6. associate-/l* 68.9%

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

      7. *-commutative 68.9%

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

      8. distribute-rgt-out-- 68.7%

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

      9. unsub-neg 68.7%

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

      10. distribute-rgt-out-- 68.9%

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

      11. *-commutative 68.9%

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

      12. associate-/l* 77.4%

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

   6. Simplified 77.4%

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

   7. Taylor expanded in y around inf 70.7%

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

      1. associate-*l/ 78.9%

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

   9. Simplified 78.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+135}:\\ \;\;\;\;t + \frac{a - y}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-85}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+33}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-154}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= z -9.6e+134)
     (+ t (/ (- a y) (/ z (- t x))))
     (if (<= z -1.3e-82)
       t_1
       (if (<= z 5.8e-154)
         (+ x (* (- t x) (/ y a)))
         (if (<= z 3.8e+33) t_1 (+ t (* (/ y z) (- x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (z <= -9.6e+134) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else if (z <= -1.3e-82) {
		tmp = t_1;
	} else if (z <= 5.8e-154) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 3.8e+33) {
		tmp = t_1;
	} else {
		tmp = t + ((y / z) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / (a - z)))
    if (z <= (-9.6d+134)) then
        tmp = t + ((a - y) / (z / (t - x)))
    else if (z <= (-1.3d-82)) then
        tmp = t_1
    else if (z <= 5.8d-154) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 3.8d+33) then
        tmp = t_1
    else
        tmp = t + ((y / z) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (z <= -9.6e+134) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else if (z <= -1.3e-82) {
		tmp = t_1;
	} else if (z <= 5.8e-154) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 3.8e+33) {
		tmp = t_1;
	} else {
		tmp = t + ((y / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if z <= -9.6e+134:
		tmp = t + ((a - y) / (z / (t - x)))
	elif z <= -1.3e-82:
		tmp = t_1
	elif z <= 5.8e-154:
		tmp = x + ((t - x) * (y / a))
	elif z <= 3.8e+33:
		tmp = t_1
	else:
		tmp = t + ((y / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (z <= -9.6e+134)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	elseif (z <= -1.3e-82)
		tmp = t_1;
	elseif (z <= 5.8e-154)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 3.8e+33)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (z <= -9.6e+134)
		tmp = t + ((a - y) / (z / (t - x)));
	elseif (z <= -1.3e-82)
		tmp = t_1;
	elseif (z <= 5.8e-154)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 3.8e+33)
		tmp = t_1;
	else
		tmp = t + ((y / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+134], N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-82], t$95$1, If[LessEqual[z, 5.8e-154], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+33], t$95$1, N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.60000000000000021e134

   1. Initial program 24.8%

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

      1. +-commutative 24.8%

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

      2. associate-*l/ 60.0%

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

      3. fma-def 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in z around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-/l* 86.3%

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

      3. distribute-lft-out-- 86.3%

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

      4. mul-1-neg 86.3%

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

      5. distribute-neg-frac 86.3%

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

      6. associate-/l* 72.8%

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

      7. *-commutative 72.8%

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

      8. distribute-rgt-out-- 72.5%

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

      9. unsub-neg 72.5%

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

      10. distribute-rgt-out-- 72.8%

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

      11. *-commutative 72.8%

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

      12. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

   if -9.60000000000000021e134 < z < -1.3e-82 or 5.8e-154 < z < 3.80000000000000002e33

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-*l/ 92.8%

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

      3. fma-def 92.8%

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

   3. Simplified 92.8%

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

      1. fma-udef 92.8%

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

      2. associate-*l/ 86.1%

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

      3. associate-*r/ 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in t around inf 72.6%

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

   if -1.3e-82 < z < 5.8e-154

   1. Initial program 92.7%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 88.7%

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

   if 3.80000000000000002e33 < z

   1. Initial program 54.2%

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

      1. +-commutative 54.2%

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

      2. associate-*l/ 81.0%

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

      3. fma-def 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-/l* 77.4%

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

      3. distribute-lft-out-- 77.4%

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

      4. mul-1-neg 77.4%

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

      5. distribute-neg-frac 77.4%

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

      6. associate-/l* 68.9%

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

      7. *-commutative 68.9%

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

      8. distribute-rgt-out-- 68.7%

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

      9. unsub-neg 68.7%

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

      10. distribute-rgt-out-- 68.9%

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

      11. *-commutative 68.9%

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

      12. associate-/l* 77.4%

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

   6. Simplified 77.4%

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

   7. Taylor expanded in y around inf 70.7%

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

      1. associate-*l/ 78.9%

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

   9. Simplified 78.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-82}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-154}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+33}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 10: 53.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+64}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;-\frac{z \cdot t}{a - z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))))
   (if (<= z -8.6e+116)
     t_1
     (if (<= z -1e+64)
       (+ x t)
       (if (<= z -6.8e+40)
         (- (/ (* z t) (- a z)))
         (if (<= z -8.5e-92)
           (* (/ y z) (- x t))
           (if (<= z 1.42e+41) (+ x (/ y (/ a t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (z <= -8.6e+116) {
		tmp = t_1;
	} else if (z <= -1e+64) {
		tmp = x + t;
	} else if (z <= -6.8e+40) {
		tmp = -((z * t) / (a - z));
	} else if (z <= -8.5e-92) {
		tmp = (y / z) * (x - t);
	} else if (z <= 1.42e+41) {
		tmp = x + (y / (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) :: tmp
    t_1 = -t / (z / (y - z))
    if (z <= (-8.6d+116)) then
        tmp = t_1
    else if (z <= (-1d+64)) then
        tmp = x + t
    else if (z <= (-6.8d+40)) then
        tmp = -((z * t) / (a - z))
    else if (z <= (-8.5d-92)) then
        tmp = (y / z) * (x - t)
    else if (z <= 1.42d+41) then
        tmp = x + (y / (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 = -t / (z / (y - z));
	double tmp;
	if (z <= -8.6e+116) {
		tmp = t_1;
	} else if (z <= -1e+64) {
		tmp = x + t;
	} else if (z <= -6.8e+40) {
		tmp = -((z * t) / (a - z));
	} else if (z <= -8.5e-92) {
		tmp = (y / z) * (x - t);
	} else if (z <= 1.42e+41) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	tmp = 0
	if z <= -8.6e+116:
		tmp = t_1
	elif z <= -1e+64:
		tmp = x + t
	elif z <= -6.8e+40:
		tmp = -((z * t) / (a - z))
	elif z <= -8.5e-92:
		tmp = (y / z) * (x - t)
	elif z <= 1.42e+41:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (z <= -8.6e+116)
		tmp = t_1;
	elseif (z <= -1e+64)
		tmp = Float64(x + t);
	elseif (z <= -6.8e+40)
		tmp = Float64(-Float64(Float64(z * t) / Float64(a - z)));
	elseif (z <= -8.5e-92)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (z <= 1.42e+41)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	tmp = 0.0;
	if (z <= -8.6e+116)
		tmp = t_1;
	elseif (z <= -1e+64)
		tmp = x + t;
	elseif (z <= -6.8e+40)
		tmp = -((z * t) / (a - z));
	elseif (z <= -8.5e-92)
		tmp = (y / z) * (x - t);
	elseif (z <= 1.42e+41)
		tmp = x + (y / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+116], t$95$1, If[LessEqual[z, -1e+64], N[(x + t), $MachinePrecision], If[LessEqual[z, -6.8e+40], (-N[(N[(z * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, -8.5e-92], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+41], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.6e116 or 1.42000000000000007e41 < z

   1. Initial program 45.7%

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

      1. +-commutative 45.7%

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

      2. associate-*l/ 75.6%

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

      3. fma-def 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in t around inf 62.6%

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

      1. div-sub 62.6%

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

      2. associate-*r/ 40.2%

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

   6. Simplified 40.2%

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

   7. Taylor expanded in a around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. associate-/l* 59.0%

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

      3. distribute-neg-frac 59.0%

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

   9. Simplified 59.0%

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

   if -8.6e116 < z < -1.00000000000000002e64

   1. Initial program 82.0%

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

      1. +-commutative 82.0%

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

      2. associate-*l/ 91.1%

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

      3. fma-def 91.1%

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

   3. Simplified 91.1%

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

      1. fma-udef 91.1%

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

      2. associate-*l/ 82.0%

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

      3. associate-*r/ 83.8%

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

   5. Applied egg-rr 83.8%

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

   6. Taylor expanded in t around inf 75.5%

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

   7. Taylor expanded in z around inf 65.3%

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

   if -1.00000000000000002e64 < z < -6.79999999999999977e40

   1. Initial program 85.7%

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

      1. +-commutative 85.7%

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

      2. associate-*l/ 85.5%

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

      3. fma-def 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in t around inf 63.6%

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

      1. div-sub 63.6%

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

      2. associate-*r/ 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in y around 0 63.7%

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

      1. associate-*r/ 63.7%

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

      2. mul-1-neg 63.7%

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

   9. Simplified 63.7%

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

   if -6.79999999999999977e40 < z < -8.50000000000000067e-92

   1. Initial program 86.2%

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

      1. +-commutative 86.2%

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

      2. associate-*l/ 86.3%

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

      3. fma-def 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in z around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. associate-/l* 57.7%

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

      3. distribute-lft-out-- 57.7%

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

      4. mul-1-neg 57.7%

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

      5. distribute-neg-frac 57.7%

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

      6. associate-/l* 60.8%

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

      7. *-commutative 60.8%

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

      8. distribute-rgt-out-- 60.8%

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

      9. unsub-neg 60.8%

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

      10. distribute-rgt-out-- 60.8%

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

      11. *-commutative 60.8%

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

      12. associate-/l* 57.7%

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

   6. Simplified 57.7%

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

   7. Taylor expanded in y around -inf 45.7%

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

      1. mul-1-neg 45.7%

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

      2. associate-*l/ 45.8%

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

      3. distribute-rgt-neg-in 45.8%

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

   9. Simplified 45.8%

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

   if -8.50000000000000067e-92 < z < 1.42000000000000007e41

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in t around inf 62.4%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+116}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+64}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;-\frac{z \cdot t}{a - z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 11: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+81}:\\ \;\;\;\;x + x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+62}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+128)
   t
   (if (<= z -7.2e+81)
     (+ x (* x (/ y a)))
     (if (<= z -1.45e+62)
       (+ x t)
       (if (<= z -9.5e-92)
         (/ (* x (- y a)) z)
         (if (<= z 7.2e+41) (+ x (/ y (/ a t))) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+128) {
		tmp = t;
	} else if (z <= -7.2e+81) {
		tmp = x + (x * (y / a));
	} else if (z <= -1.45e+62) {
		tmp = x + t;
	} else if (z <= -9.5e-92) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 7.2e+41) {
		tmp = x + (y / (a / t));
	} 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 <= (-2d+128)) then
        tmp = t
    else if (z <= (-7.2d+81)) then
        tmp = x + (x * (y / a))
    else if (z <= (-1.45d+62)) then
        tmp = x + t
    else if (z <= (-9.5d-92)) then
        tmp = (x * (y - a)) / z
    else if (z <= 7.2d+41) then
        tmp = x + (y / (a / t))
    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 <= -2e+128) {
		tmp = t;
	} else if (z <= -7.2e+81) {
		tmp = x + (x * (y / a));
	} else if (z <= -1.45e+62) {
		tmp = x + t;
	} else if (z <= -9.5e-92) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 7.2e+41) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+128:
		tmp = t
	elif z <= -7.2e+81:
		tmp = x + (x * (y / a))
	elif z <= -1.45e+62:
		tmp = x + t
	elif z <= -9.5e-92:
		tmp = (x * (y - a)) / z
	elif z <= 7.2e+41:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+128)
		tmp = t;
	elseif (z <= -7.2e+81)
		tmp = Float64(x + Float64(x * Float64(y / a)));
	elseif (z <= -1.45e+62)
		tmp = Float64(x + t);
	elseif (z <= -9.5e-92)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= 7.2e+41)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+128)
		tmp = t;
	elseif (z <= -7.2e+81)
		tmp = x + (x * (y / a));
	elseif (z <= -1.45e+62)
		tmp = x + t;
	elseif (z <= -9.5e-92)
		tmp = (x * (y - a)) / z;
	elseif (z <= 7.2e+41)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+128], t, If[LessEqual[z, -7.2e+81], N[(x + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e+62], N[(x + t), $MachinePrecision], If[LessEqual[z, -9.5e-92], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 7.2e+41], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.0000000000000002e128 or 7.20000000000000051e41 < z

   1. Initial program 45.6%

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

      1. +-commutative 45.6%

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

      2. associate-*l/ 75.2%

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

      3. fma-def 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in z around inf 50.2%

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

   if -2.0000000000000002e128 < z < -7.20000000000000011e81

   1. Initial program 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-*l/ 90.2%

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

      3. fma-def 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in z around 0 61.1%

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

      1. +-commutative 61.1%

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

      2. associate-/l* 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in t around 0 60.5%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 60.5%

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

      2. associate-*l/ 60.5%

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

      3. *-commutative 60.5%

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

      4. distribute-rgt-neg-in 60.5%

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

   9. Simplified 60.5%

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

       1. expm1-log1p-u 60.2%

          \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(-\frac{y}{a}\right)\right)\right)} \]

       2. expm1-udef 60.4%

          \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(-\frac{y}{a}\right)\right)} - 1\right)} \]

       3. add-sqr-sqrt 60.0%

          \[\leadsto x + \left(e^{\mathsf{log1p}\left(x \cdot \color{blue}{\left(\sqrt{-\frac{y}{a}} \cdot \sqrt{-\frac{y}{a}}\right)}\right)} - 1\right) \]

       4. sqrt-unprod 60.5%

          \[\leadsto x + \left(e^{\mathsf{log1p}\left(x \cdot \color{blue}{\sqrt{\left(-\frac{y}{a}\right) \cdot \left(-\frac{y}{a}\right)}}\right)} - 1\right) \]

       5. sqr-neg 60.5%

          \[\leadsto x + \left(e^{\mathsf{log1p}\left(x \cdot \sqrt{\color{blue}{\frac{y}{a} \cdot \frac{y}{a}}}\right)} - 1\right) \]

       6. sqrt-unprod 51.0%

          \[\leadsto x + \left(e^{\mathsf{log1p}\left(x \cdot \color{blue}{\left(\sqrt{\frac{y}{a}} \cdot \sqrt{\frac{y}{a}}\right)}\right)} - 1\right) \]

       7. add-sqr-sqrt 61.9%

          \[\leadsto x + \left(e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{y}{a}}\right)} - 1\right) \]

   11. Applied egg-rr 61.9%

       \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \frac{y}{a}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 62.1%

          \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{y}{a}\right)\right)} \]

       2. expm1-log1p 62.1%

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

   13. Simplified 62.1%

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

   if -7.20000000000000011e81 < z < -1.44999999999999992e62

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l/ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. associate-*l/ 99.5%

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

      3. associate-*r/ 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in t around inf 69.5%

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

   7. Taylor expanded in z around inf 69.5%

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

   if -1.44999999999999992e62 < z < -9.49999999999999946e-92

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-*l/ 86.2%

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

      3. fma-def 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around inf 61.3%

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

      1. +-commutative 61.3%

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

      2. associate-/l* 58.8%

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

      3. distribute-lft-out-- 58.8%

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

      4. mul-1-neg 58.8%

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

      5. distribute-neg-frac 58.8%

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

      6. associate-/l* 61.3%

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

      7. *-commutative 61.3%

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

      8. distribute-rgt-out-- 61.3%

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

      9. unsub-neg 61.3%

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

      10. distribute-rgt-out-- 61.3%

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

      11. *-commutative 61.3%

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

      12. associate-/l* 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in t around 0 39.4%

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

   if -9.49999999999999946e-92 < z < 7.20000000000000051e41

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in t around inf 62.4%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+81}:\\ \;\;\;\;x + x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+62}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-34} \lor \neg \left(z \leq 2.7 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e+135)
   (+ t (/ (* x (- y a)) z))
   (if (<= z -3.8e+62)
     (+ x (* (/ t z) (- z y)))
     (if (or (<= z -4e-34) (not (<= z 2.7e-22)))
       (+ t (* (/ y z) (- x t)))
       (+ x (* (- t x) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+135) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= -3.8e+62) {
		tmp = x + ((t / z) * (z - y));
	} else if ((z <= -4e-34) || !(z <= 2.7e-22)) {
		tmp = t + ((y / z) * (x - t));
	} 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 <= (-1.6d+135)) then
        tmp = t + ((x * (y - a)) / z)
    else if (z <= (-3.8d+62)) then
        tmp = x + ((t / z) * (z - y))
    else if ((z <= (-4d-34)) .or. (.not. (z <= 2.7d-22))) then
        tmp = t + ((y / z) * (x - t))
    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 <= -1.6e+135) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= -3.8e+62) {
		tmp = x + ((t / z) * (z - y));
	} else if ((z <= -4e-34) || !(z <= 2.7e-22)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e+135:
		tmp = t + ((x * (y - a)) / z)
	elif z <= -3.8e+62:
		tmp = x + ((t / z) * (z - y))
	elif (z <= -4e-34) or not (z <= 2.7e-22):
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e+135)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	elseif (z <= -3.8e+62)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(z - y)));
	elseif ((z <= -4e-34) || !(z <= 2.7e-22))
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	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 <= -1.6e+135)
		tmp = t + ((x * (y - a)) / z);
	elseif (z <= -3.8e+62)
		tmp = x + ((t / z) * (z - y));
	elseif ((z <= -4e-34) || ~((z <= 2.7e-22)))
		tmp = t + ((y / z) * (x - t));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e+135], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e+62], N[(x + N[(N[(t / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4e-34], N[Not[LessEqual[z, 2.7e-22]], $MachinePrecision]], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.59999999999999987e135

   1. Initial program 24.8%

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

      1. +-commutative 24.8%

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

      2. associate-*l/ 60.0%

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

      3. fma-def 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in z around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-/l* 86.3%

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

      3. distribute-lft-out-- 86.3%

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

      4. mul-1-neg 86.3%

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

      5. distribute-neg-frac 86.3%

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

      6. associate-/l* 72.8%

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

      7. *-commutative 72.8%

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

      8. distribute-rgt-out-- 72.5%

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

      9. unsub-neg 72.5%

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

      10. distribute-rgt-out-- 72.8%

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

      11. *-commutative 72.8%

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

      12. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in t around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 79.3%

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

      4. neg-mul-1 79.3%

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

   9. Simplified 79.3%

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

   if -1.59999999999999987e135 < z < -3.79999999999999984e62

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-*l/ 93.9%

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

      3. fma-def 93.9%

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

   3. Simplified 93.9%

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

      1. fma-udef 93.9%

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

      2. associate-*l/ 75.5%

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

      3. associate-*r/ 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in t around inf 83.0%

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

   7. Taylor expanded in a around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

   9. Simplified 77.1%

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

   if -3.79999999999999984e62 < z < -3.99999999999999971e-34 or 2.7000000000000002e-22 < z

   1. Initial program 66.5%

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

      1. +-commutative 66.5%

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

      2. associate-*l/ 84.1%

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

      3. fma-def 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in z around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. associate-/l* 71.4%

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

      3. distribute-lft-out-- 71.4%

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

      4. mul-1-neg 71.4%

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

      5. distribute-neg-frac 71.4%

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

      6. associate-/l* 66.8%

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

      7. *-commutative 66.8%

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

      8. distribute-rgt-out-- 66.6%

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

      9. unsub-neg 66.6%

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

      10. distribute-rgt-out-- 66.8%

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

      11. *-commutative 66.8%

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

      12. associate-/l* 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in y around inf 67.1%

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

      1. associate-*l/ 72.6%

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

   9. Simplified 72.6%

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

   if -3.99999999999999971e-34 < z < 2.7000000000000002e-22

   1. Initial program 90.7%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around 0 79.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+135}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-34} \lor \neg \left(z \leq 2.7 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 13: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y z) (- x t))))
   (if (<= z -2.8e+128)
     t
     (if (<= z -2.6e-92)
       t_1
       (if (<= z 1.95e+33) (+ x (/ y (/ a t))) (if (<= z 4.8e+173) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * (x - t);
	double tmp;
	if (z <= -2.8e+128) {
		tmp = t;
	} else if (z <= -2.6e-92) {
		tmp = t_1;
	} else if (z <= 1.95e+33) {
		tmp = x + (y / (a / t));
	} else if (z <= 4.8e+173) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) * (x - t)
    if (z <= (-2.8d+128)) then
        tmp = t
    else if (z <= (-2.6d-92)) then
        tmp = t_1
    else if (z <= 1.95d+33) then
        tmp = x + (y / (a / t))
    else if (z <= 4.8d+173) then
        tmp = t_1
    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 t_1 = (y / z) * (x - t);
	double tmp;
	if (z <= -2.8e+128) {
		tmp = t;
	} else if (z <= -2.6e-92) {
		tmp = t_1;
	} else if (z <= 1.95e+33) {
		tmp = x + (y / (a / t));
	} else if (z <= 4.8e+173) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / z) * (x - t)
	tmp = 0
	if z <= -2.8e+128:
		tmp = t
	elif z <= -2.6e-92:
		tmp = t_1
	elif z <= 1.95e+33:
		tmp = x + (y / (a / t))
	elif z <= 4.8e+173:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / z) * Float64(x - t))
	tmp = 0.0
	if (z <= -2.8e+128)
		tmp = t;
	elseif (z <= -2.6e-92)
		tmp = t_1;
	elseif (z <= 1.95e+33)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 4.8e+173)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / z) * (x - t);
	tmp = 0.0;
	if (z <= -2.8e+128)
		tmp = t;
	elseif (z <= -2.6e-92)
		tmp = t_1;
	elseif (z <= 1.95e+33)
		tmp = x + (y / (a / t));
	elseif (z <= 4.8e+173)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+128], t, If[LessEqual[z, -2.6e-92], t$95$1, If[LessEqual[z, 1.95e+33], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+173], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999983e128 or 4.7999999999999998e173 < z

   1. Initial program 29.1%

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

      1. +-commutative 29.1%

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

      2. associate-*l/ 68.4%

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

      3. fma-def 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in z around inf 57.3%

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

   if -2.79999999999999983e128 < z < -2.6e-92 or 1.9500000000000001e33 < z < 4.7999999999999998e173

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*l/ 87.8%

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

      3. fma-def 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in z around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. associate-/l* 63.1%

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

      3. distribute-lft-out-- 63.1%

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

      4. mul-1-neg 63.1%

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

      5. distribute-neg-frac 63.1%

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

      6. associate-/l* 63.2%

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

      7. *-commutative 63.2%

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

      8. distribute-rgt-out-- 63.2%

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

      9. unsub-neg 63.2%

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

      10. distribute-rgt-out-- 63.2%

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

      11. *-commutative 63.2%

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

      12. associate-/l* 63.1%

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

   6. Simplified 63.1%

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

   7. Taylor expanded in y around -inf 40.7%

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

      1. mul-1-neg 40.7%

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

      2. associate-*l/ 43.8%

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

      3. distribute-rgt-neg-in 43.8%

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

   9. Simplified 43.8%

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

   if -2.6e-92 < z < 1.9500000000000001e33

   1. Initial program 92.2%

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

      1. +-commutative 92.2%

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

      2. associate-*l/ 97.7%

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

      3. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around 0 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-/l* 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in t around inf 64.1%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+173}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+129}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-25}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+173}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+129)
   t
   (if (<= z -2.9e-25)
     (- x (* z (/ t a)))
     (if (<= z 3.25e+32)
       (+ x (/ y (/ a t)))
       (if (<= z 2.4e+173) (* (/ y z) (- x t)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+129) {
		tmp = t;
	} else if (z <= -2.9e-25) {
		tmp = x - (z * (t / a));
	} else if (z <= 3.25e+32) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.4e+173) {
		tmp = (y / z) * (x - t);
	} 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 <= (-4d+129)) then
        tmp = t
    else if (z <= (-2.9d-25)) then
        tmp = x - (z * (t / a))
    else if (z <= 3.25d+32) then
        tmp = x + (y / (a / t))
    else if (z <= 2.4d+173) then
        tmp = (y / z) * (x - t)
    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 <= -4e+129) {
		tmp = t;
	} else if (z <= -2.9e-25) {
		tmp = x - (z * (t / a));
	} else if (z <= 3.25e+32) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.4e+173) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+129:
		tmp = t
	elif z <= -2.9e-25:
		tmp = x - (z * (t / a))
	elif z <= 3.25e+32:
		tmp = x + (y / (a / t))
	elif z <= 2.4e+173:
		tmp = (y / z) * (x - t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+129)
		tmp = t;
	elseif (z <= -2.9e-25)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	elseif (z <= 3.25e+32)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 2.4e+173)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+129)
		tmp = t;
	elseif (z <= -2.9e-25)
		tmp = x - (z * (t / a));
	elseif (z <= 3.25e+32)
		tmp = x + (y / (a / t));
	elseif (z <= 2.4e+173)
		tmp = (y / z) * (x - t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+129], t, If[LessEqual[z, -2.9e-25], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.25e+32], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+173], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4e129 or 2.3999999999999999e173 < z

   1. Initial program 29.1%

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

      1. +-commutative 29.1%

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

      2. associate-*l/ 68.4%

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

      3. fma-def 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in z around inf 57.3%

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

   if -4e129 < z < -2.9000000000000001e-25

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-*l/ 90.8%

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

      3. fma-def 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in a around inf 47.3%

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

      1. +-commutative 47.3%

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

      2. associate-/l* 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in t around inf 50.2%

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

   8. Taylor expanded in y around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate-*l/ 47.2%

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

      3. distribute-rgt-neg-in 47.2%

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

   10. Simplified 47.2%

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

   if -2.9000000000000001e-25 < z < 3.2499999999999997e32

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. associate-*l/ 95.5%

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

      3. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-/l* 72.0%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in t around inf 59.6%

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

   if 3.2499999999999997e32 < z < 2.3999999999999999e173

   1. Initial program 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-*l/ 87.8%

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

      3. fma-def 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in z around inf 70.9%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 70.9%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 76.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 76.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 76.1%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 76.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 70.9%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 70.9%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 70.9%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 70.9%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 70.9%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 70.9%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 76.1%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 76.1%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in y around -inf 39.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto \color{blue}{-\frac{y \cdot \left(t - x\right)}{z}} \]

      2. associate-*l/ 46.8%

         \[\leadsto -\color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

      3. distribute-rgt-neg-in 46.8%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(-\left(t - x\right)\right)} \]

   9. Simplified 46.8%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(-\left(t - x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+129}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-25}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+173}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 53.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ \mathbf{if}\;z \leq -1.48 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))))
   (if (<= z -1.48e+103)
     t_1
     (if (<= z -8.5e-92)
       (* (/ y z) (- x t))
       (if (<= z 4.3e+41) (+ x (/ y (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (z <= -1.48e+103) {
		tmp = t_1;
	} else if (z <= -8.5e-92) {
		tmp = (y / z) * (x - t);
	} else if (z <= 4.3e+41) {
		tmp = x + (y / (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) :: tmp
    t_1 = -t / (z / (y - z))
    if (z <= (-1.48d+103)) then
        tmp = t_1
    else if (z <= (-8.5d-92)) then
        tmp = (y / z) * (x - t)
    else if (z <= 4.3d+41) then
        tmp = x + (y / (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 = -t / (z / (y - z));
	double tmp;
	if (z <= -1.48e+103) {
		tmp = t_1;
	} else if (z <= -8.5e-92) {
		tmp = (y / z) * (x - t);
	} else if (z <= 4.3e+41) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	tmp = 0
	if z <= -1.48e+103:
		tmp = t_1
	elif z <= -8.5e-92:
		tmp = (y / z) * (x - t)
	elif z <= 4.3e+41:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (z <= -1.48e+103)
		tmp = t_1;
	elseif (z <= -8.5e-92)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (z <= 4.3e+41)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	tmp = 0.0;
	if (z <= -1.48e+103)
		tmp = t_1;
	elseif (z <= -8.5e-92)
		tmp = (y / z) * (x - t);
	elseif (z <= 4.3e+41)
		tmp = x + (y / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.48e+103], t$95$1, If[LessEqual[z, -8.5e-92], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+41], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.48000000000000009e103 or 4.30000000000000024e41 < z

   1. Initial program 46.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 46.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 76.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 76.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in t around inf 61.8%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 61.8%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

      2. associate-*r/ 40.1%

         \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   7. Taylor expanded in a around 0 39.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - z\right)}{z}} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto \color{blue}{-\frac{t \cdot \left(y - z\right)}{z}} \]

      2. associate-/l* 58.3%

         \[\leadsto -\color{blue}{\frac{t}{\frac{z}{y - z}}} \]

      3. distribute-neg-frac 58.3%

         \[\leadsto \color{blue}{\frac{-t}{\frac{z}{y - z}}} \]

   9. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{-t}{\frac{z}{y - z}}} \]

   if -1.48000000000000009e103 < z < -8.50000000000000067e-92

   1. Initial program 86.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 86.4%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 86.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 86.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 59.8%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 59.8%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 55.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 55.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 55.6%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 55.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 59.8%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 59.8%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 59.8%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 59.8%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 59.8%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 59.8%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 55.6%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 55.6%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in y around -inf 43.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. mul-1-neg 43.7%

         \[\leadsto \color{blue}{-\frac{y \cdot \left(t - x\right)}{z}} \]

      2. associate-*l/ 43.8%

         \[\leadsto -\color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

      3. distribute-rgt-neg-in 43.8%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(-\left(t - x\right)\right)} \]

   9. Simplified 43.8%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(-\left(t - x\right)\right)} \]

   if -8.50000000000000067e-92 < z < 4.30000000000000024e41

   1. Initial program 90.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 90.7%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 96.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 96.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 70.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 70.7%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 74.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in t around inf 62.4%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+103}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 16: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e+126)
   t
   (if (<= z -6.1e-92)
     (/ (* y (- x t)) z)
     (if (<= z 3e+41) (+ x (/ y (/ a t))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e+126) {
		tmp = t;
	} else if (z <= -6.1e-92) {
		tmp = (y * (x - t)) / z;
	} else if (z <= 3e+41) {
		tmp = x + (y / (a / t));
	} 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 <= (-1.22d+126)) then
        tmp = t
    else if (z <= (-6.1d-92)) then
        tmp = (y * (x - t)) / z
    else if (z <= 3d+41) then
        tmp = x + (y / (a / t))
    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 <= -1.22e+126) {
		tmp = t;
	} else if (z <= -6.1e-92) {
		tmp = (y * (x - t)) / z;
	} else if (z <= 3e+41) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.22e+126:
		tmp = t
	elif z <= -6.1e-92:
		tmp = (y * (x - t)) / z
	elif z <= 3e+41:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.22e+126)
		tmp = t;
	elseif (z <= -6.1e-92)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (z <= 3e+41)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.22e+126)
		tmp = t;
	elseif (z <= -6.1e-92)
		tmp = (y * (x - t)) / z;
	elseif (z <= 3e+41)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.22e+126], t, If[LessEqual[z, -6.1e-92], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3e+41], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999995e126 or 2.9999999999999998e41 < z

   1. Initial program 45.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 75.2%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 75.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 75.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 50.2%

      \[\leadsto \color{blue}{t} \]

   if -1.21999999999999995e126 < z < -6.09999999999999988e-92

   1. Initial program 83.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 83.8%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 87.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 87.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in y around -inf 45.3%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

   5. Taylor expanded in a around 0 41.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto \color{blue}{-\frac{y \cdot \left(t - x\right)}{z}} \]

   7. Simplified 41.7%

      \[\leadsto \color{blue}{-\frac{y \cdot \left(t - x\right)}{z}} \]

   if -6.09999999999999988e-92 < z < 2.9999999999999998e41

   1. Initial program 90.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 90.7%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 96.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 96.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 70.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 70.7%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 74.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in t around inf 62.4%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-33} \lor \neg \left(z \leq 6.1 \cdot 10^{-34}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.9e-33) (not (<= z 6.1e-34)))
   (* 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 <= -3.9e-33) || !(z <= 6.1e-34)) {
		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 <= (-3.9d-33)) .or. (.not. (z <= 6.1d-34))) 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 <= -3.9e-33) || !(z <= 6.1e-34)) {
		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 <= -3.9e-33) or not (z <= 6.1e-34):
		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 <= -3.9e-33) || !(z <= 6.1e-34))
		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 <= -3.9e-33) || ~((z <= 6.1e-34)))
		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, -3.9e-33], N[Not[LessEqual[z, 6.1e-34]], $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 < -3.89999999999999974e-33 or 6.0999999999999998e-34 < z

   1. Initial program 58.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 58.3%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 79.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 79.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in t around inf 56.9%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   5. Step-by-step derivation

      1. div-sub 56.9%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   6. Simplified 56.9%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -3.89999999999999974e-33 < z < 6.0999999999999998e-34

   1. Initial program 92.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 80.1%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-33} \lor \neg \left(z \leq 6.1 \cdot 10^{-34}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 18: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-34} \lor \neg \left(z \leq 2.3 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.1e-34) (not (<= z 2.3e-22)))
   (+ t (* (/ y z) (- x t)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.1e-34) || !(z <= 2.3e-22)) {
		tmp = t + ((y / z) * (x - t));
	} 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 <= (-6.1d-34)) .or. (.not. (z <= 2.3d-22))) then
        tmp = t + ((y / z) * (x - t))
    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 <= -6.1e-34) || !(z <= 2.3e-22)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.1e-34) or not (z <= 2.3e-22):
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.1e-34) || !(z <= 2.3e-22))
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	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 <= -6.1e-34) || ~((z <= 2.3e-22)))
		tmp = t + ((y / z) * (x - t));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.1e-34], N[Not[LessEqual[z, 2.3e-22]], $MachinePrecision]], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $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 < -6.0999999999999998e-34 or 2.2999999999999998e-22 < z

   1. Initial program 58.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 58.4%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 80.0%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 80.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 67.2%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
   5. Step-by-step derivation

      1. +-commutative 67.2%

         \[\leadsto \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 72.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot y - -1 \cdot a}{\frac{z}{t - x}}} \]

      3. distribute-lft-out-- 72.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y - a\right)}}{\frac{z}{t - x}} \]

      4. mul-1-neg 72.6%

         \[\leadsto t + \frac{\color{blue}{-\left(y - a\right)}}{\frac{z}{t - x}} \]

      5. distribute-neg-frac 72.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y - a}{\frac{z}{t - x}}\right)} \]

      6. associate-/l* 67.2%

         \[\leadsto t + \left(-\color{blue}{\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}}\right) \]

      7. *-commutative 67.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      8. distribute-rgt-out-- 67.0%

         \[\leadsto t + \left(-\frac{\color{blue}{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}}{z}\right) \]

      9. unsub-neg 67.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      10. distribute-rgt-out-- 67.2%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      11. *-commutative 67.2%

          \[\leadsto t - \frac{\color{blue}{\left(y - a\right) \cdot \left(t - x\right)}}{z} \]

      12. associate-/l* 72.6%

          \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   6. Simplified 72.6%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]

   7. Taylor expanded in y around inf 64.0%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-*l/ 70.4%

         \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   9. Simplified 70.4%

      \[\leadsto t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   if -6.0999999999999998e-34 < z < 2.2999999999999998e-22

   1. Initial program 90.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   4. Taylor expanded in z around 0 79.0%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-34} \lor \neg \left(z \leq 2.3 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 19: 47.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+239}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+125)
   t
   (if (<= z 9.2e-34) (* x (- 1.0 (/ y a))) (if (<= z 6e+239) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+125) {
		tmp = t;
	} else if (z <= 9.2e-34) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 6e+239) {
		tmp = x + t;
	} 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 <= (-1.95d+125)) then
        tmp = t
    else if (z <= 9.2d-34) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 6d+239) then
        tmp = x + t
    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 <= -1.95e+125) {
		tmp = t;
	} else if (z <= 9.2e-34) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 6e+239) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+125:
		tmp = t
	elif z <= 9.2e-34:
		tmp = x * (1.0 - (y / a))
	elif z <= 6e+239:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+125)
		tmp = t;
	elseif (z <= 9.2e-34)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 6e+239)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+125)
		tmp = t;
	elseif (z <= 9.2e-34)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 6e+239)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+125], t, If[LessEqual[z, 9.2e-34], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+239], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9500000000000001e125 or 5.9999999999999997e239 < z

   1. Initial program 30.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 30.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 65.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 65.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 60.4%

      \[\leadsto \color{blue}{t} \]

   if -1.9500000000000001e125 < z < 9.20000000000000045e-34

   1. Initial program 90.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 90.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 94.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 94.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 64.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 64.1%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 66.1%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 66.1%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in t around 0 50.6%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{y \cdot x}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 50.6%

         \[\leadsto x + \color{blue}{\left(-\frac{y \cdot x}{a}\right)} \]

      2. associate-*l/ 54.5%

         \[\leadsto x + \left(-\color{blue}{\frac{y}{a} \cdot x}\right) \]

      3. *-commutative 54.5%

         \[\leadsto x + \left(-\color{blue}{x \cdot \frac{y}{a}}\right) \]

      4. distribute-rgt-neg-in 54.5%

         \[\leadsto x + \color{blue}{x \cdot \left(-\frac{y}{a}\right)} \]

   9. Simplified 54.5%

      \[\leadsto x + \color{blue}{x \cdot \left(-\frac{y}{a}\right)} \]

   10. Taylor expanded in x around 0 54.5%

       \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{y}{a}\right) \cdot x} \]
   11. Step-by-step derivation

       1. mul-1-neg 54.5%

          \[\leadsto \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \cdot x \]

       2. sub-neg 54.5%

          \[\leadsto \color{blue}{\left(1 - \frac{y}{a}\right)} \cdot x \]

       3. *-commutative 54.5%

          \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]

   12. Simplified 54.5%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]

   if 9.20000000000000045e-34 < z < 5.9999999999999997e239

   1. Initial program 66.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 66.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 86.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 86.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 86.4%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right) + x} \]

      2. associate-*l/ 66.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} + x \]

      3. associate-*r/ 83.3%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x \]

   5. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

   6. Taylor expanded in t around inf 62.6%

      \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} + x \]

   7. Taylor expanded in z around inf 43.2%

      \[\leadsto \color{blue}{t} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+239}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 52.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+125) t (if (<= z 1.05e+42) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+125) {
		tmp = t;
	} else if (z <= 1.05e+42) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.25d+125)) then
        tmp = t
    else if (z <= 1.05d+42) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+125) {
		tmp = t;
	} else if (z <= 1.05e+42) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+125:
		tmp = t
	elif z <= 1.05e+42:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+125)
		tmp = t;
	elseif (z <= 1.05e+42)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+125)
		tmp = t;
	elseif (z <= 1.05e+42)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+125], t, If[LessEqual[z, 1.05e+42], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999991e125 or 1.04999999999999998e42 < z

   1. Initial program 45.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 75.2%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 75.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 75.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 50.2%

      \[\leadsto \color{blue}{t} \]

   if -1.24999999999999991e125 < z < 1.04999999999999998e42

   1. Initial program 88.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 88.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 93.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 93.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 60.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 60.5%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 62.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 62.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in t around inf 51.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot t}{a}} \]
   8. Step-by-step derivation

      1. associate-*l/ 53.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot t} \]

      2. *-commutative 53.0%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]

   9. Simplified 53.0%

      \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 51.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+125) t (if (<= z 1.5e+42) (+ x (/ y (/ a t))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+125) {
		tmp = t;
	} else if (z <= 1.5e+42) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d+125)) then
        tmp = t
    else if (z <= 1.5d+42) then
        tmp = x + (y / (a / t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+125) {
		tmp = t;
	} else if (z <= 1.5e+42) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+125:
		tmp = t
	elif z <= 1.5e+42:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+125)
		tmp = t;
	elseif (z <= 1.5e+42)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+125)
		tmp = t;
	elseif (z <= 1.5e+42)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+125], t, If[LessEqual[z, 1.5e+42], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999983e125 or 1.50000000000000014e42 < z

   1. Initial program 45.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 75.2%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 75.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 75.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 50.2%

      \[\leadsto \color{blue}{t} \]

   if -3.19999999999999983e125 < z < 1.50000000000000014e42

   1. Initial program 88.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 88.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 93.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 93.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around 0 60.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 60.5%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 62.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   6. Simplified 62.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]

   7. Taylor expanded in t around inf 53.0%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22: 38.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+240}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+125) t (if (<= z 5.2e-115) x (if (<= z 2.7e+240) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+125) {
		tmp = t;
	} else if (z <= 5.2e-115) {
		tmp = x;
	} else if (z <= 2.7e+240) {
		tmp = x + t;
	} 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 <= (-2.5d+125)) then
        tmp = t
    else if (z <= 5.2d-115) then
        tmp = x
    else if (z <= 2.7d+240) then
        tmp = x + t
    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 <= -2.5e+125) {
		tmp = t;
	} else if (z <= 5.2e-115) {
		tmp = x;
	} else if (z <= 2.7e+240) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+125:
		tmp = t
	elif z <= 5.2e-115:
		tmp = x
	elif z <= 2.7e+240:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+125)
		tmp = t;
	elseif (z <= 5.2e-115)
		tmp = x;
	elseif (z <= 2.7e+240)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+125)
		tmp = t;
	elseif (z <= 5.2e-115)
		tmp = x;
	elseif (z <= 2.7e+240)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+125], t, If[LessEqual[z, 5.2e-115], x, If[LessEqual[z, 2.7e+240], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999981e125 or 2.6999999999999999e240 < z

   1. Initial program 30.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 30.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 65.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 65.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 60.4%

      \[\leadsto \color{blue}{t} \]

   if -2.49999999999999981e125 < z < 5.20000000000000008e-115

   1. Initial program 89.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 89.8%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 93.8%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 93.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in a around inf 37.6%

      \[\leadsto \color{blue}{x} \]

   if 5.20000000000000008e-115 < z < 2.6999999999999999e240

   1. Initial program 72.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 89.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 89.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 89.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right) + x} \]

      2. associate-*l/ 72.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} + x \]

      3. associate-*r/ 87.6%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x \]

   5. Applied egg-rr 87.6%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

   6. Taylor expanded in t around inf 67.8%

      \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} + x \]

   7. Taylor expanded in z around inf 42.5%

      \[\leadsto \color{blue}{t} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+240}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 23: 37.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.55e+128) t (if (<= z 1.6e-37) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.55e+128) {
		tmp = t;
	} else if (z <= 1.6e-37) {
		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 <= (-2.55d+128)) then
        tmp = t
    else if (z <= 1.6d-37) 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 <= -2.55e+128) {
		tmp = t;
	} else if (z <= 1.6e-37) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.55e+128:
		tmp = t
	elif z <= 1.6e-37:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.55e+128)
		tmp = t;
	elseif (z <= 1.6e-37)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.55e+128)
		tmp = t;
	elseif (z <= 1.6e-37)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.55e+128], t, If[LessEqual[z, 1.6e-37], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e128 or 1.5999999999999999e-37 < z

   1. Initial program 49.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 49.1%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 76.9%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in z around inf 46.1%

      \[\leadsto \color{blue}{t} \]

   if -2.5499999999999999e128 < z < 1.5999999999999999e-37

   1. Initial program 90.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 90.5%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. associate-*l/ 94.6%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

      3. fma-def 94.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   4. Taylor expanded in a around inf 38.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 24: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 72.1%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. +-commutative 72.1%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

   2. associate-*r/ 82.0%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x \]

   3. fma-def 82.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

3. Simplified 82.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

4. Taylor expanded in t around 0 43.3%

   \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{-1 \cdot \frac{x}{a - z}}, x\right) \]
5. Step-by-step derivation

   1. neg-mul-1 43.3%

      \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{-\frac{x}{a - z}}, x\right) \]

   2. distribute-neg-frac 43.3%

      \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{-x}{a - z}}, x\right) \]

6. Simplified 43.3%

   \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{-x}{a - z}}, x\right) \]

7. Taylor expanded in z around inf 2.8%

   \[\leadsto \color{blue}{-1 \cdot x + x} \]
8. Step-by-step derivation

   1. mul-1-neg 2.8%

      \[\leadsto \color{blue}{\left(-x\right)} + x \]

   2. +-commutative 2.8%

      \[\leadsto \color{blue}{x + \left(-x\right)} \]

   3. sub-neg 2.8%

      \[\leadsto \color{blue}{x - x} \]

   4. +-inverses 2.8%

      \[\leadsto \color{blue}{0} \]

9. Simplified 2.8%

   \[\leadsto \color{blue}{0} \]

10. Final simplification 2.8%

    \[\leadsto 0 \]

Alternative 25: 24.9% 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 72.1%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. +-commutative 72.1%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

   2. associate-*l/ 86.7%

      \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]

   3. fma-def 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

3. Simplified 86.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

4. Taylor expanded in z around inf 25.7%

   \[\leadsto \color{blue}{t} \]

5. Final simplification 25.7%

   \[\leadsto t \]

Developer target: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))