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

Percentage Accurate: 68.3% → 88.9%

Time: 14.4s

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: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+215} \lor \neg \left(z \leq 1.38 \cdot 10^{+129}\right):\\ \;\;\;\;\left(t + \frac{y}{z} \cdot \left(x - t\right)\right) + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\left(a - z\right) \cdot \frac{1}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e+215) (not (<= z 1.38e+129)))
   (+ (+ t (* (/ y z) (- x t))) (/ a (/ z (- t x))))
   (- x (/ (- x t) (* (- a z) (/ 1.0 (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+215) || !(z <= 1.38e+129)) {
		tmp = (t + ((y / z) * (x - t))) + (a / (z / (t - x)));
	} else {
		tmp = x - ((x - t) / ((a - z) * (1.0 / (y - z))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7d+215)) .or. (.not. (z <= 1.38d+129))) then
        tmp = (t + ((y / z) * (x - t))) + (a / (z / (t - x)))
    else
        tmp = x - ((x - t) / ((a - z) * (1.0d0 / (y - z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+215) || !(z <= 1.38e+129)) {
		tmp = (t + ((y / z) * (x - t))) + (a / (z / (t - x)));
	} else {
		tmp = x - ((x - t) / ((a - z) * (1.0 / (y - z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e+215) or not (z <= 1.38e+129):
		tmp = (t + ((y / z) * (x - t))) + (a / (z / (t - x)))
	else:
		tmp = x - ((x - t) / ((a - z) * (1.0 / (y - z))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e+215) || !(z <= 1.38e+129))
		tmp = Float64(Float64(t + Float64(Float64(y / z) * Float64(x - t))) + Float64(a / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) * Float64(1.0 / Float64(y - z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7e+215) || ~((z <= 1.38e+129)))
		tmp = (t + ((y / z) * (x - t))) + (a / (z / (t - x)));
	else
		tmp = x - ((x - t) / ((a - z) * (1.0 / (y - z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7e+215], N[Not[LessEqual[z, 1.38e+129]], $MachinePrecision]], N[(N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] * N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999954e215 or 1.3800000000000001e129 < z

   1. Initial program 18.9%

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

      1. associate-*l/ 58.1%

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

   3. Simplified 58.1%

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

      1. *-commutative 58.1%

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

      2. clear-num 58.0%

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

      3. un-div-inv 58.1%

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

   5. Applied egg-rr 58.1%

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

   6. Taylor expanded in z around inf 69.5%

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

      1. sub-neg 69.5%

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

      2. +-commutative 69.5%

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

      3. mul-1-neg 69.5%

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

      4. unsub-neg 69.5%

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

      5. associate-/l* 75.8%

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

      6. associate-/r/ 80.6%

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

      7. mul-1-neg 80.6%

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

      8. remove-double-neg 80.6%

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

      9. associate-/l* 91.9%

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

   8. Simplified 91.9%

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

   if -6.99999999999999954e215 < z < 1.3800000000000001e129

   1. Initial program 80.7%

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

      1. *-commutative 89.7%

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

      2. clear-num 89.6%

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

      3. un-div-inv 89.9%

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

   5. Applied egg-rr 89.9%

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

      1. div-inv 89.9%

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

   7. Applied egg-rr 89.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+215} \lor \neg \left(z \leq 1.38 \cdot 10^{+129}\right):\\ \;\;\;\;\left(t + \frac{y}{z} \cdot \left(x - t\right)\right) + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\left(a - z\right) \cdot \frac{1}{y - z}}\\ \end{array} \]

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-277} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- t x) (- y z)) (- a z)))))
   (if (or (<= t_1 -1e-277) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-277) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((t - x) * (y - z)) / (a - z))
    if ((t_1 <= (-1d-277)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-277) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - x) * (y - z)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-277) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-277) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - x) * (y - z)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-277) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-277], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999969e-278 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 71.5%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   if -9.99999999999999969e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.8%

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

      1. associate-*l/ 4.8%

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

   3. Simplified 4.8%

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

   4. Taylor expanded in z around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. mul-1-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-rgt-out-- 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq -1 \cdot 10^{-277} \lor \neg \left(x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 3: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-277}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- t x) (- y z)) (- a z)))))
   (if (<= t_1 -1e-277)
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if (t_1 <= -1e-277) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((t - x) * (y - z)) / (a - z))
    if (t_1 <= (-1d-277)) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else if (t_1 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if (t_1 <= -1e-277) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - x) * (y - z)) / (a - z))
	tmp = 0
	if t_1 <= -1e-277:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	elif t_1 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-277)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - x) * (y - z)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -1e-277)
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-277], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999969e-278

   1. Initial program 70.1%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

   if -9.99999999999999969e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.8%

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

      1. associate-*l/ 4.8%

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

   3. Simplified 4.8%

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

   4. Taylor expanded in z around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. mul-1-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-rgt-out-- 100.0%

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

   6. Simplified 100.0%

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

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

   1. Initial program 72.6%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

      1. *-commutative 87.8%

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

      2. clear-num 87.7%

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

      3. un-div-inv 88.1%

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

   5. Applied egg-rr 88.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq -1 \cdot 10^{-277}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 4: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-277}:\\ \;\;\;\;x - \frac{x - t}{\left(a - z\right) \cdot \frac{1}{y - z}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- t x) (- y z)) (- a z)))))
   (if (<= t_1 -1e-277)
     (- x (/ (- x t) (* (- a z) (/ 1.0 (- y z)))))
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if (t_1 <= -1e-277) {
		tmp = x - ((x - t) / ((a - z) * (1.0 / (y - z))));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((t - x) * (y - z)) / (a - z))
    if (t_1 <= (-1d-277)) then
        tmp = x - ((x - t) / ((a - z) * (1.0d0 / (y - z))))
    else if (t_1 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) * (y - z)) / (a - z));
	double tmp;
	if (t_1 <= -1e-277) {
		tmp = x - ((x - t) / ((a - z) * (1.0 / (y - z))));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - x) * (y - z)) / (a - z))
	tmp = 0
	if t_1 <= -1e-277:
		tmp = x - ((x - t) / ((a - z) * (1.0 / (y - z))))
	elif t_1 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-277)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) * Float64(1.0 / Float64(y - z)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - x) * (y - z)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -1e-277)
		tmp = x - ((x - t) / ((a - z) * (1.0 / (y - z))));
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-277], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] * N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999969e-278

   1. Initial program 70.1%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

      1. *-commutative 90.1%

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

      2. clear-num 90.0%

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

      3. un-div-inv 90.1%

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

   5. Applied egg-rr 90.1%

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

      1. div-inv 90.1%

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

   7. Applied egg-rr 90.1%

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

   if -9.99999999999999969e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.8%

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

      1. associate-*l/ 4.8%

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

   3. Simplified 4.8%

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

   4. Taylor expanded in z around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. mul-1-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-rgt-out-- 100.0%

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

   6. Simplified 100.0%

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

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

   1. Initial program 72.6%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

      1. *-commutative 87.8%

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

      2. clear-num 87.7%

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

      3. un-div-inv 88.1%

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

   5. Applied egg-rr 88.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq -1 \cdot 10^{-277}:\\ \;\;\;\;x - \frac{x - t}{\left(a - z\right) \cdot \frac{1}{y - z}}\\ \mathbf{elif}\;x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 5: 63.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+124}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-282}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (- x (/ (- x t) (/ a y)))))
   (if (<= z -7e+124)
     (+ t (/ a (/ z (- t x))))
     (if (<= z -1.55e-29)
       t_1
       (if (<= z -1.4e-115)
         t_2
         (if (<= z -1.9e-147)
           t_1
           (if (<= z 3e-282)
             (+ x (/ (* y (- t x)) a))
             (if (<= z 3.3e-53)
               t_2
               (if (<= z 9e+44) t_1 (* t (/ (- y z) (- a z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x - ((x - t) / (a / y));
	double tmp;
	if (z <= -7e+124) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -1.55e-29) {
		tmp = t_1;
	} else if (z <= -1.4e-115) {
		tmp = t_2;
	} else if (z <= -1.9e-147) {
		tmp = t_1;
	} else if (z <= 3e-282) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 3.3e-53) {
		tmp = t_2;
	} else if (z <= 9e+44) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (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) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = x - ((x - t) / (a / y))
    if (z <= (-7d+124)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-1.55d-29)) then
        tmp = t_1
    else if (z <= (-1.4d-115)) then
        tmp = t_2
    else if (z <= (-1.9d-147)) then
        tmp = t_1
    else if (z <= 3d-282) then
        tmp = x + ((y * (t - x)) / a)
    else if (z <= 3.3d-53) then
        tmp = t_2
    else if (z <= 9d+44) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (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 = y * ((t - x) / (a - z));
	double t_2 = x - ((x - t) / (a / y));
	double tmp;
	if (z <= -7e+124) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -1.55e-29) {
		tmp = t_1;
	} else if (z <= -1.4e-115) {
		tmp = t_2;
	} else if (z <= -1.9e-147) {
		tmp = t_1;
	} else if (z <= 3e-282) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 3.3e-53) {
		tmp = t_2;
	} else if (z <= 9e+44) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = x - ((x - t) / (a / y))
	tmp = 0
	if z <= -7e+124:
		tmp = t + (a / (z / (t - x)))
	elif z <= -1.55e-29:
		tmp = t_1
	elif z <= -1.4e-115:
		tmp = t_2
	elif z <= -1.9e-147:
		tmp = t_1
	elif z <= 3e-282:
		tmp = x + ((y * (t - x)) / a)
	elif z <= 3.3e-53:
		tmp = t_2
	elif z <= 9e+44:
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(x - Float64(Float64(x - t) / Float64(a / y)))
	tmp = 0.0
	if (z <= -7e+124)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -1.55e-29)
		tmp = t_1;
	elseif (z <= -1.4e-115)
		tmp = t_2;
	elseif (z <= -1.9e-147)
		tmp = t_1;
	elseif (z <= 3e-282)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (z <= 3.3e-53)
		tmp = t_2;
	elseif (z <= 9e+44)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = x - ((x - t) / (a / y));
	tmp = 0.0;
	if (z <= -7e+124)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -1.55e-29)
		tmp = t_1;
	elseif (z <= -1.4e-115)
		tmp = t_2;
	elseif (z <= -1.9e-147)
		tmp = t_1;
	elseif (z <= 3e-282)
		tmp = x + ((y * (t - x)) / a);
	elseif (z <= 3.3e-53)
		tmp = t_2;
	elseif (z <= 9e+44)
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+124], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-29], t$95$1, If[LessEqual[z, -1.4e-115], t$95$2, If[LessEqual[z, -1.9e-147], t$95$1, If[LessEqual[z, 3e-282], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-53], t$95$2, If[LessEqual[z, 9e+44], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.0000000000000002e124

   1. Initial program 37.2%

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

      1. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around -inf 58.8%

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

      1. +-commutative 58.8%

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

      2. sub-neg 58.8%

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

      3. mul-1-neg 58.8%

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

      4. +-commutative 58.8%

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

      5. mul-1-neg 58.8%

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

      6. unsub-neg 58.8%

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

      7. +-commutative 58.8%

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

      8. mul-1-neg 58.8%

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

      9. sub-neg 58.8%

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

      10. distribute-rgt-out-- 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in y around 0 59.4%

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

      1. sub-neg 59.4%

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

      2. mul-1-neg 59.4%

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

      3. remove-double-neg 59.4%

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

      4. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

   if -7.0000000000000002e124 < z < -1.55000000000000013e-29 or -1.39999999999999994e-115 < z < -1.90000000000000014e-147 or 3.30000000000000004e-53 < z < 9e44

   1. Initial program 74.3%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around inf 66.7%

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

      1. div-sub 66.7%

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

      2. *-commutative 66.7%

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

   6. Simplified 66.7%

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

   if -1.55000000000000013e-29 < z < -1.39999999999999994e-115 or 3.0000000000000001e-282 < z < 3.30000000000000004e-53

   1. Initial program 85.2%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

      1. *-commutative 95.8%

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

      2. clear-num 95.6%

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

      3. un-div-inv 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in z around 0 79.2%

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

   if -1.90000000000000014e-147 < z < 3.0000000000000001e-282

   1. Initial program 98.8%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

      1. *-commutative 90.9%

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

      2. clear-num 90.8%

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

      3. un-div-inv 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in z around 0 89.6%

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

   if 9e44 < z

   1. Initial program 30.2%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in x around 0 35.5%

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

      1. associate-*r/ 69.0%

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

   6. Simplified 69.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+124}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-115}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-282}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-53}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 6: 36.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-279}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 185000000:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e-16)
   t
   (if (<= z -6.4e-110)
     x
     (if (<= z 5.2e-279)
       (/ (* t y) a)
       (if (<= z 2.4e-150)
         x
         (if (<= z 7.5e-99)
           (/ y (/ a t))
           (if (<= z 2.1e-53) x (if (<= z 185000000.0) (/ (* y x) z) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e-16) {
		tmp = t;
	} else if (z <= -6.4e-110) {
		tmp = x;
	} else if (z <= 5.2e-279) {
		tmp = (t * y) / a;
	} else if (z <= 2.4e-150) {
		tmp = x;
	} else if (z <= 7.5e-99) {
		tmp = y / (a / t);
	} else if (z <= 2.1e-53) {
		tmp = x;
	} else if (z <= 185000000.0) {
		tmp = (y * x) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d-16)) then
        tmp = t
    else if (z <= (-6.4d-110)) then
        tmp = x
    else if (z <= 5.2d-279) then
        tmp = (t * y) / a
    else if (z <= 2.4d-150) then
        tmp = x
    else if (z <= 7.5d-99) then
        tmp = y / (a / t)
    else if (z <= 2.1d-53) then
        tmp = x
    else if (z <= 185000000.0d0) then
        tmp = (y * x) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e-16) {
		tmp = t;
	} else if (z <= -6.4e-110) {
		tmp = x;
	} else if (z <= 5.2e-279) {
		tmp = (t * y) / a;
	} else if (z <= 2.4e-150) {
		tmp = x;
	} else if (z <= 7.5e-99) {
		tmp = y / (a / t);
	} else if (z <= 2.1e-53) {
		tmp = x;
	} else if (z <= 185000000.0) {
		tmp = (y * x) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e-16:
		tmp = t
	elif z <= -6.4e-110:
		tmp = x
	elif z <= 5.2e-279:
		tmp = (t * y) / a
	elif z <= 2.4e-150:
		tmp = x
	elif z <= 7.5e-99:
		tmp = y / (a / t)
	elif z <= 2.1e-53:
		tmp = x
	elif z <= 185000000.0:
		tmp = (y * x) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e-16)
		tmp = t;
	elseif (z <= -6.4e-110)
		tmp = x;
	elseif (z <= 5.2e-279)
		tmp = Float64(Float64(t * y) / a);
	elseif (z <= 2.4e-150)
		tmp = x;
	elseif (z <= 7.5e-99)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 2.1e-53)
		tmp = x;
	elseif (z <= 185000000.0)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e-16)
		tmp = t;
	elseif (z <= -6.4e-110)
		tmp = x;
	elseif (z <= 5.2e-279)
		tmp = (t * y) / a;
	elseif (z <= 2.4e-150)
		tmp = x;
	elseif (z <= 7.5e-99)
		tmp = y / (a / t);
	elseif (z <= 2.1e-53)
		tmp = x;
	elseif (z <= 185000000.0)
		tmp = (y * x) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e-16], t, If[LessEqual[z, -6.4e-110], x, If[LessEqual[z, 5.2e-279], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.4e-150], x, If[LessEqual[z, 7.5e-99], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-53], x, If[LessEqual[z, 185000000.0], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.8e-16 or 1.85e8 < z

   1. Initial program 40.9%

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

      1. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in z around inf 44.9%

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

   if -6.8e-16 < z < -6.40000000000000056e-110 or 5.2000000000000004e-279 < z < 2.4e-150 or 7.4999999999999999e-99 < z < 2.09999999999999977e-53

   1. Initial program 84.9%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in a around inf 54.3%

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

   if -6.40000000000000056e-110 < z < 5.2000000000000004e-279

   1. Initial program 97.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 48.3%

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

   5. Taylor expanded in z around 0 38.1%

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

   if 2.4e-150 < z < 7.4999999999999999e-99

   1. Initial program 86.5%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 45.3%

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

   5. Taylor expanded in z around 0 45.2%

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

      1. associate-/l* 58.5%

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

   7. Simplified 58.5%

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

   if 2.09999999999999977e-53 < z < 1.85e8

   1. Initial program 86.2%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in a around 0 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. associate-/l* 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in x around -inf 39.8%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-279}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 185000000:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 56.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t \cdot y}{a}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ t_3 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-283}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.12 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* t y) a)))
        (t_2 (* y (/ (- t x) (- a z))))
        (t_3 (* t (/ (- y z) (- a z)))))
   (if (<= y -9.2e-58)
     t_2
     (if (<= y -9e-250)
       t_1
       (if (<= y 3e-283)
         t_3
         (if (<= y 1.05e-206) t_1 (if (<= y 2.12e+55) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double t_2 = y * ((t - x) / (a - z));
	double t_3 = t * ((y - z) / (a - z));
	double tmp;
	if (y <= -9.2e-58) {
		tmp = t_2;
	} else if (y <= -9e-250) {
		tmp = t_1;
	} else if (y <= 3e-283) {
		tmp = t_3;
	} else if (y <= 1.05e-206) {
		tmp = t_1;
	} else if (y <= 2.12e+55) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((t * y) / a)
    t_2 = y * ((t - x) / (a - z))
    t_3 = t * ((y - z) / (a - z))
    if (y <= (-9.2d-58)) then
        tmp = t_2
    else if (y <= (-9d-250)) then
        tmp = t_1
    else if (y <= 3d-283) then
        tmp = t_3
    else if (y <= 1.05d-206) then
        tmp = t_1
    else if (y <= 2.12d+55) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double t_2 = y * ((t - x) / (a - z));
	double t_3 = t * ((y - z) / (a - z));
	double tmp;
	if (y <= -9.2e-58) {
		tmp = t_2;
	} else if (y <= -9e-250) {
		tmp = t_1;
	} else if (y <= 3e-283) {
		tmp = t_3;
	} else if (y <= 1.05e-206) {
		tmp = t_1;
	} else if (y <= 2.12e+55) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t * y) / a)
	t_2 = y * ((t - x) / (a - z))
	t_3 = t * ((y - z) / (a - z))
	tmp = 0
	if y <= -9.2e-58:
		tmp = t_2
	elif y <= -9e-250:
		tmp = t_1
	elif y <= 3e-283:
		tmp = t_3
	elif y <= 1.05e-206:
		tmp = t_1
	elif y <= 2.12e+55:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t * y) / a))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_3 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (y <= -9.2e-58)
		tmp = t_2;
	elseif (y <= -9e-250)
		tmp = t_1;
	elseif (y <= 3e-283)
		tmp = t_3;
	elseif (y <= 1.05e-206)
		tmp = t_1;
	elseif (y <= 2.12e+55)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t * y) / a);
	t_2 = y * ((t - x) / (a - z));
	t_3 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (y <= -9.2e-58)
		tmp = t_2;
	elseif (y <= -9e-250)
		tmp = t_1;
	elseif (y <= 3e-283)
		tmp = t_3;
	elseif (y <= 1.05e-206)
		tmp = t_1;
	elseif (y <= 2.12e+55)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e-58], t$95$2, If[LessEqual[y, -9e-250], t$95$1, If[LessEqual[y, 3e-283], t$95$3, If[LessEqual[y, 1.05e-206], t$95$1, If[LessEqual[y, 2.12e+55], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.1999999999999995e-58 or 2.12000000000000007e55 < y

   1. Initial program 68.0%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in y around inf 74.6%

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

      1. div-sub 75.3%

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

      2. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   if -9.1999999999999995e-58 < y < -8.99999999999999987e-250 or 2.99999999999999996e-283 < y < 1.05000000000000005e-206

   1. Initial program 71.5%

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

      1. associate-*l/ 76.9%

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

   3. Simplified 76.9%

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

      1. *-commutative 76.9%

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

      2. clear-num 76.8%

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

      3. un-div-inv 76.8%

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

   5. Applied egg-rr 76.8%

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

   6. Taylor expanded in z around 0 59.0%

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

   7. Taylor expanded in t around inf 57.3%

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

   if -8.99999999999999987e-250 < y < 2.99999999999999996e-283 or 1.05000000000000005e-206 < y < 2.12000000000000007e55

   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/ 71.4%

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

   3. Simplified 71.4%

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

   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/ 67.2%

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

   6. Simplified 67.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-283}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-206}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;y \leq 2.12 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 8: 53.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t \cdot y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2700000000:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* t y) a))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= z -4.6e-16)
     t_2
     (if (<= z 1.6e-306)
       t_1
       (if (<= z 9.5e-151)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.4e-14)
           t_1
           (if (<= z 2700000000.0) (/ (* y x) z) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -4.6e-16) {
		tmp = t_2;
	} else if (z <= 1.6e-306) {
		tmp = t_1;
	} else if (z <= 9.5e-151) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.4e-14) {
		tmp = t_1;
	} else if (z <= 2700000000.0) {
		tmp = (y * x) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t * y) / a)
    t_2 = t * (1.0d0 - (y / z))
    if (z <= (-4.6d-16)) then
        tmp = t_2
    else if (z <= 1.6d-306) then
        tmp = t_1
    else if (z <= 9.5d-151) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.4d-14) then
        tmp = t_1
    else if (z <= 2700000000.0d0) then
        tmp = (y * x) / z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -4.6e-16) {
		tmp = t_2;
	} else if (z <= 1.6e-306) {
		tmp = t_1;
	} else if (z <= 9.5e-151) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.4e-14) {
		tmp = t_1;
	} else if (z <= 2700000000.0) {
		tmp = (y * x) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t * y) / a)
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -4.6e-16:
		tmp = t_2
	elif z <= 1.6e-306:
		tmp = t_1
	elif z <= 9.5e-151:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.4e-14:
		tmp = t_1
	elif z <= 2700000000.0:
		tmp = (y * x) / z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t * y) / a))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -4.6e-16)
		tmp = t_2;
	elseif (z <= 1.6e-306)
		tmp = t_1;
	elseif (z <= 9.5e-151)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.4e-14)
		tmp = t_1;
	elseif (z <= 2700000000.0)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t * y) / a);
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -4.6e-16)
		tmp = t_2;
	elseif (z <= 1.6e-306)
		tmp = t_1;
	elseif (z <= 9.5e-151)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.4e-14)
		tmp = t_1;
	elseif (z <= 2700000000.0)
		tmp = (y * x) / z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e-16], t$95$2, If[LessEqual[z, 1.6e-306], t$95$1, If[LessEqual[z, 9.5e-151], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-14], t$95$1, If[LessEqual[z, 2700000000.0], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5999999999999998e-16 or 2.7e9 < z

   1. Initial program 40.9%

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

      1. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in a around 0 29.3%

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

      1. +-commutative 29.3%

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

      2. mul-1-neg 29.3%

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

      3. unsub-neg 29.3%

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

      4. associate-/l* 47.3%

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

   6. Simplified 47.3%

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

   7. Taylor expanded in t around inf 55.6%

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

   if -4.5999999999999998e-16 < z < 1.59999999999999985e-306 or 9.4999999999999996e-151 < z < 1.4e-14

   1. Initial program 89.5%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

      1. *-commutative 92.2%

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

      2. clear-num 92.1%

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

      3. un-div-inv 92.6%

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

   5. Applied egg-rr 92.6%

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

   6. Taylor expanded in z around 0 68.3%

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

   7. Taylor expanded in t around inf 63.6%

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

   if 1.59999999999999985e-306 < z < 9.4999999999999996e-151

   1. Initial program 96.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around 0 88.4%

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

   7. Taylor expanded in x around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. mul-1-neg 80.9%

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

      3. unsub-neg 80.9%

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

   9. Simplified 80.9%

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

   if 1.4e-14 < z < 2.7e9

   1. Initial program 80.9%

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

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in a around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. mul-1-neg 80.9%

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

      3. unsub-neg 80.9%

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

      4. associate-/l* 80.9%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in x around -inf 85.7%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-306}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 2700000000:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 9: 53.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t \cdot y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* t y) a))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= z -2.35e-14)
     t_2
     (if (<= z 6.2e-307)
       t_1
       (if (<= z 1.25e-151)
         (* x (- 1.0 (/ y a)))
         (if (<= z 2.9e-14)
           t_1
           (if (<= z 18000.0) (* x (/ (- y a) z)) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -2.35e-14) {
		tmp = t_2;
	} else if (z <= 6.2e-307) {
		tmp = t_1;
	} else if (z <= 1.25e-151) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.9e-14) {
		tmp = t_1;
	} else if (z <= 18000.0) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t * y) / a)
    t_2 = t * (1.0d0 - (y / z))
    if (z <= (-2.35d-14)) then
        tmp = t_2
    else if (z <= 6.2d-307) then
        tmp = t_1
    else if (z <= 1.25d-151) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.9d-14) then
        tmp = t_1
    else if (z <= 18000.0d0) then
        tmp = x * ((y - a) / z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * y) / a);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -2.35e-14) {
		tmp = t_2;
	} else if (z <= 6.2e-307) {
		tmp = t_1;
	} else if (z <= 1.25e-151) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.9e-14) {
		tmp = t_1;
	} else if (z <= 18000.0) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t * y) / a)
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -2.35e-14:
		tmp = t_2
	elif z <= 6.2e-307:
		tmp = t_1
	elif z <= 1.25e-151:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.9e-14:
		tmp = t_1
	elif z <= 18000.0:
		tmp = x * ((y - a) / z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t * y) / a))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.35e-14)
		tmp = t_2;
	elseif (z <= 6.2e-307)
		tmp = t_1;
	elseif (z <= 1.25e-151)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.9e-14)
		tmp = t_1;
	elseif (z <= 18000.0)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t * y) / a);
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.35e-14)
		tmp = t_2;
	elseif (z <= 6.2e-307)
		tmp = t_1;
	elseif (z <= 1.25e-151)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.9e-14)
		tmp = t_1;
	elseif (z <= 18000.0)
		tmp = x * ((y - a) / z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e-14], t$95$2, If[LessEqual[z, 6.2e-307], t$95$1, If[LessEqual[z, 1.25e-151], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-14], t$95$1, If[LessEqual[z, 18000.0], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3500000000000001e-14 or 18000 < z

   1. Initial program 40.9%

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

      1. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in a around 0 29.3%

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

      1. +-commutative 29.3%

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

      2. mul-1-neg 29.3%

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

      3. unsub-neg 29.3%

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

      4. associate-/l* 47.3%

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

   6. Simplified 47.3%

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

   7. Taylor expanded in t around inf 55.6%

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

   if -2.3500000000000001e-14 < z < 6.1999999999999996e-307 or 1.25000000000000001e-151 < z < 2.9000000000000003e-14

   1. Initial program 89.5%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

      1. *-commutative 92.2%

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

      2. clear-num 92.1%

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

      3. un-div-inv 92.6%

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

   5. Applied egg-rr 92.6%

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

   6. Taylor expanded in z around 0 68.3%

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

   7. Taylor expanded in t around inf 63.6%

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

   if 6.1999999999999996e-307 < z < 1.25000000000000001e-151

   1. Initial program 96.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around 0 88.4%

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

   7. Taylor expanded in x around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. mul-1-neg 80.9%

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

      3. unsub-neg 80.9%

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

   9. Simplified 80.9%

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

   if 2.9000000000000003e-14 < z < 18000

   1. Initial program 80.9%

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

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in z around -inf 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. mul-1-neg 99.7%

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

      6. unsub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. mul-1-neg 99.7%

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

      9. sub-neg 99.7%

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

      10. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around -inf 86.0%

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

      1. div-sub 86.0%

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

      2. associate-*r* 86.0%

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

      3. mul-1-neg 86.0%

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

   9. Simplified 86.0%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-307}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 10: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= z -1.4e+130)
     (+ t (/ a (/ z (- t x))))
     (if (<= z -4.2e-33)
       t_1
       (if (<= z 1.45e-48)
         (+ x (/ y (/ a (- t x))))
         (if (<= z 1.8e+30) t_1 (* t (/ (- y z) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (z <= -1.4e+130) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -4.2e-33) {
		tmp = t_1;
	} else if (z <= 1.45e-48) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 1.8e+30) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (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 = y * ((t - x) / (a - z))
    if (z <= (-1.4d+130)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-4.2d-33)) then
        tmp = t_1
    else if (z <= 1.45d-48) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 1.8d+30) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (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 = y * ((t - x) / (a - z));
	double tmp;
	if (z <= -1.4e+130) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -4.2e-33) {
		tmp = t_1;
	} else if (z <= 1.45e-48) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 1.8e+30) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if z <= -1.4e+130:
		tmp = t + (a / (z / (t - x)))
	elif z <= -4.2e-33:
		tmp = t_1
	elif z <= 1.45e-48:
		tmp = x + (y / (a / (t - x)))
	elif z <= 1.8e+30:
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.4e+130)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -4.2e-33)
		tmp = t_1;
	elseif (z <= 1.45e-48)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 1.8e+30)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (z <= -1.4e+130)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -4.2e-33)
		tmp = t_1;
	elseif (z <= 1.45e-48)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 1.8e+30)
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+130], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-33], t$95$1, If[LessEqual[z, 1.45e-48], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+30], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3999999999999999e130

   1. Initial program 37.2%

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

      1. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around -inf 58.8%

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

      1. +-commutative 58.8%

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

      2. sub-neg 58.8%

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

      3. mul-1-neg 58.8%

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

      4. +-commutative 58.8%

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

      5. mul-1-neg 58.8%

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

      6. unsub-neg 58.8%

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

      7. +-commutative 58.8%

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

      8. mul-1-neg 58.8%

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

      9. sub-neg 58.8%

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

      10. distribute-rgt-out-- 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in y around 0 59.4%

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

      1. sub-neg 59.4%

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

      2. mul-1-neg 59.4%

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

      3. remove-double-neg 59.4%

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

      4. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

   if -1.3999999999999999e130 < z < -4.2e-33 or 1.4500000000000001e-48 < z < 1.8000000000000001e30

   1. Initial program 70.5%

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

      1. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in y around inf 65.9%

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

      1. div-sub 65.9%

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

      2. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   if -4.2e-33 < z < 1.4500000000000001e-48

   1. Initial program 91.6%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 74.9%

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

      1. +-commutative 74.9%

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

      2. associate-/l* 76.9%

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

   6. Simplified 76.9%

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

   if 1.8000000000000001e30 < z

   1. Initial program 30.2%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in x around 0 35.5%

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

      1. associate-*r/ 69.0%

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

   6. Simplified 69.0%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 11: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+122}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-52}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= z -2.8e+122)
     (+ t (/ a (/ z (- t x))))
     (if (<= z -2.5e-30)
       t_1
       (if (<= z 1.3e-52)
         (- x (/ (- x t) (/ a y)))
         (if (<= z 7.5e+43) t_1 (* t (/ (- y z) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (z <= -2.8e+122) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -2.5e-30) {
		tmp = t_1;
	} else if (z <= 1.3e-52) {
		tmp = x - ((x - t) / (a / y));
	} else if (z <= 7.5e+43) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (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 = y * ((t - x) / (a - z))
    if (z <= (-2.8d+122)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-2.5d-30)) then
        tmp = t_1
    else if (z <= 1.3d-52) then
        tmp = x - ((x - t) / (a / y))
    else if (z <= 7.5d+43) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (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 = y * ((t - x) / (a - z));
	double tmp;
	if (z <= -2.8e+122) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -2.5e-30) {
		tmp = t_1;
	} else if (z <= 1.3e-52) {
		tmp = x - ((x - t) / (a / y));
	} else if (z <= 7.5e+43) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if z <= -2.8e+122:
		tmp = t + (a / (z / (t - x)))
	elif z <= -2.5e-30:
		tmp = t_1
	elif z <= 1.3e-52:
		tmp = x - ((x - t) / (a / y))
	elif z <= 7.5e+43:
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.8e+122)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -2.5e-30)
		tmp = t_1;
	elseif (z <= 1.3e-52)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	elseif (z <= 7.5e+43)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (z <= -2.8e+122)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -2.5e-30)
		tmp = t_1;
	elseif (z <= 1.3e-52)
		tmp = x - ((x - t) / (a / y));
	elseif (z <= 7.5e+43)
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+122], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-30], t$95$1, If[LessEqual[z, 1.3e-52], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+43], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e122

   1. Initial program 37.2%

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

      1. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around -inf 58.8%

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

      1. +-commutative 58.8%

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

      2. sub-neg 58.8%

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

      3. mul-1-neg 58.8%

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

      4. +-commutative 58.8%

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

      5. mul-1-neg 58.8%

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

      6. unsub-neg 58.8%

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

      7. +-commutative 58.8%

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

      8. mul-1-neg 58.8%

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

      9. sub-neg 58.8%

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

      10. distribute-rgt-out-- 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in y around 0 59.4%

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

      1. sub-neg 59.4%

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

      2. mul-1-neg 59.4%

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

      3. remove-double-neg 59.4%

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

      4. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

   if -2.8e122 < z < -2.49999999999999986e-30 or 1.2999999999999999e-52 < z < 7.49999999999999967e43

   1. Initial program 70.5%

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

      1. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in y around inf 65.9%

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

      1. div-sub 65.9%

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

      2. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   if -2.49999999999999986e-30 < z < 1.2999999999999999e-52

   1. Initial program 91.6%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

      1. *-commutative 94.0%

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

      2. clear-num 93.9%

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

      3. un-div-inv 94.4%

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

   5. Applied egg-rr 94.4%

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

   6. Taylor expanded in z around 0 78.4%

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

   if 7.49999999999999967e43 < z

   1. Initial program 30.2%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in x around 0 35.5%

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

      1. associate-*r/ 69.0%

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

   6. Simplified 69.0%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+122}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-52}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 12: 37.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.95e-14)
     t
     (if (<= z -4.9e-71)
       x
       (if (<= z 6.5e-279)
         t_1
         (if (<= z 2.45e-149)
           x
           (if (<= z 3e-96) t_1 (if (<= z 3e-18) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.95e-14) {
		tmp = t;
	} else if (z <= -4.9e-71) {
		tmp = x;
	} else if (z <= 6.5e-279) {
		tmp = t_1;
	} else if (z <= 2.45e-149) {
		tmp = x;
	} else if (z <= 3e-96) {
		tmp = t_1;
	} else if (z <= 3e-18) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-1.95d-14)) then
        tmp = t
    else if (z <= (-4.9d-71)) then
        tmp = x
    else if (z <= 6.5d-279) then
        tmp = t_1
    else if (z <= 2.45d-149) then
        tmp = x
    else if (z <= 3d-96) then
        tmp = t_1
    else if (z <= 3d-18) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.95e-14) {
		tmp = t;
	} else if (z <= -4.9e-71) {
		tmp = x;
	} else if (z <= 6.5e-279) {
		tmp = t_1;
	} else if (z <= 2.45e-149) {
		tmp = x;
	} else if (z <= 3e-96) {
		tmp = t_1;
	} else if (z <= 3e-18) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.95e-14:
		tmp = t
	elif z <= -4.9e-71:
		tmp = x
	elif z <= 6.5e-279:
		tmp = t_1
	elif z <= 2.45e-149:
		tmp = x
	elif z <= 3e-96:
		tmp = t_1
	elif z <= 3e-18:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.95e-14)
		tmp = t;
	elseif (z <= -4.9e-71)
		tmp = x;
	elseif (z <= 6.5e-279)
		tmp = t_1;
	elseif (z <= 2.45e-149)
		tmp = x;
	elseif (z <= 3e-96)
		tmp = t_1;
	elseif (z <= 3e-18)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.95e-14)
		tmp = t;
	elseif (z <= -4.9e-71)
		tmp = x;
	elseif (z <= 6.5e-279)
		tmp = t_1;
	elseif (z <= 2.45e-149)
		tmp = x;
	elseif (z <= 3e-96)
		tmp = t_1;
	elseif (z <= 3e-18)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e-14], t, If[LessEqual[z, -4.9e-71], x, If[LessEqual[z, 6.5e-279], t$95$1, If[LessEqual[z, 2.45e-149], x, If[LessEqual[z, 3e-96], t$95$1, If[LessEqual[z, 3e-18], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9499999999999999e-14 or 2.99999999999999983e-18 < z

   1. Initial program 42.8%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 43.1%

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

   if -1.9499999999999999e-14 < z < -4.8999999999999997e-71 or 6.4999999999999997e-279 < z < 2.4500000000000002e-149 or 3e-96 < z < 2.99999999999999983e-18

   1. Initial program 86.3%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in a around inf 49.3%

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

   if -4.8999999999999997e-71 < z < 6.4999999999999997e-279 or 2.4500000000000002e-149 < z < 3e-96

   1. Initial program 93.5%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around 0 46.1%

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

   5. Taylor expanded in z around 0 37.4%

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

      1. associate-/l* 41.0%

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

   7. Simplified 41.0%

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

      1. associate-/r/ 39.9%

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

   9. Applied egg-rr 39.9%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-279}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-96}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 37.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a t))))
   (if (<= z -3.4e-15)
     t
     (if (<= z -6.8e-108)
       x
       (if (<= z 8e-282)
         t_1
         (if (<= z 1.7e-149)
           x
           (if (<= z 4e-102) t_1 (if (<= z 2.9e-15) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / t);
	double tmp;
	if (z <= -3.4e-15) {
		tmp = t;
	} else if (z <= -6.8e-108) {
		tmp = x;
	} else if (z <= 8e-282) {
		tmp = t_1;
	} else if (z <= 1.7e-149) {
		tmp = x;
	} else if (z <= 4e-102) {
		tmp = t_1;
	} else if (z <= 2.9e-15) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a / t)
    if (z <= (-3.4d-15)) then
        tmp = t
    else if (z <= (-6.8d-108)) then
        tmp = x
    else if (z <= 8d-282) then
        tmp = t_1
    else if (z <= 1.7d-149) then
        tmp = x
    else if (z <= 4d-102) then
        tmp = t_1
    else if (z <= 2.9d-15) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / t);
	double tmp;
	if (z <= -3.4e-15) {
		tmp = t;
	} else if (z <= -6.8e-108) {
		tmp = x;
	} else if (z <= 8e-282) {
		tmp = t_1;
	} else if (z <= 1.7e-149) {
		tmp = x;
	} else if (z <= 4e-102) {
		tmp = t_1;
	} else if (z <= 2.9e-15) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / t)
	tmp = 0
	if z <= -3.4e-15:
		tmp = t
	elif z <= -6.8e-108:
		tmp = x
	elif z <= 8e-282:
		tmp = t_1
	elif z <= 1.7e-149:
		tmp = x
	elif z <= 4e-102:
		tmp = t_1
	elif z <= 2.9e-15:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / t))
	tmp = 0.0
	if (z <= -3.4e-15)
		tmp = t;
	elseif (z <= -6.8e-108)
		tmp = x;
	elseif (z <= 8e-282)
		tmp = t_1;
	elseif (z <= 1.7e-149)
		tmp = x;
	elseif (z <= 4e-102)
		tmp = t_1;
	elseif (z <= 2.9e-15)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / t);
	tmp = 0.0;
	if (z <= -3.4e-15)
		tmp = t;
	elseif (z <= -6.8e-108)
		tmp = x;
	elseif (z <= 8e-282)
		tmp = t_1;
	elseif (z <= 1.7e-149)
		tmp = x;
	elseif (z <= 4e-102)
		tmp = t_1;
	elseif (z <= 2.9e-15)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-15], t, If[LessEqual[z, -6.8e-108], x, If[LessEqual[z, 8e-282], t$95$1, If[LessEqual[z, 1.7e-149], x, If[LessEqual[z, 4e-102], t$95$1, If[LessEqual[z, 2.9e-15], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4e-15 or 2.90000000000000019e-15 < z

   1. Initial program 42.8%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 43.1%

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

   if -3.4e-15 < z < -6.80000000000000004e-108 or 8.0000000000000001e-282 < z < 1.6999999999999999e-149 or 3.99999999999999973e-102 < z < 2.90000000000000019e-15

   1. Initial program 85.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 a around inf 48.6%

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

   if -6.80000000000000004e-108 < z < 8.0000000000000001e-282 or 1.6999999999999999e-149 < z < 3.99999999999999973e-102

   1. Initial program 95.1%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around 0 47.7%

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

   5. Taylor expanded in z around 0 39.5%

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

      1. associate-/l* 42.1%

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

   7. Simplified 42.1%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-282}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 37.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-277}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.25e-14)
   t
   (if (<= z -6e-110)
     x
     (if (<= z 1.55e-277)
       (/ (* t y) a)
       (if (<= z 1.4e-150)
         x
         (if (<= z 1.8e-99) (/ y (/ a t)) (if (<= z 2.15e-15) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.25e-14) {
		tmp = t;
	} else if (z <= -6e-110) {
		tmp = x;
	} else if (z <= 1.55e-277) {
		tmp = (t * y) / a;
	} else if (z <= 1.4e-150) {
		tmp = x;
	} else if (z <= 1.8e-99) {
		tmp = y / (a / t);
	} else if (z <= 2.15e-15) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.25d-14)) then
        tmp = t
    else if (z <= (-6d-110)) then
        tmp = x
    else if (z <= 1.55d-277) then
        tmp = (t * y) / a
    else if (z <= 1.4d-150) then
        tmp = x
    else if (z <= 1.8d-99) then
        tmp = y / (a / t)
    else if (z <= 2.15d-15) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.25e-14) {
		tmp = t;
	} else if (z <= -6e-110) {
		tmp = x;
	} else if (z <= 1.55e-277) {
		tmp = (t * y) / a;
	} else if (z <= 1.4e-150) {
		tmp = x;
	} else if (z <= 1.8e-99) {
		tmp = y / (a / t);
	} else if (z <= 2.15e-15) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.25e-14:
		tmp = t
	elif z <= -6e-110:
		tmp = x
	elif z <= 1.55e-277:
		tmp = (t * y) / a
	elif z <= 1.4e-150:
		tmp = x
	elif z <= 1.8e-99:
		tmp = y / (a / t)
	elif z <= 2.15e-15:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.25e-14)
		tmp = t;
	elseif (z <= -6e-110)
		tmp = x;
	elseif (z <= 1.55e-277)
		tmp = Float64(Float64(t * y) / a);
	elseif (z <= 1.4e-150)
		tmp = x;
	elseif (z <= 1.8e-99)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 2.15e-15)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.25e-14)
		tmp = t;
	elseif (z <= -6e-110)
		tmp = x;
	elseif (z <= 1.55e-277)
		tmp = (t * y) / a;
	elseif (z <= 1.4e-150)
		tmp = x;
	elseif (z <= 1.8e-99)
		tmp = y / (a / t);
	elseif (z <= 2.15e-15)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.25e-14], t, If[LessEqual[z, -6e-110], x, If[LessEqual[z, 1.55e-277], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.4e-150], x, If[LessEqual[z, 1.8e-99], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-15], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2499999999999999e-14 or 2.1499999999999998e-15 < z

   1. Initial program 42.8%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 43.1%

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

   if -2.2499999999999999e-14 < z < -5.99999999999999972e-110 or 1.5499999999999999e-277 < z < 1.39999999999999998e-150 or 1.8e-99 < z < 2.1499999999999998e-15

   1. Initial program 85.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 a around inf 48.6%

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

   if -5.99999999999999972e-110 < z < 1.5499999999999999e-277

   1. Initial program 97.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 48.3%

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

   5. Taylor expanded in z around 0 38.1%

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

   if 1.39999999999999998e-150 < z < 1.8e-99

   1. Initial program 86.5%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 45.3%

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

   5. Taylor expanded in z around 0 45.2%

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

      1. associate-/l* 58.5%

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

   7. Simplified 58.5%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-277}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 48.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 14500:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -6.6e+97)
     t
     (if (<= z 1.2e-46)
       t_1
       (if (<= z 14500.0) (/ (* y x) z) (if (<= z 4.2e+50) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.6e+97) {
		tmp = t;
	} else if (z <= 1.2e-46) {
		tmp = t_1;
	} else if (z <= 14500.0) {
		tmp = (y * x) / z;
	} else if (z <= 4.2e+50) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-6.6d+97)) then
        tmp = t
    else if (z <= 1.2d-46) then
        tmp = t_1
    else if (z <= 14500.0d0) then
        tmp = (y * x) / z
    else if (z <= 4.2d+50) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.6e+97) {
		tmp = t;
	} else if (z <= 1.2e-46) {
		tmp = t_1;
	} else if (z <= 14500.0) {
		tmp = (y * x) / z;
	} else if (z <= 4.2e+50) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -6.6e+97:
		tmp = t
	elif z <= 1.2e-46:
		tmp = t_1
	elif z <= 14500.0:
		tmp = (y * x) / z
	elif z <= 4.2e+50:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -6.6e+97)
		tmp = t;
	elseif (z <= 1.2e-46)
		tmp = t_1;
	elseif (z <= 14500.0)
		tmp = Float64(Float64(y * x) / z);
	elseif (z <= 4.2e+50)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -6.6e+97)
		tmp = t;
	elseif (z <= 1.2e-46)
		tmp = t_1;
	elseif (z <= 14500.0)
		tmp = (y * x) / z;
	elseif (z <= 4.2e+50)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+97], t, If[LessEqual[z, 1.2e-46], t$95$1, If[LessEqual[z, 14500.0], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.2e+50], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6000000000000003e97 or 4.1999999999999999e50 < z

   1. Initial program 33.2%

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

      1. associate-*l/ 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in z around inf 51.3%

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

   if -6.6000000000000003e97 < z < 1.20000000000000007e-46 or 14500 < z < 4.1999999999999999e50

   1. Initial program 86.8%

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

      1. *-commutative 93.1%

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

      2. clear-num 93.0%

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

      3. un-div-inv 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in z around 0 64.4%

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

   7. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

   9. Simplified 52.2%

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

   if 1.20000000000000007e-46 < z < 14500

   1. Initial program 86.2%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in a around 0 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. associate-/l* 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in x around -inf 39.8%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 14500:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 57.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -1.1e+183)
     t_1
     (if (<= x 7.2e-24)
       (* t (/ (- y z) (- a z)))
       (if (<= x 2.05e+157) t_1 (* x (/ (- y a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.1e+183) {
		tmp = t_1;
	} else if (x <= 7.2e-24) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 2.05e+157) {
		tmp = t_1;
	} else {
		tmp = 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 * (1.0d0 - (y / a))
    if (x <= (-1.1d+183)) then
        tmp = t_1
    else if (x <= 7.2d-24) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 2.05d+157) then
        tmp = t_1
    else
        tmp = 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 * (1.0 - (y / a));
	double tmp;
	if (x <= -1.1e+183) {
		tmp = t_1;
	} else if (x <= 7.2e-24) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 2.05e+157) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -1.1e+183:
		tmp = t_1
	elif x <= 7.2e-24:
		tmp = t * ((y - z) / (a - z))
	elif x <= 2.05e+157:
		tmp = t_1
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -1.1e+183)
		tmp = t_1;
	elseif (x <= 7.2e-24)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 2.05e+157)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -1.1e+183)
		tmp = t_1;
	elseif (x <= 7.2e-24)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 2.05e+157)
		tmp = t_1;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+183], t$95$1, If[LessEqual[x, 7.2e-24], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+157], t$95$1, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.09999999999999995e183 or 7.2000000000000002e-24 < x < 2.05000000000000008e157

   1. Initial program 59.7%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

      1. *-commutative 80.1%

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

      2. clear-num 80.0%

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

      3. un-div-inv 80.1%

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

   5. Applied egg-rr 80.1%

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

   6. Taylor expanded in z around 0 51.8%

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

   7. Taylor expanded in x around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

   9. Simplified 60.4%

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

   if -1.09999999999999995e183 < x < 7.2000000000000002e-24

   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/ 86.4%

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

   3. Simplified 86.4%

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

   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/ 68.0%

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

   6. Simplified 68.0%

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

   if 2.05000000000000008e157 < x

   1. Initial program 52.1%

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

      1. associate-*l/ 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in z around -inf 51.9%

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

      1. +-commutative 51.9%

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

      2. sub-neg 51.9%

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

      3. mul-1-neg 51.9%

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

      4. +-commutative 51.9%

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

      5. mul-1-neg 51.9%

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

      6. unsub-neg 51.9%

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

      7. +-commutative 51.9%

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

      8. mul-1-neg 51.9%

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

      9. sub-neg 51.9%

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

      10. distribute-rgt-out-- 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in x around -inf 60.8%

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

      1. div-sub 60.8%

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

      2. associate-*r* 60.8%

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

      3. mul-1-neg 60.8%

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

   9. Simplified 60.8%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 17: 70.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-15} \lor \neg \left(z \leq 5 \cdot 10^{-14}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.6e-15) (not (<= z 5e-14)))
   (+ t (* (/ y z) (- x t)))
   (- x (/ (- x t) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.6e-15) || !(z <= 5e-14)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x - ((x - t) / (a / 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 <= (-7.6d-15)) .or. (.not. (z <= 5d-14))) then
        tmp = t + ((y / z) * (x - t))
    else
        tmp = x - ((x - t) / (a / 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 <= -7.6e-15) || !(z <= 5e-14)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x - ((x - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.6e-15) or not (z <= 5e-14):
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = x - ((x - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.6e-15) || !(z <= 5e-14))
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.6e-15) || ~((z <= 5e-14)))
		tmp = t + ((y / z) * (x - t));
	else
		tmp = x - ((x - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.6e-15], N[Not[LessEqual[z, 5e-14]], $MachinePrecision]], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6000000000000004e-15 or 5.0000000000000002e-14 < z

   1. Initial program 42.4%

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

      1. +-commutative 42.4%

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

      2. associate-*r/ 67.2%

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

      3. fma-def 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in a around 0 49.4%

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

      1. mul-1-neg 49.4%

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

   6. Simplified 49.4%

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

   7. Taylor expanded in z around -inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. associate-/l* 72.9%

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

      5. associate-/r/ 75.2%

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

   9. Simplified 75.2%

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

   if -7.6000000000000004e-15 < z < 5.0000000000000002e-14

   1. Initial program 90.8%

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

      1. *-commutative 93.8%

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

      2. clear-num 93.6%

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

      3. un-div-inv 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in z around 0 76.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-15} \lor \neg \left(z \leq 5 \cdot 10^{-14}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 18: 51.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+26} \lor \neg \left(z \leq 2.4 \cdot 10^{-50}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e+26) (not (<= z 2.4e-50)))
   (* t (- 1.0 (/ y z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+26) || !(z <= 2.4e-50)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.2d+26)) .or. (.not. (z <= 2.4d-50))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+26) || !(z <= 2.4e-50)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e+26) or not (z <= 2.4e-50):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e+26) || !(z <= 2.4e-50))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.2e+26) || ~((z <= 2.4e-50)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e+26], N[Not[LessEqual[z, 2.4e-50]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000007e26 or 2.40000000000000002e-50 < z

   1. Initial program 45.0%

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

      1. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in a around 0 31.8%

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

      1. +-commutative 31.8%

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

      2. mul-1-neg 31.8%

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

      3. unsub-neg 31.8%

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

      4. associate-/l* 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in t around inf 54.7%

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

   if -2.20000000000000007e26 < z < 2.40000000000000002e-50

   1. Initial program 88.5%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

      1. *-commutative 92.9%

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

      2. clear-num 92.8%

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

      3. un-div-inv 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in z around 0 69.2%

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

   7. Taylor expanded in x around inf 55.4%

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

      1. *-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

   9. Simplified 55.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+26} \lor \neg \left(z \leq 2.4 \cdot 10^{-50}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 19: 38.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.9e-16) t (if (<= z 1.22e-24) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.9e-16) {
		tmp = t;
	} else if (z <= 1.22e-24) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.9d-16)) then
        tmp = t
    else if (z <= 1.22d-24) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.9e-16) {
		tmp = t;
	} else if (z <= 1.22e-24) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.9e-16:
		tmp = t
	elif z <= 1.22e-24:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.9e-16)
		tmp = t;
	elseif (z <= 1.22e-24)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.9e-16)
		tmp = t;
	elseif (z <= 1.22e-24)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.9e-16], t, If[LessEqual[z, 1.22e-24], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9000000000000002e-16 or 1.22000000000000004e-24 < z

   1. Initial program 42.8%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 43.1%

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

   if -7.9000000000000002e-16 < z < 1.22000000000000004e-24

   1. Initial program 90.8%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in a around inf 34.3%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 25.3% 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 66.2%

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

   1. associate-*l/ 82.3%

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

3. Simplified 82.3%

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

4. Taylor expanded in z around inf 24.8%

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

5. Final simplification 24.8%

   \[\leadsto t \]

Developer target: 83.3% 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 2023208 
(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))))