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

Percentage Accurate: 68.3% → 90.3%

Time: 18.5s

Alternatives: 20

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: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\mathsf{fma}\left(t_1, t - x, x\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-293}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z))) (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -1e-288)
     (fma t_1 (- t x) x)
     (if (<= t_2 5e-293) (+ 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) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -1e-288) {
		tmp = fma(t_1, (t - x), x);
	} else if (t_2 <= 5e-293) {
		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(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -1e-288)
		tmp = fma(t_1, Float64(t - x), x);
	elseif (t_2 <= 5e-293)
		tmp = Float64(t + Float64(x * Float64(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[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-288], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 5e-293], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $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))) < -1.00000000000000006e-288

   1. Initial program 76.7%

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

      1. +-commutative 76.7%

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

      2. associate-*l/ 94.3%

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

      3. fma-def 94.3%

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

   3. Simplified 94.3%

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

   if -1.00000000000000006e-288 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000003e-293

   1. Initial program 6.2%

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

      1. associate-*l/ 6.2%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-rgt-out-- 99.8%

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

      8. mul-1-neg 99.8%

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

      9. unsub-neg 99.8%

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

      10. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-*r/ 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

   9. Simplified 99.8%

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

   if 5.0000000000000003e-293 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 76.2%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{-293}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 2: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-288} \lor \neg \left(t_1 \leq 5 \cdot 10^{-293}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-288) (not (<= t_1 5e-293)))
     (+ 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) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-288) || !(t_1 <= 5e-293)) {
		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) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-288)) .or. (.not. (t_1 <= 5d-293))) 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) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-288) || !(t_1 <= 5e-293)) {
		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) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-288) or not (t_1 <= 5e-293):
		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(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-288) || !(t_1 <= 5e-293))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-288) || ~((t_1 <= 5e-293)))
		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[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-288], N[Not[LessEqual[t$95$1, 5e-293]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000006e-288 or 5.0000000000000003e-293 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 76.5%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   if -1.00000000000000006e-288 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000003e-293

   1. Initial program 6.2%

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

      1. associate-*l/ 6.2%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-rgt-out-- 99.8%

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

      8. mul-1-neg 99.8%

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

      9. unsub-neg 99.8%

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

      10. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-*r/ 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-288} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{-293}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 3: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{z}{z - a}\\ t_2 := t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -230:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ z (- z a))))) (t_2 (+ t (/ (- x t) (/ z y)))))
   (if (<= a -230.0)
     t_1
     (if (<= a -2.85e-30)
       (+ x (/ y (/ a (- t x))))
       (if (<= a -1.9e-101)
         t_2
         (if (<= a -3.8e-156)
           (* y (/ (- t x) (- a z)))
           (if (<= a 1.6e-119)
             t_2
             (if (<= a 3.3e+54) (/ t (/ (- a z) (- y z))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (z / (z - a)));
	double t_2 = t + ((x - t) / (z / y));
	double tmp;
	if (a <= -230.0) {
		tmp = t_1;
	} else if (a <= -2.85e-30) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= -1.9e-101) {
		tmp = t_2;
	} else if (a <= -3.8e-156) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.6e-119) {
		tmp = t_2;
	} else if (a <= 3.3e+54) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (z / (z - a)))
    t_2 = t + ((x - t) / (z / y))
    if (a <= (-230.0d0)) then
        tmp = t_1
    else if (a <= (-2.85d-30)) then
        tmp = x + (y / (a / (t - x)))
    else if (a <= (-1.9d-101)) then
        tmp = t_2
    else if (a <= (-3.8d-156)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.6d-119) then
        tmp = t_2
    else if (a <= 3.3d+54) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (z / (z - a)));
	double t_2 = t + ((x - t) / (z / y));
	double tmp;
	if (a <= -230.0) {
		tmp = t_1;
	} else if (a <= -2.85e-30) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= -1.9e-101) {
		tmp = t_2;
	} else if (a <= -3.8e-156) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.6e-119) {
		tmp = t_2;
	} else if (a <= 3.3e+54) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (z / (z - a)))
	t_2 = t + ((x - t) / (z / y))
	tmp = 0
	if a <= -230.0:
		tmp = t_1
	elif a <= -2.85e-30:
		tmp = x + (y / (a / (t - x)))
	elif a <= -1.9e-101:
		tmp = t_2
	elif a <= -3.8e-156:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.6e-119:
		tmp = t_2
	elif a <= 3.3e+54:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(z / Float64(z - a))))
	t_2 = Float64(t + Float64(Float64(x - t) / Float64(z / y)))
	tmp = 0.0
	if (a <= -230.0)
		tmp = t_1;
	elseif (a <= -2.85e-30)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (a <= -1.9e-101)
		tmp = t_2;
	elseif (a <= -3.8e-156)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.6e-119)
		tmp = t_2;
	elseif (a <= 3.3e+54)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (z / (z - a)));
	t_2 = t + ((x - t) / (z / y));
	tmp = 0.0;
	if (a <= -230.0)
		tmp = t_1;
	elseif (a <= -2.85e-30)
		tmp = x + (y / (a / (t - x)));
	elseif (a <= -1.9e-101)
		tmp = t_2;
	elseif (a <= -3.8e-156)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.6e-119)
		tmp = t_2;
	elseif (a <= 3.3e+54)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -230.0], t$95$1, If[LessEqual[a, -2.85e-30], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e-101], t$95$2, If[LessEqual[a, -3.8e-156], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-119], t$95$2, If[LessEqual[a, 3.3e+54], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -230 or 3.3e54 < a

   1. Initial program 71.3%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around 0 74.7%

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

      1. neg-mul-1 74.7%

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

      2. distribute-neg-frac 74.7%

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

   6. Simplified 74.7%

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

      1. frac-2neg 74.7%

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

      2. div-inv 74.6%

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

      3. remove-double-neg 74.6%

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

      4. sub-neg 74.6%

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

      5. distribute-neg-in 74.6%

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

      6. remove-double-neg 74.6%

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

   8. Applied egg-rr 74.6%

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

      1. associate-*r/ 74.7%

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

      2. *-rgt-identity 74.7%

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

      3. +-commutative 74.7%

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

      4. unsub-neg 74.7%

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

   10. Simplified 74.7%

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

   if -230 < a < -2.84999999999999989e-30

   1. Initial program 87.8%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   if -2.84999999999999989e-30 < a < -1.90000000000000005e-101 or -3.80000000000000008e-156 < a < 1.59999999999999997e-119

   1. Initial program 69.4%

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

      1. associate-*l/ 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in z around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. associate-*r/ 81.8%

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

      3. associate-*r/ 81.8%

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

      4. div-sub 81.8%

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

      5. distribute-lft-out-- 81.8%

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

      6. associate-*r/ 81.8%

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

      7. distribute-rgt-out-- 81.8%

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

      8. mul-1-neg 81.8%

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

      9. unsub-neg 81.8%

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

      10. associate-/l* 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in y around inf 86.4%

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

   if -1.90000000000000005e-101 < a < -3.80000000000000008e-156

   1. Initial program 68.6%

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

      1. associate-*l/ 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in y around inf 83.5%

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

      1. div-sub 83.5%

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

   6. Simplified 83.5%

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

   if 1.59999999999999997e-119 < a < 3.3e54

   1. Initial program 75.9%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around 0 67.4%

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

      1. associate-/l* 81.4%

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

   6. Simplified 81.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -230:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-101}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-119}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 4: 56.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-273}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -9.6e+119)
     x
     (if (<= a -1.9e-101)
       t_1
       (if (<= a -4.2e-147)
         (* y (/ (- t x) (- a z)))
         (if (<= a -1.8e-239)
           t_1
           (if (<= a 1.7e-273)
             (* (/ y z) (- x t))
             (if (<= a 6e+126) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -9.6e+119) {
		tmp = x;
	} else if (a <= -1.9e-101) {
		tmp = t_1;
	} else if (a <= -4.2e-147) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -1.8e-239) {
		tmp = t_1;
	} else if (a <= 1.7e-273) {
		tmp = (y / z) * (x - t);
	} else if (a <= 6e+126) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-9.6d+119)) then
        tmp = x
    else if (a <= (-1.9d-101)) then
        tmp = t_1
    else if (a <= (-4.2d-147)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= (-1.8d-239)) then
        tmp = t_1
    else if (a <= 1.7d-273) then
        tmp = (y / z) * (x - t)
    else if (a <= 6d+126) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -9.6e+119) {
		tmp = x;
	} else if (a <= -1.9e-101) {
		tmp = t_1;
	} else if (a <= -4.2e-147) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -1.8e-239) {
		tmp = t_1;
	} else if (a <= 1.7e-273) {
		tmp = (y / z) * (x - t);
	} else if (a <= 6e+126) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -9.6e+119:
		tmp = x
	elif a <= -1.9e-101:
		tmp = t_1
	elif a <= -4.2e-147:
		tmp = y * ((t - x) / (a - z))
	elif a <= -1.8e-239:
		tmp = t_1
	elif a <= 1.7e-273:
		tmp = (y / z) * (x - t)
	elif a <= 6e+126:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -9.6e+119)
		tmp = x;
	elseif (a <= -1.9e-101)
		tmp = t_1;
	elseif (a <= -4.2e-147)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= -1.8e-239)
		tmp = t_1;
	elseif (a <= 1.7e-273)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 6e+126)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -9.6e+119)
		tmp = x;
	elseif (a <= -1.9e-101)
		tmp = t_1;
	elseif (a <= -4.2e-147)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= -1.8e-239)
		tmp = t_1;
	elseif (a <= 1.7e-273)
		tmp = (y / z) * (x - t);
	elseif (a <= 6e+126)
		tmp = t_1;
	else
		tmp = 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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.6e+119], x, If[LessEqual[a, -1.9e-101], t$95$1, If[LessEqual[a, -4.2e-147], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.8e-239], t$95$1, If[LessEqual[a, 1.7e-273], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+126], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.6e119 or 6.0000000000000005e126 < a

   1. Initial program 71.1%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in a around inf 57.2%

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

   if -9.6e119 < a < -1.90000000000000005e-101 or -4.2e-147 < a < -1.8000000000000001e-239 or 1.69999999999999996e-273 < a < 6.0000000000000005e126

   1. Initial program 72.2%

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

      1. associate-*l/ 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around 0 52.2%

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

      1. associate-*r/ 68.9%

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

   6. Simplified 68.9%

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

   if -1.90000000000000005e-101 < a < -4.2e-147

   1. Initial program 78.7%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in y around inf 88.5%

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

      1. div-sub 88.5%

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

   6. Simplified 88.5%

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

   if -1.8000000000000001e-239 < a < 1.69999999999999996e-273

   1. Initial program 69.0%

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

      1. associate-*l/ 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in y around -inf 70.7%

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

      1. associate-*l/ 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in a around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. neg-mul-1 74.9%

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

   9. Simplified 74.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-273}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 47.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-274}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+54}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= a -1.75e+47)
     x
     (if (<= a -1e-101)
       t_1
       (if (<= a -2.9e-136)
         (/ x (/ z y))
         (if (<= a -1.75e-239)
           t_1
           (if (<= a 1.9e-274)
             (* (/ y z) (- x t))
             (if (<= a 4e+54) (/ (- t) (/ z (- y z))) x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -1.75e+47) {
		tmp = x;
	} else if (a <= -1e-101) {
		tmp = t_1;
	} else if (a <= -2.9e-136) {
		tmp = x / (z / y);
	} else if (a <= -1.75e-239) {
		tmp = t_1;
	} else if (a <= 1.9e-274) {
		tmp = (y / z) * (x - t);
	} else if (a <= 4e+54) {
		tmp = -t / (z / (y - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    if (a <= (-1.75d+47)) then
        tmp = x
    else if (a <= (-1d-101)) then
        tmp = t_1
    else if (a <= (-2.9d-136)) then
        tmp = x / (z / y)
    else if (a <= (-1.75d-239)) then
        tmp = t_1
    else if (a <= 1.9d-274) then
        tmp = (y / z) * (x - t)
    else if (a <= 4d+54) then
        tmp = -t / (z / (y - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -1.75e+47) {
		tmp = x;
	} else if (a <= -1e-101) {
		tmp = t_1;
	} else if (a <= -2.9e-136) {
		tmp = x / (z / y);
	} else if (a <= -1.75e-239) {
		tmp = t_1;
	} else if (a <= 1.9e-274) {
		tmp = (y / z) * (x - t);
	} else if (a <= 4e+54) {
		tmp = -t / (z / (y - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if a <= -1.75e+47:
		tmp = x
	elif a <= -1e-101:
		tmp = t_1
	elif a <= -2.9e-136:
		tmp = x / (z / y)
	elif a <= -1.75e-239:
		tmp = t_1
	elif a <= 1.9e-274:
		tmp = (y / z) * (x - t)
	elif a <= 4e+54:
		tmp = -t / (z / (y - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (a <= -1.75e+47)
		tmp = x;
	elseif (a <= -1e-101)
		tmp = t_1;
	elseif (a <= -2.9e-136)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= -1.75e-239)
		tmp = t_1;
	elseif (a <= 1.9e-274)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 4e+54)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (a <= -1.75e+47)
		tmp = x;
	elseif (a <= -1e-101)
		tmp = t_1;
	elseif (a <= -2.9e-136)
		tmp = x / (z / y);
	elseif (a <= -1.75e-239)
		tmp = t_1;
	elseif (a <= 1.9e-274)
		tmp = (y / z) * (x - t);
	elseif (a <= 4e+54)
		tmp = -t / (z / (y - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+47], x, If[LessEqual[a, -1e-101], t$95$1, If[LessEqual[a, -2.9e-136], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.75e-239], t$95$1, If[LessEqual[a, 1.9e-274], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+54], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.75000000000000008e47 or 4.0000000000000003e54 < a

   1. Initial program 69.5%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 53.7%

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

   if -1.75000000000000008e47 < a < -1.00000000000000005e-101 or -2.89999999999999995e-136 < a < -1.75000000000000003e-239

   1. Initial program 79.5%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around 0 56.8%

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

      1. associate-*r/ 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in a around 0 60.6%

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

      1. associate-*r/ 60.6%

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

      2. neg-mul-1 60.6%

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

   9. Simplified 60.6%

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

   if -1.00000000000000005e-101 < a < -2.89999999999999995e-136

   1. Initial program 68.5%

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

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in y around -inf 68.5%

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

      1. associate-*l/ 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in a around 0 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-*r/ 66.6%

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

      3. *-commutative 66.6%

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

      4. distribute-rgt-neg-in 66.6%

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

   9. Simplified 66.6%

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

   10. Taylor expanded in t around 0 52.4%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 83.3%

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

   12. Simplified 83.3%

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

   if -1.75000000000000003e-239 < a < 1.89999999999999992e-274

   1. Initial program 69.0%

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

      1. associate-*l/ 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in y around -inf 70.7%

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

      1. associate-*l/ 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in a around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. neg-mul-1 74.9%

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

   9. Simplified 74.9%

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

   if 1.89999999999999992e-274 < a < 4.0000000000000003e54

   1. Initial program 71.0%

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

      1. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in x around 0 55.6%

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

      1. associate-/l* 73.3%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in a around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. associate-/l* 56.1%

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

      3. distribute-neg-frac 56.1%

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

   9. Simplified 56.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-274}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+54}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 47.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-274}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= a -1.95e+48)
     x
     (if (<= a -1e-101)
       t_1
       (if (<= a -2.9e-136)
         (/ x (/ z y))
         (if (<= a -1.75e-239)
           t_1
           (if (<= a 1.8e-274)
             (* (/ y z) (- x t))
             (if (<= a 5.5e+54) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -1.95e+48) {
		tmp = x;
	} else if (a <= -1e-101) {
		tmp = t_1;
	} else if (a <= -2.9e-136) {
		tmp = x / (z / y);
	} else if (a <= -1.75e-239) {
		tmp = t_1;
	} else if (a <= 1.8e-274) {
		tmp = (y / z) * (x - t);
	} else if (a <= 5.5e+54) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    if (a <= (-1.95d+48)) then
        tmp = x
    else if (a <= (-1d-101)) then
        tmp = t_1
    else if (a <= (-2.9d-136)) then
        tmp = x / (z / y)
    else if (a <= (-1.75d-239)) then
        tmp = t_1
    else if (a <= 1.8d-274) then
        tmp = (y / z) * (x - t)
    else if (a <= 5.5d+54) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -1.95e+48) {
		tmp = x;
	} else if (a <= -1e-101) {
		tmp = t_1;
	} else if (a <= -2.9e-136) {
		tmp = x / (z / y);
	} else if (a <= -1.75e-239) {
		tmp = t_1;
	} else if (a <= 1.8e-274) {
		tmp = (y / z) * (x - t);
	} else if (a <= 5.5e+54) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if a <= -1.95e+48:
		tmp = x
	elif a <= -1e-101:
		tmp = t_1
	elif a <= -2.9e-136:
		tmp = x / (z / y)
	elif a <= -1.75e-239:
		tmp = t_1
	elif a <= 1.8e-274:
		tmp = (y / z) * (x - t)
	elif a <= 5.5e+54:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (a <= -1.95e+48)
		tmp = x;
	elseif (a <= -1e-101)
		tmp = t_1;
	elseif (a <= -2.9e-136)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= -1.75e-239)
		tmp = t_1;
	elseif (a <= 1.8e-274)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 5.5e+54)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (a <= -1.95e+48)
		tmp = x;
	elseif (a <= -1e-101)
		tmp = t_1;
	elseif (a <= -2.9e-136)
		tmp = x / (z / y);
	elseif (a <= -1.75e-239)
		tmp = t_1;
	elseif (a <= 1.8e-274)
		tmp = (y / z) * (x - t);
	elseif (a <= 5.5e+54)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e+48], x, If[LessEqual[a, -1e-101], t$95$1, If[LessEqual[a, -2.9e-136], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.75e-239], t$95$1, If[LessEqual[a, 1.8e-274], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+54], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.95e48 or 5.50000000000000026e54 < a

   1. Initial program 69.5%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 53.7%

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

   if -1.95e48 < a < -1.00000000000000005e-101 or -2.89999999999999995e-136 < a < -1.75000000000000003e-239 or 1.79999999999999991e-274 < a < 5.50000000000000026e54

   1. Initial program 74.2%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around 0 56.1%

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

      1. associate-*r/ 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in a around 0 57.7%

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

      1. associate-*r/ 57.7%

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

      2. neg-mul-1 57.7%

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

   9. Simplified 57.7%

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

   if -1.00000000000000005e-101 < a < -2.89999999999999995e-136

   1. Initial program 68.5%

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

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in y around -inf 68.5%

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

      1. associate-*l/ 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in a around 0 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-*r/ 66.6%

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

      3. *-commutative 66.6%

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

      4. distribute-rgt-neg-in 66.6%

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

   9. Simplified 66.6%

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

   10. Taylor expanded in t around 0 52.4%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 83.3%

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

   12. Simplified 83.3%

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

   if -1.75000000000000003e-239 < a < 1.79999999999999991e-274

   1. Initial program 69.0%

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

      1. associate-*l/ 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in y around -inf 70.7%

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

      1. associate-*l/ 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in a around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. neg-mul-1 74.9%

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

   9. Simplified 74.9%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-274}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 37.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-291}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-240}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a - z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2e+31)
   (* (- t x) (/ y a))
   (if (<= y -8e-291)
     t
     (if (<= y 3.1e-240)
       (/ (* t (- z)) (- a z))
       (if (<= y 2.7e-100) t (if (<= y 7000.0) x (/ t (/ (- a z) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2e+31) {
		tmp = (t - x) * (y / a);
	} else if (y <= -8e-291) {
		tmp = t;
	} else if (y <= 3.1e-240) {
		tmp = (t * -z) / (a - z);
	} else if (y <= 2.7e-100) {
		tmp = t;
	} else if (y <= 7000.0) {
		tmp = x;
	} else {
		tmp = t / ((a - z) / y);
	}
	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 (y <= (-2d+31)) then
        tmp = (t - x) * (y / a)
    else if (y <= (-8d-291)) then
        tmp = t
    else if (y <= 3.1d-240) then
        tmp = (t * -z) / (a - z)
    else if (y <= 2.7d-100) then
        tmp = t
    else if (y <= 7000.0d0) then
        tmp = x
    else
        tmp = t / ((a - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2e+31) {
		tmp = (t - x) * (y / a);
	} else if (y <= -8e-291) {
		tmp = t;
	} else if (y <= 3.1e-240) {
		tmp = (t * -z) / (a - z);
	} else if (y <= 2.7e-100) {
		tmp = t;
	} else if (y <= 7000.0) {
		tmp = x;
	} else {
		tmp = t / ((a - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2e+31:
		tmp = (t - x) * (y / a)
	elif y <= -8e-291:
		tmp = t
	elif y <= 3.1e-240:
		tmp = (t * -z) / (a - z)
	elif y <= 2.7e-100:
		tmp = t
	elif y <= 7000.0:
		tmp = x
	else:
		tmp = t / ((a - z) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2e+31)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (y <= -8e-291)
		tmp = t;
	elseif (y <= 3.1e-240)
		tmp = Float64(Float64(t * Float64(-z)) / Float64(a - z));
	elseif (y <= 2.7e-100)
		tmp = t;
	elseif (y <= 7000.0)
		tmp = x;
	else
		tmp = Float64(t / Float64(Float64(a - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2e+31)
		tmp = (t - x) * (y / a);
	elseif (y <= -8e-291)
		tmp = t;
	elseif (y <= 3.1e-240)
		tmp = (t * -z) / (a - z);
	elseif (y <= 2.7e-100)
		tmp = t;
	elseif (y <= 7000.0)
		tmp = x;
	else
		tmp = t / ((a - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2e+31], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-291], t, If[LessEqual[y, 3.1e-240], N[(N[(t * (-z)), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-100], t, If[LessEqual[y, 7000.0], x, N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.9999999999999999e31

   1. Initial program 71.7%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around -inf 56.0%

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

      1. associate-*l/ 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in a around inf 44.6%

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

   if -1.9999999999999999e31 < y < -7.9999999999999997e-291 or 3.10000000000000017e-240 < y < 2.70000000000000016e-100

   1. Initial program 66.8%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 47.9%

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

   if -7.9999999999999997e-291 < y < 3.10000000000000017e-240

   1. Initial program 87.9%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around 0 54.9%

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

      1. associate-*r/ 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in y around 0 54.9%

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

      1. mul-1-neg 54.9%

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

   9. Simplified 54.9%

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

   if 2.70000000000000016e-100 < y < 7e3

   1. Initial program 72.7%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around inf 48.9%

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

   if 7e3 < y

   1. Initial program 73.8%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y around inf 47.6%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-291}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-240}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a - z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 8: 56.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-274}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -1.7e+120)
     x
     (if (<= a -1.75e-239)
       t_1
       (if (<= a 1.9e-274) (* (/ y z) (- x t)) (if (<= a 9.2e+126) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.7e+120) {
		tmp = x;
	} else if (a <= -1.75e-239) {
		tmp = t_1;
	} else if (a <= 1.9e-274) {
		tmp = (y / z) * (x - t);
	} else if (a <= 9.2e+126) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-1.7d+120)) then
        tmp = x
    else if (a <= (-1.75d-239)) then
        tmp = t_1
    else if (a <= 1.9d-274) then
        tmp = (y / z) * (x - t)
    else if (a <= 9.2d+126) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.7e+120) {
		tmp = x;
	} else if (a <= -1.75e-239) {
		tmp = t_1;
	} else if (a <= 1.9e-274) {
		tmp = (y / z) * (x - t);
	} else if (a <= 9.2e+126) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -1.7e+120:
		tmp = x
	elif a <= -1.75e-239:
		tmp = t_1
	elif a <= 1.9e-274:
		tmp = (y / z) * (x - t)
	elif a <= 9.2e+126:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.7e+120)
		tmp = x;
	elseif (a <= -1.75e-239)
		tmp = t_1;
	elseif (a <= 1.9e-274)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 9.2e+126)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -1.7e+120)
		tmp = x;
	elseif (a <= -1.75e-239)
		tmp = t_1;
	elseif (a <= 1.9e-274)
		tmp = (y / z) * (x - t);
	elseif (a <= 9.2e+126)
		tmp = t_1;
	else
		tmp = 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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+120], x, If[LessEqual[a, -1.75e-239], t$95$1, If[LessEqual[a, 1.9e-274], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+126], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999999e120 or 9.2000000000000002e126 < a

   1. Initial program 71.1%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in a around inf 57.2%

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

   if -1.69999999999999999e120 < a < -1.75000000000000003e-239 or 1.89999999999999992e-274 < a < 9.2000000000000002e126

   1. Initial program 72.5%

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

      1. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in x around 0 50.7%

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

      1. associate-*r/ 66.5%

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

   6. Simplified 66.5%

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

   if -1.75000000000000003e-239 < a < 1.89999999999999992e-274

   1. Initial program 69.0%

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

      1. associate-*l/ 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in y around -inf 70.7%

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

      1. associate-*l/ 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in a around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. neg-mul-1 74.9%

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

   9. Simplified 74.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-274}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+38}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -2.25e-29)
     t_1
     (if (<= z 2.8e-14)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 2.05e+38) (+ x (* (- t x) (/ z (- z a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -2.25e-29) {
		tmp = t_1;
	} else if (z <= 2.8e-14) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2.05e+38) {
		tmp = x + ((t - x) * (z / (z - a)));
	} 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 + ((x - t) / (z / (y - a)))
    if (z <= (-2.25d-29)) then
        tmp = t_1
    else if (z <= 2.8d-14) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 2.05d+38) then
        tmp = x + ((t - x) * (z / (z - a)))
    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 + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -2.25e-29) {
		tmp = t_1;
	} else if (z <= 2.8e-14) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2.05e+38) {
		tmp = x + ((t - x) * (z / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -2.25e-29:
		tmp = t_1
	elif z <= 2.8e-14:
		tmp = x + ((t - x) * (y / a))
	elif z <= 2.05e+38:
		tmp = x + ((t - x) * (z / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -2.25e-29)
		tmp = t_1;
	elseif (z <= 2.8e-14)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 2.05e+38)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(z / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -2.25e-29)
		tmp = t_1;
	elseif (z <= 2.8e-14)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 2.05e+38)
		tmp = x + ((t - x) * (z / (z - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-29], t$95$1, If[LessEqual[z, 2.8e-14], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+38], N[(x + N[(N[(t - x), $MachinePrecision] * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e-29 or 2.0500000000000002e38 < 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. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in z around inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. associate-*r/ 63.4%

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

      3. associate-*r/ 63.4%

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

      4. div-sub 63.4%

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

      5. distribute-lft-out-- 63.4%

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

      6. associate-*r/ 63.4%

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

      7. distribute-rgt-out-- 63.4%

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

      8. mul-1-neg 63.4%

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

      9. unsub-neg 63.4%

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

      10. associate-/l* 76.2%

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

   6. Simplified 76.2%

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

   if -2.2499999999999999e-29 < z < 2.8000000000000001e-14

   1. Initial program 91.0%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 78.1%

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

   if 2.8000000000000001e-14 < z < 2.0500000000000002e38

   1. Initial program 92.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 84.8%

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

      1. neg-mul-1 84.8%

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

      2. distribute-neg-frac 84.8%

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

   6. Simplified 84.8%

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

      1. frac-2neg 84.8%

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

      2. div-inv 84.8%

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

      3. remove-double-neg 84.8%

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

      4. sub-neg 84.8%

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

      5. distribute-neg-in 84.8%

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

      6. remove-double-neg 84.8%

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

   8. Applied egg-rr 84.8%

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

      1. associate-*r/ 84.8%

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

      2. *-rgt-identity 84.8%

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

      3. +-commutative 84.8%

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

      4. unsub-neg 84.8%

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

   10. Simplified 84.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+38}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 10: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+36}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -5.4e-32)
     t_1
     (if (<= z 4.6e-14)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 2e+36) (+ x (* z (/ (- x t) (- a z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -5.4e-32) {
		tmp = t_1;
	} else if (z <= 4.6e-14) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2e+36) {
		tmp = x + (z * ((x - t) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / (y - a)))
    if (z <= (-5.4d-32)) then
        tmp = t_1
    else if (z <= 4.6d-14) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 2d+36) then
        tmp = x + (z * ((x - t) / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -5.4e-32) {
		tmp = t_1;
	} else if (z <= 4.6e-14) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2e+36) {
		tmp = x + (z * ((x - t) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -5.4e-32:
		tmp = t_1
	elif z <= 4.6e-14:
		tmp = x + ((t - x) * (y / a))
	elif z <= 2e+36:
		tmp = x + (z * ((x - t) / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -5.4e-32)
		tmp = t_1;
	elseif (z <= 4.6e-14)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 2e+36)
		tmp = Float64(x + Float64(z * Float64(Float64(x - t) / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -5.4e-32)
		tmp = t_1;
	elseif (z <= 4.6e-14)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 2e+36)
		tmp = x + (z * ((x - t) / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-32], t$95$1, If[LessEqual[z, 4.6e-14], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+36], N[(x + N[(z * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999962e-32 or 2.00000000000000008e36 < 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. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in z around inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. associate-*r/ 63.4%

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

      3. associate-*r/ 63.4%

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

      4. div-sub 63.4%

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

      5. distribute-lft-out-- 63.4%

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

      6. associate-*r/ 63.4%

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

      7. distribute-rgt-out-- 63.4%

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

      8. mul-1-neg 63.4%

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

      9. unsub-neg 63.4%

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

      10. associate-/l* 76.2%

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

   6. Simplified 76.2%

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

   if -5.39999999999999962e-32 < z < 4.59999999999999996e-14

   1. Initial program 91.0%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 78.1%

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

   if 4.59999999999999996e-14 < z < 2.00000000000000008e36

   1. Initial program 92.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. associate-*r/ 85.0%

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

      3. unsub-neg 85.0%

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

   6. Simplified 85.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-32}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+36}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 11: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-101}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))))
   (if (<= a -2.7e-30)
     x
     (if (<= a -1.15e-101)
       t
       (if (<= a -9.5e-174)
         t_1
         (if (<= a -1.75e-239)
           t
           (if (<= a 1.25e-269) t_1 (if (<= a 5.3e+54) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z / y);
	double tmp;
	if (a <= -2.7e-30) {
		tmp = x;
	} else if (a <= -1.15e-101) {
		tmp = t;
	} else if (a <= -9.5e-174) {
		tmp = t_1;
	} else if (a <= -1.75e-239) {
		tmp = t;
	} else if (a <= 1.25e-269) {
		tmp = t_1;
	} else if (a <= 5.3e+54) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / y)
    if (a <= (-2.7d-30)) then
        tmp = x
    else if (a <= (-1.15d-101)) then
        tmp = t
    else if (a <= (-9.5d-174)) then
        tmp = t_1
    else if (a <= (-1.75d-239)) then
        tmp = t
    else if (a <= 1.25d-269) then
        tmp = t_1
    else if (a <= 5.3d+54) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z / y);
	double tmp;
	if (a <= -2.7e-30) {
		tmp = x;
	} else if (a <= -1.15e-101) {
		tmp = t;
	} else if (a <= -9.5e-174) {
		tmp = t_1;
	} else if (a <= -1.75e-239) {
		tmp = t;
	} else if (a <= 1.25e-269) {
		tmp = t_1;
	} else if (a <= 5.3e+54) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z / y)
	tmp = 0
	if a <= -2.7e-30:
		tmp = x
	elif a <= -1.15e-101:
		tmp = t
	elif a <= -9.5e-174:
		tmp = t_1
	elif a <= -1.75e-239:
		tmp = t
	elif a <= 1.25e-269:
		tmp = t_1
	elif a <= 5.3e+54:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (a <= -2.7e-30)
		tmp = x;
	elseif (a <= -1.15e-101)
		tmp = t;
	elseif (a <= -9.5e-174)
		tmp = t_1;
	elseif (a <= -1.75e-239)
		tmp = t;
	elseif (a <= 1.25e-269)
		tmp = t_1;
	elseif (a <= 5.3e+54)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (z / y);
	tmp = 0.0;
	if (a <= -2.7e-30)
		tmp = x;
	elseif (a <= -1.15e-101)
		tmp = t;
	elseif (a <= -9.5e-174)
		tmp = t_1;
	elseif (a <= -1.75e-239)
		tmp = t;
	elseif (a <= 1.25e-269)
		tmp = t_1;
	elseif (a <= 5.3e+54)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e-30], x, If[LessEqual[a, -1.15e-101], t, If[LessEqual[a, -9.5e-174], t$95$1, If[LessEqual[a, -1.75e-239], t, If[LessEqual[a, 1.25e-269], t$95$1, If[LessEqual[a, 5.3e+54], t, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.69999999999999987e-30 or 5.30000000000000018e54 < a

   1. Initial program 72.4%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around inf 50.2%

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

   if -2.69999999999999987e-30 < a < -1.15e-101 or -9.50000000000000075e-174 < a < -1.75000000000000003e-239 or 1.24999999999999995e-269 < a < 5.30000000000000018e54

   1. Initial program 70.9%

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

      1. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in z around inf 47.4%

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

   if -1.15e-101 < a < -9.50000000000000075e-174 or -1.75000000000000003e-239 < a < 1.24999999999999995e-269

   1. Initial program 72.1%

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

      1. associate-*l/ 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in y around -inf 70.6%

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

      1. associate-*l/ 77.7%

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

   6. Simplified 77.7%

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

   7. Taylor expanded in a around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. associate-*r/ 64.7%

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

      3. *-commutative 64.7%

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

      4. distribute-rgt-neg-in 64.7%

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

   9. Simplified 64.7%

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

   10. Taylor expanded in t around 0 42.1%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 51.9%

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

   12. Simplified 51.9%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-101}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-239}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-269}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 48.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= a -6.5e+48)
     x
     (if (<= a -1e-101)
       t_1
       (if (<= a -2.8e-136) (/ x (/ z y)) (if (<= a 3.8e+54) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -6.5e+48) {
		tmp = x;
	} else if (a <= -1e-101) {
		tmp = t_1;
	} else if (a <= -2.8e-136) {
		tmp = x / (z / y);
	} else if (a <= 3.8e+54) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    if (a <= (-6.5d+48)) then
        tmp = x
    else if (a <= (-1d-101)) then
        tmp = t_1
    else if (a <= (-2.8d-136)) then
        tmp = x / (z / y)
    else if (a <= 3.8d+54) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -6.5e+48) {
		tmp = x;
	} else if (a <= -1e-101) {
		tmp = t_1;
	} else if (a <= -2.8e-136) {
		tmp = x / (z / y);
	} else if (a <= 3.8e+54) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if a <= -6.5e+48:
		tmp = x
	elif a <= -1e-101:
		tmp = t_1
	elif a <= -2.8e-136:
		tmp = x / (z / y)
	elif a <= 3.8e+54:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (a <= -6.5e+48)
		tmp = x;
	elseif (a <= -1e-101)
		tmp = t_1;
	elseif (a <= -2.8e-136)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 3.8e+54)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (a <= -6.5e+48)
		tmp = x;
	elseif (a <= -1e-101)
		tmp = t_1;
	elseif (a <= -2.8e-136)
		tmp = x / (z / y);
	elseif (a <= 3.8e+54)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+48], x, If[LessEqual[a, -1e-101], t$95$1, If[LessEqual[a, -2.8e-136], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+54], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.49999999999999972e48 or 3.8000000000000002e54 < a

   1. Initial program 69.5%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 53.7%

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

   if -6.49999999999999972e48 < a < -1.00000000000000005e-101 or -2.8000000000000001e-136 < a < 3.8000000000000002e54

   1. Initial program 73.4%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around 0 54.8%

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

      1. associate-*r/ 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in a around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

   9. Simplified 56.8%

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

   if -1.00000000000000005e-101 < a < -2.8000000000000001e-136

   1. Initial program 68.5%

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

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in y around -inf 68.5%

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

      1. associate-*l/ 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in a around 0 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-*r/ 66.6%

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

      3. *-commutative 66.6%

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

      4. distribute-rgt-neg-in 66.6%

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

   9. Simplified 66.6%

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

   10. Taylor expanded in t around 0 52.4%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   11. Step-by-step derivation

       1. associate-/l* 83.3%

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

   12. Simplified 83.3%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 57.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+29}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -3.6e-94)
     t_1
     (if (<= t -1.6e-183) x (if (<= t 5e+29) (* (- t x) (/ y (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.6e-94) {
		tmp = t_1;
	} else if (t <= -1.6e-183) {
		tmp = x;
	} else if (t <= 5e+29) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-3.6d-94)) then
        tmp = t_1
    else if (t <= (-1.6d-183)) then
        tmp = x
    else if (t <= 5d+29) then
        tmp = (t - x) * (y / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.6e-94) {
		tmp = t_1;
	} else if (t <= -1.6e-183) {
		tmp = x;
	} else if (t <= 5e+29) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -3.6e-94:
		tmp = t_1
	elif t <= -1.6e-183:
		tmp = x
	elif t <= 5e+29:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -3.6e-94)
		tmp = t_1;
	elseif (t <= -1.6e-183)
		tmp = x;
	elseif (t <= 5e+29)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -3.6e-94)
		tmp = t_1;
	elseif (t <= -1.6e-183)
		tmp = x;
	elseif (t <= 5e+29)
		tmp = (t - x) * (y / (a - z));
	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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e-94], t$95$1, If[LessEqual[t, -1.6e-183], x, If[LessEqual[t, 5e+29], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6e-94 or 5.0000000000000001e29 < t

   1. Initial program 67.4%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around 0 48.9%

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

      1. associate-*r/ 70.7%

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

   6. Simplified 70.7%

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

   if -3.6e-94 < t < -1.6000000000000001e-183

   1. Initial program 95.6%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around inf 70.6%

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

   if -1.6000000000000001e-183 < t < 5.0000000000000001e29

   1. Initial program 75.3%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in y around -inf 43.0%

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

      1. associate-*l/ 46.6%

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

   6. Simplified 46.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+29}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 14: 36.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-101}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 720000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -7.5e+50)
     t_1
     (if (<= y 2.15e-101) t (if (<= y 720000000000.0) x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -7.5e+50) {
		tmp = t_1;
	} else if (y <= 2.15e-101) {
		tmp = t;
	} else if (y <= 720000000000.0) {
		tmp = 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 / (a - z))
    if (y <= (-7.5d+50)) then
        tmp = t_1
    else if (y <= 2.15d-101) then
        tmp = t
    else if (y <= 720000000000.0d0) then
        tmp = 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 / (a - z));
	double tmp;
	if (y <= -7.5e+50) {
		tmp = t_1;
	} else if (y <= 2.15e-101) {
		tmp = t;
	} else if (y <= 720000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -7.5e+50:
		tmp = t_1
	elif y <= 2.15e-101:
		tmp = t
	elif y <= 720000000000.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -7.5e+50)
		tmp = t_1;
	elseif (y <= 2.15e-101)
		tmp = t;
	elseif (y <= 720000000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -7.5e+50)
		tmp = t_1;
	elseif (y <= 2.15e-101)
		tmp = t;
	elseif (y <= 720000000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+50], t$95$1, If[LessEqual[y, 2.15e-101], t, If[LessEqual[y, 720000000000.0], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999999e50 or 7.2e11 < y

   1. Initial program 73.3%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around -inf 61.5%

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

      1. associate-*l/ 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in t around inf 36.2%

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

      1. associate-*r/ 43.4%

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

   9. Simplified 43.4%

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

   if -7.4999999999999999e50 < y < 2.1499999999999999e-101

   1. Initial program 70.4%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around inf 44.0%

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

   if 2.1499999999999999e-101 < y < 7.2e11

   1. Initial program 72.7%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around inf 48.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-101}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 720000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 15: 37.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-103}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.55e+31)
   (* (- t x) (/ y a))
   (if (<= y 1.05e-103) t (if (<= y 1.4) x (* t (/ y (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+31) {
		tmp = (t - x) * (y / a);
	} else if (y <= 1.05e-103) {
		tmp = t;
	} else if (y <= 1.4) {
		tmp = x;
	} else {
		tmp = t * (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) :: tmp
    if (y <= (-1.55d+31)) then
        tmp = (t - x) * (y / a)
    else if (y <= 1.05d-103) then
        tmp = t
    else if (y <= 1.4d0) then
        tmp = x
    else
        tmp = t * (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 tmp;
	if (y <= -1.55e+31) {
		tmp = (t - x) * (y / a);
	} else if (y <= 1.05e-103) {
		tmp = t;
	} else if (y <= 1.4) {
		tmp = x;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.55e+31:
		tmp = (t - x) * (y / a)
	elif y <= 1.05e-103:
		tmp = t
	elif y <= 1.4:
		tmp = x
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.55e+31)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (y <= 1.05e-103)
		tmp = t;
	elseif (y <= 1.4)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.55e+31)
		tmp = (t - x) * (y / a);
	elseif (y <= 1.05e-103)
		tmp = t;
	elseif (y <= 1.4)
		tmp = x;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.55e+31], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-103], t, If[LessEqual[y, 1.4], x, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5500000000000001e31

   1. Initial program 71.7%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around -inf 56.0%

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

      1. associate-*l/ 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in a around inf 44.6%

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

   if -1.5500000000000001e31 < y < 1.05000000000000002e-103

   1. Initial program 70.8%

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

      1. associate-*l/ 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in z around inf 45.1%

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

   if 1.05000000000000002e-103 < y < 1.3999999999999999

   1. Initial program 72.7%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around inf 48.9%

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

   if 1.3999999999999999 < y

   1. Initial program 73.8%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around -inf 64.5%

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

      1. associate-*l/ 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in t around inf 40.3%

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

      1. associate-*r/ 47.6%

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

   9. Simplified 47.6%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-103}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 16: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-103}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 52000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.55e+31)
   (* (- t x) (/ y a))
   (if (<= y 1.82e-103) t (if (<= y 52000000.0) x (/ t (/ (- a z) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+31) {
		tmp = (t - x) * (y / a);
	} else if (y <= 1.82e-103) {
		tmp = t;
	} else if (y <= 52000000.0) {
		tmp = x;
	} else {
		tmp = t / ((a - z) / y);
	}
	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 (y <= (-1.55d+31)) then
        tmp = (t - x) * (y / a)
    else if (y <= 1.82d-103) then
        tmp = t
    else if (y <= 52000000.0d0) then
        tmp = x
    else
        tmp = t / ((a - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+31) {
		tmp = (t - x) * (y / a);
	} else if (y <= 1.82e-103) {
		tmp = t;
	} else if (y <= 52000000.0) {
		tmp = x;
	} else {
		tmp = t / ((a - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.55e+31:
		tmp = (t - x) * (y / a)
	elif y <= 1.82e-103:
		tmp = t
	elif y <= 52000000.0:
		tmp = x
	else:
		tmp = t / ((a - z) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.55e+31)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (y <= 1.82e-103)
		tmp = t;
	elseif (y <= 52000000.0)
		tmp = x;
	else
		tmp = Float64(t / Float64(Float64(a - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.55e+31)
		tmp = (t - x) * (y / a);
	elseif (y <= 1.82e-103)
		tmp = t;
	elseif (y <= 52000000.0)
		tmp = x;
	else
		tmp = t / ((a - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.55e+31], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.82e-103], t, If[LessEqual[y, 52000000.0], x, N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5500000000000001e31

   1. Initial program 71.7%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around -inf 56.0%

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

      1. associate-*l/ 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in a around inf 44.6%

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

   if -1.5500000000000001e31 < y < 1.8199999999999999e-103

   1. Initial program 70.8%

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

      1. associate-*l/ 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in z around inf 45.1%

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

   if 1.8199999999999999e-103 < y < 5.2e7

   1. Initial program 72.7%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around inf 48.9%

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

   if 5.2e7 < y

   1. Initial program 73.8%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y around inf 47.6%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-103}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 52000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 17: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-8} \lor \neg \left(z \leq 5.5 \cdot 10^{-46}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e-8) (not (<= z 5.5e-46)))
   (* 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 <= -5.8e-8) || !(z <= 5.5e-46)) {
		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 <= (-5.8d-8)) .or. (.not. (z <= 5.5d-46))) 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 <= -5.8e-8) || !(z <= 5.5e-46)) {
		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 <= -5.8e-8) or not (z <= 5.5e-46):
		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 <= -5.8e-8) || !(z <= 5.5e-46))
		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 <= -5.8e-8) || ~((z <= 5.5e-46)))
		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, -5.8e-8], N[Not[LessEqual[z, 5.5e-46]], $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 < -5.8000000000000003e-8 or 5.49999999999999983e-46 < z

   1. Initial program 56.4%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in x around 0 44.3%

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

      1. associate-*r/ 66.1%

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

   6. Simplified 66.1%

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

   if -5.8000000000000003e-8 < z < 5.49999999999999983e-46

   1. Initial program 94.3%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around 0 79.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-8} \lor \neg \left(z \leq 5.5 \cdot 10^{-46}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 18: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-15}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e-7)
   (* t (/ (- y z) (- a z)))
   (if (<= z 9.2e-15) (+ x (* (- t x) (/ y a))) (+ t (/ (- x t) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e-7) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 9.2e-15) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	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 <= (-7.2d-7)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 9.2d-15) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + ((x - t) / (z / y))
    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 <= -7.2e-7) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 9.2e-15) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e-7:
		tmp = t * ((y - z) / (a - z))
	elif z <= 9.2e-15:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e-7)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 9.2e-15)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e-7)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 9.2e-15)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e-7], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-15], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999989e-7

   1. Initial program 52.6%

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

      1. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in x around 0 41.3%

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

      1. associate-*r/ 70.3%

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

   6. Simplified 70.3%

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

   if -7.19999999999999989e-7 < z < 9.19999999999999961e-15

   1. Initial program 91.3%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 78.0%

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

   if 9.19999999999999961e-15 < z

   1. Initial program 60.9%

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

      1. associate-*l/ 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in z around inf 59.7%

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

      1. associate--l+ 59.7%

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

      2. associate-*r/ 59.7%

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

      3. associate-*r/ 59.7%

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

      4. div-sub 59.7%

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

      5. distribute-lft-out-- 59.7%

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

      6. associate-*r/ 59.7%

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

      7. distribute-rgt-out-- 59.7%

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

      8. mul-1-neg 59.7%

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

      9. unsub-neg 59.7%

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

      10. associate-/l* 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in y around inf 65.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-15}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 19: 38.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.75e-30) x (if (<= a 3.2e+54) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.75e-30) {
		tmp = x;
	} else if (a <= 3.2e+54) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.75d-30)) then
        tmp = x
    else if (a <= 3.2d+54) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.75e-30) {
		tmp = x;
	} else if (a <= 3.2e+54) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.75e-30:
		tmp = x
	elif a <= 3.2e+54:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.75e-30)
		tmp = x;
	elseif (a <= 3.2e+54)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.75e-30)
		tmp = x;
	elseif (a <= 3.2e+54)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.75e-30], x, If[LessEqual[a, 3.2e+54], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.74999999999999988e-30 or 3.2e54 < a

   1. Initial program 72.4%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around inf 50.2%

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

   if -2.74999999999999988e-30 < a < 3.2e54

   1. Initial program 71.2%

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

      1. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in z around inf 40.4%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.0% 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 71.8%

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

   1. associate-*l/ 86.6%

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

3. Simplified 86.6%

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

4. Taylor expanded in z around inf 29.2%

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

5. Final simplification 29.2%

   \[\leadsto t \]

Developer target: 83.8% 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 2023318 
(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))))