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

Percentage Accurate: 67.8% → 90.7%

Time: 17.3s

Alternatives: 22

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-238} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -2e-238) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-238) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if ((t_1 <= (-2d-238)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-238) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if (t_1 <= -2e-238) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -2e-238) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -2e-238) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-238], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2e-238 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 75.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

      1. *-commutative 91.9%

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

      2. clear-num 91.8%

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

      3. un-div-inv 92.1%

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

   5. Applied egg-rr 92.1%

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

   if -2e-238 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 7.9%

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

      1. associate-*l/ 7.9%

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

   3. Simplified 7.9%

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

   4. Taylor expanded in z around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. mul-1-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. mul-1-neg 99.8%

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

      6. unsub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. mul-1-neg 99.8%

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

      9. sub-neg 99.8%

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

      10. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

      1. expm1-log1p-u 91.3%

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

      2. expm1-udef 59.3%

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

      3. associate-/l* 59.3%

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

   8. Applied egg-rr 59.3%

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

      1. expm1-def 91.4%

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

      2. expm1-log1p 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -2 \cdot 10^{-238} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-238} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{y - z}{a - z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -2e-238) (not (<= t_1 0.0)))
     (- x (* (/ (- y z) (- a z)) (- x t)))
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-238) || !(t_1 <= 0.0)) {
		tmp = x - (((y - z) / (a - z)) * (x - t));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if ((t_1 <= (-2d-238)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - (((y - z) / (a - z)) * (x - t))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-238) || !(t_1 <= 0.0)) {
		tmp = x - (((y - z) / (a - z)) * (x - t));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if (t_1 <= -2e-238) or not (t_1 <= 0.0):
		tmp = x - (((y - z) / (a - z)) * (x - t))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -2e-238) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(Float64(y - z) / Float64(a - z)) * Float64(x - t)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -2e-238) || ~((t_1 <= 0.0)))
		tmp = x - (((y - z) / (a - z)) * (x - t));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-238], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2e-238 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 75.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   if -2e-238 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 7.9%

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

      1. associate-*l/ 7.9%

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

   3. Simplified 7.9%

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

   4. Taylor expanded in z around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. mul-1-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. mul-1-neg 99.8%

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

      6. unsub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. mul-1-neg 99.8%

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

      9. sub-neg 99.8%

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

      10. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

      1. expm1-log1p-u 91.3%

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

      2. expm1-udef 59.3%

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

      3. associate-/l* 59.3%

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

   8. Applied egg-rr 59.3%

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

      1. expm1-def 91.4%

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

      2. expm1-log1p 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -2 \cdot 10^{-238} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;x - \frac{y - z}{a - z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (* (/ y a) (- x t)))))
   (if (<= z -1.15e+33)
     t_1
     (if (<= z -8.2e+24)
       (/ (- y a) (/ z x))
       (if (<= z -3e-25)
         t_1
         (if (<= z -3.8e-89)
           t_2
           (if (<= z -2.6e-110)
             (* (- y z) (/ t (- a z)))
             (if (<= z 2.45e+17)
               t_2
               (if (<= z 1.6e+90)
                 t_1
                 (if (<= z 4.1e+130) t_2 (+ t (/ a (/ z (- t x))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((y / a) * (x - t));
	double tmp;
	if (z <= -1.15e+33) {
		tmp = t_1;
	} else if (z <= -8.2e+24) {
		tmp = (y - a) / (z / x);
	} else if (z <= -3e-25) {
		tmp = t_1;
	} else if (z <= -3.8e-89) {
		tmp = t_2;
	} else if (z <= -2.6e-110) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 2.45e+17) {
		tmp = t_2;
	} else if (z <= 1.6e+90) {
		tmp = t_1;
	} else if (z <= 4.1e+130) {
		tmp = t_2;
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - ((y / a) * (x - t))
    if (z <= (-1.15d+33)) then
        tmp = t_1
    else if (z <= (-8.2d+24)) then
        tmp = (y - a) / (z / x)
    else if (z <= (-3d-25)) then
        tmp = t_1
    else if (z <= (-3.8d-89)) then
        tmp = t_2
    else if (z <= (-2.6d-110)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 2.45d+17) then
        tmp = t_2
    else if (z <= 1.6d+90) then
        tmp = t_1
    else if (z <= 4.1d+130) then
        tmp = t_2
    else
        tmp = t + (a / (z / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((y / a) * (x - t));
	double tmp;
	if (z <= -1.15e+33) {
		tmp = t_1;
	} else if (z <= -8.2e+24) {
		tmp = (y - a) / (z / x);
	} else if (z <= -3e-25) {
		tmp = t_1;
	} else if (z <= -3.8e-89) {
		tmp = t_2;
	} else if (z <= -2.6e-110) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 2.45e+17) {
		tmp = t_2;
	} else if (z <= 1.6e+90) {
		tmp = t_1;
	} else if (z <= 4.1e+130) {
		tmp = t_2;
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - ((y / a) * (x - t))
	tmp = 0
	if z <= -1.15e+33:
		tmp = t_1
	elif z <= -8.2e+24:
		tmp = (y - a) / (z / x)
	elif z <= -3e-25:
		tmp = t_1
	elif z <= -3.8e-89:
		tmp = t_2
	elif z <= -2.6e-110:
		tmp = (y - z) * (t / (a - z))
	elif z <= 2.45e+17:
		tmp = t_2
	elif z <= 1.6e+90:
		tmp = t_1
	elif z <= 4.1e+130:
		tmp = t_2
	else:
		tmp = t + (a / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(Float64(y / a) * Float64(x - t)))
	tmp = 0.0
	if (z <= -1.15e+33)
		tmp = t_1;
	elseif (z <= -8.2e+24)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (z <= -3e-25)
		tmp = t_1;
	elseif (z <= -3.8e-89)
		tmp = t_2;
	elseif (z <= -2.6e-110)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 2.45e+17)
		tmp = t_2;
	elseif (z <= 1.6e+90)
		tmp = t_1;
	elseif (z <= 4.1e+130)
		tmp = t_2;
	else
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - ((y / a) * (x - t));
	tmp = 0.0;
	if (z <= -1.15e+33)
		tmp = t_1;
	elseif (z <= -8.2e+24)
		tmp = (y - a) / (z / x);
	elseif (z <= -3e-25)
		tmp = t_1;
	elseif (z <= -3.8e-89)
		tmp = t_2;
	elseif (z <= -2.6e-110)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 2.45e+17)
		tmp = t_2;
	elseif (z <= 1.6e+90)
		tmp = t_1;
	elseif (z <= 4.1e+130)
		tmp = t_2;
	else
		tmp = t + (a / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+33], t$95$1, If[LessEqual[z, -8.2e+24], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-25], t$95$1, If[LessEqual[z, -3.8e-89], t$95$2, If[LessEqual[z, -2.6e-110], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+17], t$95$2, If[LessEqual[z, 1.6e+90], t$95$1, If[LessEqual[z, 4.1e+130], t$95$2, N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.15000000000000005e33 or -8.2000000000000002e24 < z < -2.9999999999999998e-25 or 2.45e17 < z < 1.59999999999999999e90

   1. Initial program 53.5%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in x around 0 47.2%

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

      1. associate-*r/ 68.5%

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

   6. Simplified 68.5%

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

   if -1.15000000000000005e33 < z < -8.2000000000000002e24

   1. Initial program 72.3%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in z around -inf 99.6%

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

      1. +-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. mul-1-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. mul-1-neg 99.6%

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

      6. unsub-neg 99.6%

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

      7. +-commutative 99.6%

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

      8. mul-1-neg 99.6%

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

      9. sub-neg 99.6%

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

      10. distribute-rgt-out-- 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in t around 0 82.1%

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

      1. associate-/l* 82.3%

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

   9. Simplified 82.3%

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

   if -2.9999999999999998e-25 < z < -3.8000000000000001e-89 or -2.5999999999999999e-110 < z < 2.45e17 or 1.59999999999999999e90 < z < 4.09999999999999978e130

   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/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 80.5%

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

   if -3.8000000000000001e-89 < z < -2.5999999999999999e-110

   1. Initial program 99.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

      1. *-commutative 76.4%

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

      2. clear-num 72.4%

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

      3. un-div-inv 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in x around 0 94.1%

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

      1. associate-/l* 69.3%

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

      2. associate-/r/ 93.9%

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

   8. Simplified 93.9%

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

   if 4.09999999999999978e130 < z

   1. Initial program 36.9%

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

      1. associate-*l/ 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in z around -inf 71.9%

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

      1. +-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. mul-1-neg 71.9%

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

      4. +-commutative 71.9%

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

      5. mul-1-neg 71.9%

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

      6. unsub-neg 71.9%

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

      7. +-commutative 71.9%

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

      8. mul-1-neg 71.9%

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

      9. sub-neg 71.9%

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

      10. distribute-rgt-out-- 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in y around 0 69.2%

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

      1. sub-neg 69.2%

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

      2. mul-1-neg 69.2%

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

      3. remove-double-neg 69.2%

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

      4. associate-/l* 74.4%

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

   9. Simplified 74.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+17}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+130}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 4: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (* (/ y a) (- x t)))))
   (if (<= z -1.15e+33)
     t_1
     (if (<= z -2.4e+23)
       (/ (- y a) (/ z x))
       (if (<= z -2.15e-19)
         t_1
         (if (<= z -6.2e-89)
           t_2
           (if (<= z -2.6e-110)
             (* (- y z) (/ t (- a z)))
             (if (<= z 2.9e+15)
               (+ x (/ (- t x) (/ a y)))
               (if (<= z 1.15e+90)
                 t_1
                 (if (<= z 2.55e+130) t_2 (+ t (/ a (/ z (- t x))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((y / a) * (x - t));
	double tmp;
	if (z <= -1.15e+33) {
		tmp = t_1;
	} else if (z <= -2.4e+23) {
		tmp = (y - a) / (z / x);
	} else if (z <= -2.15e-19) {
		tmp = t_1;
	} else if (z <= -6.2e-89) {
		tmp = t_2;
	} else if (z <= -2.6e-110) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 2.9e+15) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 1.15e+90) {
		tmp = t_1;
	} else if (z <= 2.55e+130) {
		tmp = t_2;
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - ((y / a) * (x - t))
    if (z <= (-1.15d+33)) then
        tmp = t_1
    else if (z <= (-2.4d+23)) then
        tmp = (y - a) / (z / x)
    else if (z <= (-2.15d-19)) then
        tmp = t_1
    else if (z <= (-6.2d-89)) then
        tmp = t_2
    else if (z <= (-2.6d-110)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 2.9d+15) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 1.15d+90) then
        tmp = t_1
    else if (z <= 2.55d+130) then
        tmp = t_2
    else
        tmp = t + (a / (z / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((y / a) * (x - t));
	double tmp;
	if (z <= -1.15e+33) {
		tmp = t_1;
	} else if (z <= -2.4e+23) {
		tmp = (y - a) / (z / x);
	} else if (z <= -2.15e-19) {
		tmp = t_1;
	} else if (z <= -6.2e-89) {
		tmp = t_2;
	} else if (z <= -2.6e-110) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 2.9e+15) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 1.15e+90) {
		tmp = t_1;
	} else if (z <= 2.55e+130) {
		tmp = t_2;
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - ((y / a) * (x - t))
	tmp = 0
	if z <= -1.15e+33:
		tmp = t_1
	elif z <= -2.4e+23:
		tmp = (y - a) / (z / x)
	elif z <= -2.15e-19:
		tmp = t_1
	elif z <= -6.2e-89:
		tmp = t_2
	elif z <= -2.6e-110:
		tmp = (y - z) * (t / (a - z))
	elif z <= 2.9e+15:
		tmp = x + ((t - x) / (a / y))
	elif z <= 1.15e+90:
		tmp = t_1
	elif z <= 2.55e+130:
		tmp = t_2
	else:
		tmp = t + (a / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(Float64(y / a) * Float64(x - t)))
	tmp = 0.0
	if (z <= -1.15e+33)
		tmp = t_1;
	elseif (z <= -2.4e+23)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (z <= -2.15e-19)
		tmp = t_1;
	elseif (z <= -6.2e-89)
		tmp = t_2;
	elseif (z <= -2.6e-110)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 2.9e+15)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 1.15e+90)
		tmp = t_1;
	elseif (z <= 2.55e+130)
		tmp = t_2;
	else
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - ((y / a) * (x - t));
	tmp = 0.0;
	if (z <= -1.15e+33)
		tmp = t_1;
	elseif (z <= -2.4e+23)
		tmp = (y - a) / (z / x);
	elseif (z <= -2.15e-19)
		tmp = t_1;
	elseif (z <= -6.2e-89)
		tmp = t_2;
	elseif (z <= -2.6e-110)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 2.9e+15)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 1.15e+90)
		tmp = t_1;
	elseif (z <= 2.55e+130)
		tmp = t_2;
	else
		tmp = t + (a / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+33], t$95$1, If[LessEqual[z, -2.4e+23], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-19], t$95$1, If[LessEqual[z, -6.2e-89], t$95$2, If[LessEqual[z, -2.6e-110], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+15], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+90], t$95$1, If[LessEqual[z, 2.55e+130], t$95$2, N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.15000000000000005e33 or -2.4e23 < z < -2.15e-19 or 2.9e15 < z < 1.15e90

   1. Initial program 53.5%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in x around 0 47.2%

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

      1. associate-*r/ 68.5%

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

   6. Simplified 68.5%

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

   if -1.15000000000000005e33 < z < -2.4e23

   1. Initial program 72.3%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in z around -inf 99.6%

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

      1. +-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. mul-1-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. mul-1-neg 99.6%

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

      6. unsub-neg 99.6%

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

      7. +-commutative 99.6%

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

      8. mul-1-neg 99.6%

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

      9. sub-neg 99.6%

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

      10. distribute-rgt-out-- 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in t around 0 82.1%

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

      1. associate-/l* 82.3%

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

   9. Simplified 82.3%

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

   if -2.15e-19 < z < -6.19999999999999993e-89 or 1.15e90 < z < 2.5499999999999998e130

   1. Initial program 69.9%

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

      1. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around 0 70.0%

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

   if -6.19999999999999993e-89 < z < -2.5999999999999999e-110

   1. Initial program 99.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

      1. *-commutative 76.4%

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

      2. clear-num 72.4%

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

      3. un-div-inv 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in x around 0 94.1%

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

      1. associate-/l* 69.3%

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

      2. associate-/r/ 93.9%

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

   8. Simplified 93.9%

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

   if -2.5999999999999999e-110 < z < 2.9e15

   1. Initial program 88.7%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

      1. *-commutative 95.1%

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

      2. clear-num 95.1%

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

      3. un-div-inv 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in z around 0 83.5%

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

   if 2.5499999999999998e130 < z

   1. Initial program 36.9%

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

      1. associate-*l/ 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in z around -inf 71.9%

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

      1. +-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. mul-1-neg 71.9%

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

      4. +-commutative 71.9%

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

      5. mul-1-neg 71.9%

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

      6. unsub-neg 71.9%

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

      7. +-commutative 71.9%

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

      8. mul-1-neg 71.9%

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

      9. sub-neg 71.9%

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

      10. distribute-rgt-out-- 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in y around 0 69.2%

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

      1. sub-neg 69.2%

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

      2. mul-1-neg 69.2%

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

      3. remove-double-neg 69.2%

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

      4. associate-/l* 74.4%

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

   9. Simplified 74.4%

      \[\leadsto \color{blue}{t + \frac{a}{\frac{z}{t - x}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+130}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 5: 64.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-21}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (* (/ y a) (- x t)))))
   (if (<= z -8.8e+61)
     t_1
     (if (<= z -2.7e-21)
       (+ t (/ (* y (- x t)) z))
       (if (<= z -3.8e-89)
         t_2
         (if (<= z -2.6e-110)
           (* (- y z) (/ t (- a z)))
           (if (<= z 2.7e+15)
             (+ x (/ (- t x) (/ a y)))
             (if (<= z 1.6e+90)
               t_1
               (if (<= z 7e+130) t_2 (+ t (/ a (/ z (- t x)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((y / a) * (x - t));
	double tmp;
	if (z <= -8.8e+61) {
		tmp = t_1;
	} else if (z <= -2.7e-21) {
		tmp = t + ((y * (x - t)) / z);
	} else if (z <= -3.8e-89) {
		tmp = t_2;
	} else if (z <= -2.6e-110) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 2.7e+15) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 1.6e+90) {
		tmp = t_1;
	} else if (z <= 7e+130) {
		tmp = t_2;
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - ((y / a) * (x - t))
    if (z <= (-8.8d+61)) then
        tmp = t_1
    else if (z <= (-2.7d-21)) then
        tmp = t + ((y * (x - t)) / z)
    else if (z <= (-3.8d-89)) then
        tmp = t_2
    else if (z <= (-2.6d-110)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 2.7d+15) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 1.6d+90) then
        tmp = t_1
    else if (z <= 7d+130) then
        tmp = t_2
    else
        tmp = t + (a / (z / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((y / a) * (x - t));
	double tmp;
	if (z <= -8.8e+61) {
		tmp = t_1;
	} else if (z <= -2.7e-21) {
		tmp = t + ((y * (x - t)) / z);
	} else if (z <= -3.8e-89) {
		tmp = t_2;
	} else if (z <= -2.6e-110) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 2.7e+15) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 1.6e+90) {
		tmp = t_1;
	} else if (z <= 7e+130) {
		tmp = t_2;
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - ((y / a) * (x - t))
	tmp = 0
	if z <= -8.8e+61:
		tmp = t_1
	elif z <= -2.7e-21:
		tmp = t + ((y * (x - t)) / z)
	elif z <= -3.8e-89:
		tmp = t_2
	elif z <= -2.6e-110:
		tmp = (y - z) * (t / (a - z))
	elif z <= 2.7e+15:
		tmp = x + ((t - x) / (a / y))
	elif z <= 1.6e+90:
		tmp = t_1
	elif z <= 7e+130:
		tmp = t_2
	else:
		tmp = t + (a / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(Float64(y / a) * Float64(x - t)))
	tmp = 0.0
	if (z <= -8.8e+61)
		tmp = t_1;
	elseif (z <= -2.7e-21)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (z <= -3.8e-89)
		tmp = t_2;
	elseif (z <= -2.6e-110)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 2.7e+15)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 1.6e+90)
		tmp = t_1;
	elseif (z <= 7e+130)
		tmp = t_2;
	else
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - ((y / a) * (x - t));
	tmp = 0.0;
	if (z <= -8.8e+61)
		tmp = t_1;
	elseif (z <= -2.7e-21)
		tmp = t + ((y * (x - t)) / z);
	elseif (z <= -3.8e-89)
		tmp = t_2;
	elseif (z <= -2.6e-110)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 2.7e+15)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 1.6e+90)
		tmp = t_1;
	elseif (z <= 7e+130)
		tmp = t_2;
	else
		tmp = t + (a / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+61], t$95$1, If[LessEqual[z, -2.7e-21], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-89], t$95$2, If[LessEqual[z, -2.6e-110], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+15], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+90], t$95$1, If[LessEqual[z, 7e+130], t$95$2, N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.8000000000000001e61 or 2.7e15 < z < 1.59999999999999999e90

   1. Initial program 48.5%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in x around 0 47.6%

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

      1. associate-*r/ 72.4%

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

   6. Simplified 72.4%

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

   if -8.8000000000000001e61 < z < -2.7000000000000001e-21

   1. Initial program 74.0%

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

      1. associate-*l/ 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in z around -inf 73.7%

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

      1. +-commutative 73.7%

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

      2. sub-neg 73.7%

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

      3. mul-1-neg 73.7%

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

      4. +-commutative 73.7%

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

      5. mul-1-neg 73.7%

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

      6. unsub-neg 73.7%

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

      7. +-commutative 73.7%

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

      8. mul-1-neg 73.7%

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

      9. sub-neg 73.7%

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

      10. distribute-rgt-out-- 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in y around inf 65.6%

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

   if -2.7000000000000001e-21 < z < -3.8000000000000001e-89 or 1.59999999999999999e90 < z < 7.0000000000000002e130

   1. Initial program 69.9%

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

      1. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around 0 70.0%

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

   if -3.8000000000000001e-89 < z < -2.5999999999999999e-110

   1. Initial program 99.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

      1. *-commutative 76.4%

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

      2. clear-num 72.4%

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

      3. un-div-inv 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in x around 0 94.1%

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

      1. associate-/l* 69.3%

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

      2. associate-/r/ 93.9%

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

   8. Simplified 93.9%

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

   if -2.5999999999999999e-110 < z < 2.7e15

   1. Initial program 88.7%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

      1. *-commutative 95.1%

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

      2. clear-num 95.1%

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

      3. un-div-inv 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in z around 0 83.5%

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

   if 7.0000000000000002e130 < z

   1. Initial program 36.9%

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

      1. associate-*l/ 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in z around -inf 71.9%

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

      1. +-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. mul-1-neg 71.9%

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

      4. +-commutative 71.9%

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

      5. mul-1-neg 71.9%

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

      6. unsub-neg 71.9%

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

      7. +-commutative 71.9%

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

      8. mul-1-neg 71.9%

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

      9. sub-neg 71.9%

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

      10. distribute-rgt-out-- 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in y around 0 69.2%

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

      1. sub-neg 69.2%

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

      2. mul-1-neg 69.2%

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

      3. remove-double-neg 69.2%

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

      4. associate-/l* 74.4%

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

   9. Simplified 74.4%

      \[\leadsto \color{blue}{t + \frac{a}{\frac{z}{t - x}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-21}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+130}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 6: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.62e+122)
     t
     (if (<= z -6.1e-232)
       t_1
       (if (<= z 2.8e-257)
         (/ y (/ a t))
         (if (<= z 1.05e-113)
           t_1
           (if (<= z 2.5e-69)
             (* y (/ t (- a z)))
             (if (<= z 2.5e+46) 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 <= -1.62e+122) {
		tmp = t;
	} else if (z <= -6.1e-232) {
		tmp = t_1;
	} else if (z <= 2.8e-257) {
		tmp = y / (a / t);
	} else if (z <= 1.05e-113) {
		tmp = t_1;
	} else if (z <= 2.5e-69) {
		tmp = y * (t / (a - z));
	} else if (z <= 2.5e+46) {
		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 <= (-1.62d+122)) then
        tmp = t
    else if (z <= (-6.1d-232)) then
        tmp = t_1
    else if (z <= 2.8d-257) then
        tmp = y / (a / t)
    else if (z <= 1.05d-113) then
        tmp = t_1
    else if (z <= 2.5d-69) then
        tmp = y * (t / (a - z))
    else if (z <= 2.5d+46) 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 <= -1.62e+122) {
		tmp = t;
	} else if (z <= -6.1e-232) {
		tmp = t_1;
	} else if (z <= 2.8e-257) {
		tmp = y / (a / t);
	} else if (z <= 1.05e-113) {
		tmp = t_1;
	} else if (z <= 2.5e-69) {
		tmp = y * (t / (a - z));
	} else if (z <= 2.5e+46) {
		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 <= -1.62e+122:
		tmp = t
	elif z <= -6.1e-232:
		tmp = t_1
	elif z <= 2.8e-257:
		tmp = y / (a / t)
	elif z <= 1.05e-113:
		tmp = t_1
	elif z <= 2.5e-69:
		tmp = y * (t / (a - z))
	elif z <= 2.5e+46:
		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 <= -1.62e+122)
		tmp = t;
	elseif (z <= -6.1e-232)
		tmp = t_1;
	elseif (z <= 2.8e-257)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 1.05e-113)
		tmp = t_1;
	elseif (z <= 2.5e-69)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 2.5e+46)
		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 <= -1.62e+122)
		tmp = t;
	elseif (z <= -6.1e-232)
		tmp = t_1;
	elseif (z <= 2.8e-257)
		tmp = y / (a / t);
	elseif (z <= 1.05e-113)
		tmp = t_1;
	elseif (z <= 2.5e-69)
		tmp = y * (t / (a - z));
	elseif (z <= 2.5e+46)
		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, -1.62e+122], t, If[LessEqual[z, -6.1e-232], t$95$1, If[LessEqual[z, 2.8e-257], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-113], t$95$1, If[LessEqual[z, 2.5e-69], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+46], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.61999999999999994e122 or 2.5000000000000001e46 < z

   1. Initial program 38.7%

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

      1. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in z around inf 60.0%

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

   if -1.61999999999999994e122 < z < -6.1000000000000001e-232 or 2.80000000000000001e-257 < z < 1.05e-113 or 2.50000000000000017e-69 < z < 2.5000000000000001e46

   1. Initial program 83.9%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 59.8%

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

   5. Taylor expanded in x around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

   7. Simplified 52.8%

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

   if -6.1000000000000001e-232 < z < 2.80000000000000001e-257

   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/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around 0 53.9%

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

   5. Taylor expanded in z around 0 53.9%

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

      1. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

   if 1.05e-113 < z < 2.50000000000000017e-69

   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/ 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. Taylor expanded in y around inf 73.0%

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

      1. div-sub 73.0%

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

      2. *-commutative 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in t around inf 65.7%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-26}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.4e+141)
   (* t (/ (- y z) (- a z)))
   (if (<= z -4.8e-26)
     (+ t (/ (* (- t x) (- a y)) z))
     (if (<= z -3.8e-89)
       (- x (* (/ y a) (- x t)))
       (if (<= z -2.6e-110)
         (/ (* (- y z) t) (- a z))
         (if (<= z 2e+24)
           (+ x (/ (- t x) (/ a y)))
           (+ t (/ (- x t) (/ z y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.4e+141) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -4.8e-26) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= -3.8e-89) {
		tmp = x - ((y / a) * (x - t));
	} else if (z <= -2.6e-110) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 2e+24) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.4d+141)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-4.8d-26)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= (-3.8d-89)) then
        tmp = x - ((y / a) * (x - t))
    else if (z <= (-2.6d-110)) then
        tmp = ((y - z) * t) / (a - z)
    else if (z <= 2d+24) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.4e+141) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -4.8e-26) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= -3.8e-89) {
		tmp = x - ((y / a) * (x - t));
	} else if (z <= -2.6e-110) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 2e+24) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.4e+141:
		tmp = t * ((y - z) / (a - z))
	elif z <= -4.8e-26:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= -3.8e-89:
		tmp = x - ((y / a) * (x - t))
	elif z <= -2.6e-110:
		tmp = ((y - z) * t) / (a - z)
	elif z <= 2e+24:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.4e+141)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -4.8e-26)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= -3.8e-89)
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	elseif (z <= -2.6e-110)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 2e+24)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.4e+141)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -4.8e-26)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= -3.8e-89)
		tmp = x - ((y / a) * (x - t));
	elseif (z <= -2.6e-110)
		tmp = ((y - z) * t) / (a - z);
	elseif (z <= 2e+24)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.4e+141], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-26], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-89], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-110], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+24], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.3999999999999994e141

   1. Initial program 30.0%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in x around 0 43.5%

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

      1. associate-*r/ 84.7%

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

   6. Simplified 84.7%

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

   if -8.3999999999999994e141 < z < -4.8000000000000002e-26

   1. Initial program 61.5%

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

      1. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in z around -inf 65.3%

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

      1. +-commutative 65.3%

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

      2. sub-neg 65.3%

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

      3. mul-1-neg 65.3%

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

      4. +-commutative 65.3%

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

      5. mul-1-neg 65.3%

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

      6. unsub-neg 65.3%

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

      7. +-commutative 65.3%

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

      8. mul-1-neg 65.3%

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

      9. sub-neg 65.3%

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

      10. distribute-rgt-out-- 65.3%

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

   6. Simplified 65.3%

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

   if -4.8000000000000002e-26 < z < -3.8000000000000001e-89

   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/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 79.4%

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

   if -3.8000000000000001e-89 < z < -2.5999999999999999e-110

   1. Initial program 99.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around 0 94.1%

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

   if -2.5999999999999999e-110 < z < 2e24

   1. Initial program 88.9%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

      1. *-commutative 95.2%

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

      2. clear-num 95.2%

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

      3. un-div-inv 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in z around 0 82.9%

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

   if 2e24 < z

   1. Initial program 48.0%

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

      1. associate-*l/ 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in z around -inf 68.7%

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

      1. +-commutative 68.7%

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

      2. sub-neg 68.7%

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

      3. mul-1-neg 68.7%

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

      4. +-commutative 68.7%

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

      5. mul-1-neg 68.7%

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

      6. unsub-neg 68.7%

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

      7. +-commutative 68.7%

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

      8. mul-1-neg 68.7%

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

      9. sub-neg 68.7%

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

      10. distribute-rgt-out-- 68.9%

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

   6. Simplified 68.9%

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

      1. expm1-log1p-u 51.2%

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

      2. expm1-udef 46.4%

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

      3. associate-/l* 51.4%

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

   8. Applied egg-rr 51.4%

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

      1. expm1-def 56.2%

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

      2. expm1-log1p 82.2%

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

   10. Simplified 82.2%

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

   11. Taylor expanded in y around inf 75.6%

       \[\leadsto t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-26}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 8: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -4e-26)
     t_1
     (if (<= z -3.8e-89)
       (- x (* (/ y a) (- x t)))
       (if (<= z -2.6e-110)
         (/ (* (- y z) t) (- a z))
         (if (<= z 9.2e+22) (+ x (/ (- t x) (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -4e-26) {
		tmp = t_1;
	} else if (z <= -3.8e-89) {
		tmp = x - ((y / a) * (x - t));
	} else if (z <= -2.6e-110) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 9.2e+22) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / (y - a)))
    if (z <= (-4d-26)) then
        tmp = t_1
    else if (z <= (-3.8d-89)) then
        tmp = x - ((y / a) * (x - t))
    else if (z <= (-2.6d-110)) then
        tmp = ((y - z) * t) / (a - z)
    else if (z <= 9.2d+22) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -4e-26) {
		tmp = t_1;
	} else if (z <= -3.8e-89) {
		tmp = x - ((y / a) * (x - t));
	} else if (z <= -2.6e-110) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 9.2e+22) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -4e-26:
		tmp = t_1
	elif z <= -3.8e-89:
		tmp = x - ((y / a) * (x - t))
	elif z <= -2.6e-110:
		tmp = ((y - z) * t) / (a - z)
	elif z <= 9.2e+22:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -4e-26)
		tmp = t_1;
	elseif (z <= -3.8e-89)
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	elseif (z <= -2.6e-110)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 9.2e+22)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -4e-26)
		tmp = t_1;
	elseif (z <= -3.8e-89)
		tmp = x - ((y / a) * (x - t));
	elseif (z <= -2.6e-110)
		tmp = ((y - z) * t) / (a - z);
	elseif (z <= 9.2e+22)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e-26], t$95$1, If[LessEqual[z, -3.8e-89], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-110], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+22], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.0000000000000002e-26 or 9.2000000000000008e22 < z

   1. Initial program 48.2%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around -inf 68.1%

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

      1. +-commutative 68.1%

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

      2. sub-neg 68.1%

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

      3. mul-1-neg 68.1%

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

      4. +-commutative 68.1%

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

      5. mul-1-neg 68.1%

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

      6. unsub-neg 68.1%

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

      7. +-commutative 68.1%

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

      8. mul-1-neg 68.1%

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

      9. sub-neg 68.1%

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

      10. distribute-rgt-out-- 68.2%

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

   6. Simplified 68.2%

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

      1. expm1-log1p-u 51.3%

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

      2. expm1-udef 44.5%

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

      3. associate-/l* 50.2%

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

   8. Applied egg-rr 50.2%

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

      1. expm1-def 57.1%

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

      2. expm1-log1p 79.2%

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

   10. Simplified 79.2%

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

   if -4.0000000000000002e-26 < z < -3.8000000000000001e-89

   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/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 79.4%

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

   if -3.8000000000000001e-89 < z < -2.5999999999999999e-110

   1. Initial program 99.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around 0 94.1%

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

   if -2.5999999999999999e-110 < z < 9.2000000000000008e22

   1. Initial program 88.9%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

      1. *-commutative 95.2%

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

      2. clear-num 95.2%

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

      3. un-div-inv 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in z around 0 82.9%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-26}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 9: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{z - y}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -2.35e-23)
     t_1
     (if (<= z -5.5e-89)
       (+ x (/ (- z y) (/ (- a z) x)))
       (if (<= z -2.5e-110)
         (/ (* (- y z) t) (- a z))
         (if (<= z 1.25e+23) (+ x (/ (- t x) (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -2.35e-23) {
		tmp = t_1;
	} else if (z <= -5.5e-89) {
		tmp = x + ((z - y) / ((a - z) / x));
	} else if (z <= -2.5e-110) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 1.25e+23) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / (y - a)))
    if (z <= (-2.35d-23)) then
        tmp = t_1
    else if (z <= (-5.5d-89)) then
        tmp = x + ((z - y) / ((a - z) / x))
    else if (z <= (-2.5d-110)) then
        tmp = ((y - z) * t) / (a - z)
    else if (z <= 1.25d+23) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -2.35e-23) {
		tmp = t_1;
	} else if (z <= -5.5e-89) {
		tmp = x + ((z - y) / ((a - z) / x));
	} else if (z <= -2.5e-110) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 1.25e+23) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -2.35e-23:
		tmp = t_1
	elif z <= -5.5e-89:
		tmp = x + ((z - y) / ((a - z) / x))
	elif z <= -2.5e-110:
		tmp = ((y - z) * t) / (a - z)
	elif z <= 1.25e+23:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -2.35e-23)
		tmp = t_1;
	elseif (z <= -5.5e-89)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(a - z) / x)));
	elseif (z <= -2.5e-110)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 1.25e+23)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -2.35e-23)
		tmp = t_1;
	elseif (z <= -5.5e-89)
		tmp = x + ((z - y) / ((a - z) / x));
	elseif (z <= -2.5e-110)
		tmp = ((y - z) * t) / (a - z);
	elseif (z <= 1.25e+23)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e-23], t$95$1, If[LessEqual[z, -5.5e-89], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-110], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+23], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.35e-23 or 1.25e23 < z

   1. Initial program 48.2%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around -inf 68.1%

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

      1. +-commutative 68.1%

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

      2. sub-neg 68.1%

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

      3. mul-1-neg 68.1%

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

      4. +-commutative 68.1%

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

      5. mul-1-neg 68.1%

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

      6. unsub-neg 68.1%

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

      7. +-commutative 68.1%

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

      8. mul-1-neg 68.1%

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

      9. sub-neg 68.1%

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

      10. distribute-rgt-out-- 68.2%

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

   6. Simplified 68.2%

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

      1. expm1-log1p-u 51.3%

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

      2. expm1-udef 44.5%

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

      3. associate-/l* 50.2%

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

   8. Applied egg-rr 50.2%

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

      1. expm1-def 57.1%

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

      2. expm1-log1p 79.2%

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

   10. Simplified 79.2%

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

   if -2.35e-23 < z < -5.50000000000000012e-89

   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/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. associate-/l* 86.1%

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

   6. Simplified 86.1%

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

   if -5.50000000000000012e-89 < z < -2.5e-110

   1. Initial program 99.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around 0 94.1%

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

   if -2.5e-110 < z < 1.25e23

   1. Initial program 88.9%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

      1. *-commutative 95.2%

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

      2. clear-num 95.2%

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

      3. un-div-inv 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in z around 0 82.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{z - y}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 10: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+23} \lor \neg \left(x \leq 4.4 \cdot 10^{+129}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -3.4e+113)
     t_1
     (if (<= x -2.3e+61)
       (* x (/ (- y a) z))
       (if (or (<= x -4.5e+23) (not (<= x 4.4e+129)))
         t_1
         (* t (/ (- y z) (- 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 <= -3.4e+113) {
		tmp = t_1;
	} else if (x <= -2.3e+61) {
		tmp = x * ((y - a) / z);
	} else if ((x <= -4.5e+23) || !(x <= 4.4e+129)) {
		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 = x * (1.0d0 - (y / a))
    if (x <= (-3.4d+113)) then
        tmp = t_1
    else if (x <= (-2.3d+61)) then
        tmp = x * ((y - a) / z)
    else if ((x <= (-4.5d+23)) .or. (.not. (x <= 4.4d+129))) 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 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -3.4e+113) {
		tmp = t_1;
	} else if (x <= -2.3e+61) {
		tmp = x * ((y - a) / z);
	} else if ((x <= -4.5e+23) || !(x <= 4.4e+129)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -3.4e+113:
		tmp = t_1
	elif x <= -2.3e+61:
		tmp = x * ((y - a) / z)
	elif (x <= -4.5e+23) or not (x <= 4.4e+129):
		tmp = t_1
	else:
		tmp = t * ((y - z) / (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 <= -3.4e+113)
		tmp = t_1;
	elseif (x <= -2.3e+61)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif ((x <= -4.5e+23) || !(x <= 4.4e+129))
		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 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -3.4e+113)
		tmp = t_1;
	elseif (x <= -2.3e+61)
		tmp = x * ((y - a) / z);
	elseif ((x <= -4.5e+23) || ~((x <= 4.4e+129)))
		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[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+113], t$95$1, If[LessEqual[x, -2.3e+61], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -4.5e+23], N[Not[LessEqual[x, 4.4e+129]], $MachinePrecision]], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000019e113 or -2.3e61 < x < -4.49999999999999979e23 or 4.3999999999999999e129 < x

   1. Initial program 61.7%

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

      1. associate-*l/ 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in z around 0 63.0%

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

   5. Taylor expanded in x around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

   7. Simplified 64.2%

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

   if -3.40000000000000019e113 < x < -2.3e61

   1. Initial program 39.1%

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

      1. associate-*l/ 38.4%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in z around -inf 83.2%

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

      1. +-commutative 83.2%

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

      2. sub-neg 83.2%

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

      3. mul-1-neg 83.2%

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

      4. +-commutative 83.2%

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

      5. mul-1-neg 83.2%

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

      6. unsub-neg 83.2%

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

      7. +-commutative 83.2%

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

      8. mul-1-neg 83.2%

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

      9. sub-neg 83.2%

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

      10. distribute-rgt-out-- 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in t around 0 71.0%

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

      1. associate-/l* 83.1%

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

   9. Simplified 83.1%

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

       1. associate-/r/ 83.3%

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

   11. Applied egg-rr 83.3%

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

   if -4.49999999999999979e23 < x < 4.3999999999999999e129

   1. Initial program 73.2%

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

      1. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in x around 0 59.7%

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

      1. associate-*r/ 72.9%

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

   6. Simplified 72.9%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+23} \lor \neg \left(x \leq 4.4 \cdot 10^{+129}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 11: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z y)))))
   (if (<= z -8.5e-16)
     t_1
     (if (<= z -4e-89)
       (- x (* (/ y a) (- x t)))
       (if (<= z -2.6e-110)
         (* (- y z) (/ t (- a z)))
         (if (<= z 9.2e+22) (+ x (/ (- t x) (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double tmp;
	if (z <= -8.5e-16) {
		tmp = t_1;
	} else if (z <= -4e-89) {
		tmp = x - ((y / a) * (x - t));
	} else if (z <= -2.6e-110) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 9.2e+22) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / y))
    if (z <= (-8.5d-16)) then
        tmp = t_1
    else if (z <= (-4d-89)) then
        tmp = x - ((y / a) * (x - t))
    else if (z <= (-2.6d-110)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 9.2d+22) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double tmp;
	if (z <= -8.5e-16) {
		tmp = t_1;
	} else if (z <= -4e-89) {
		tmp = x - ((y / a) * (x - t));
	} else if (z <= -2.6e-110) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 9.2e+22) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / y))
	tmp = 0
	if z <= -8.5e-16:
		tmp = t_1
	elif z <= -4e-89:
		tmp = x - ((y / a) * (x - t))
	elif z <= -2.6e-110:
		tmp = (y - z) * (t / (a - z))
	elif z <= 9.2e+22:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / y)))
	tmp = 0.0
	if (z <= -8.5e-16)
		tmp = t_1;
	elseif (z <= -4e-89)
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	elseif (z <= -2.6e-110)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 9.2e+22)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / y));
	tmp = 0.0;
	if (z <= -8.5e-16)
		tmp = t_1;
	elseif (z <= -4e-89)
		tmp = x - ((y / a) * (x - t));
	elseif (z <= -2.6e-110)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 9.2e+22)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e-16], t$95$1, If[LessEqual[z, -4e-89], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-110], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+22], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.5000000000000001e-16 or 9.2000000000000008e22 < z

   1. Initial program 48.2%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around -inf 68.1%

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

      1. +-commutative 68.1%

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

      2. sub-neg 68.1%

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

      3. mul-1-neg 68.1%

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

      4. +-commutative 68.1%

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

      5. mul-1-neg 68.1%

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

      6. unsub-neg 68.1%

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

      7. +-commutative 68.1%

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

      8. mul-1-neg 68.1%

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

      9. sub-neg 68.1%

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

      10. distribute-rgt-out-- 68.2%

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

   6. Simplified 68.2%

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

      1. expm1-log1p-u 51.3%

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

      2. expm1-udef 44.5%

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

      3. associate-/l* 50.2%

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

   8. Applied egg-rr 50.2%

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

      1. expm1-def 57.1%

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

      2. expm1-log1p 79.2%

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

   10. Simplified 79.2%

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

   11. Taylor expanded in y around inf 71.4%

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

   if -8.5000000000000001e-16 < z < -4.00000000000000015e-89

   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/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 79.4%

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

   if -4.00000000000000015e-89 < z < -2.5999999999999999e-110

   1. Initial program 99.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

      1. *-commutative 76.4%

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

      2. clear-num 72.4%

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

      3. un-div-inv 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in x around 0 94.1%

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

      1. associate-/l* 69.3%

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

      2. associate-/r/ 93.9%

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

   8. Simplified 93.9%

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

   if -2.5999999999999999e-110 < z < 9.2000000000000008e22

   1. Initial program 88.9%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

      1. *-commutative 95.2%

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

      2. clear-num 95.2%

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

      3. un-div-inv 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in z around 0 82.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 12: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 10^{+24}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z y)))))
   (if (<= z -7.5e-20)
     t_1
     (if (<= z -5e-89)
       (- x (* (/ y a) (- x t)))
       (if (<= z -2.6e-110)
         (/ (* (- y z) t) (- a z))
         (if (<= z 1e+24) (+ x (/ (- t x) (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double tmp;
	if (z <= -7.5e-20) {
		tmp = t_1;
	} else if (z <= -5e-89) {
		tmp = x - ((y / a) * (x - t));
	} else if (z <= -2.6e-110) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 1e+24) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / y))
    if (z <= (-7.5d-20)) then
        tmp = t_1
    else if (z <= (-5d-89)) then
        tmp = x - ((y / a) * (x - t))
    else if (z <= (-2.6d-110)) then
        tmp = ((y - z) * t) / (a - z)
    else if (z <= 1d+24) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double tmp;
	if (z <= -7.5e-20) {
		tmp = t_1;
	} else if (z <= -5e-89) {
		tmp = x - ((y / a) * (x - t));
	} else if (z <= -2.6e-110) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 1e+24) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / y))
	tmp = 0
	if z <= -7.5e-20:
		tmp = t_1
	elif z <= -5e-89:
		tmp = x - ((y / a) * (x - t))
	elif z <= -2.6e-110:
		tmp = ((y - z) * t) / (a - z)
	elif z <= 1e+24:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / y)))
	tmp = 0.0
	if (z <= -7.5e-20)
		tmp = t_1;
	elseif (z <= -5e-89)
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	elseif (z <= -2.6e-110)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 1e+24)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / y));
	tmp = 0.0;
	if (z <= -7.5e-20)
		tmp = t_1;
	elseif (z <= -5e-89)
		tmp = x - ((y / a) * (x - t));
	elseif (z <= -2.6e-110)
		tmp = ((y - z) * t) / (a - z);
	elseif (z <= 1e+24)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-20], t$95$1, If[LessEqual[z, -5e-89], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-110], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+24], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.49999999999999981e-20 or 9.9999999999999998e23 < z

   1. Initial program 48.2%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around -inf 68.1%

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

      1. +-commutative 68.1%

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

      2. sub-neg 68.1%

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

      3. mul-1-neg 68.1%

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

      4. +-commutative 68.1%

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

      5. mul-1-neg 68.1%

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

      6. unsub-neg 68.1%

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

      7. +-commutative 68.1%

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

      8. mul-1-neg 68.1%

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

      9. sub-neg 68.1%

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

      10. distribute-rgt-out-- 68.2%

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

   6. Simplified 68.2%

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

      1. expm1-log1p-u 51.3%

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

      2. expm1-udef 44.5%

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

      3. associate-/l* 50.2%

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

   8. Applied egg-rr 50.2%

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

      1. expm1-def 57.1%

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

      2. expm1-log1p 79.2%

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

   10. Simplified 79.2%

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

   11. Taylor expanded in y around inf 71.4%

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

   if -7.49999999999999981e-20 < z < -4.99999999999999967e-89

   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/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 79.4%

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

   if -4.99999999999999967e-89 < z < -2.5999999999999999e-110

   1. Initial program 99.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around 0 94.1%

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

   if -2.5999999999999999e-110 < z < 9.9999999999999998e23

   1. Initial program 88.9%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

      1. *-commutative 95.2%

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

      2. clear-num 95.2%

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

      3. un-div-inv 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in z around 0 82.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-20}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 10^{+24}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 13: 46.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.62e+122)
     t
     (if (<= z -3.9e-230)
       t_1
       (if (<= z 2.4e-257) (/ y (/ a t)) (if (<= z 7e+46) 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 <= -1.62e+122) {
		tmp = t;
	} else if (z <= -3.9e-230) {
		tmp = t_1;
	} else if (z <= 2.4e-257) {
		tmp = y / (a / t);
	} else if (z <= 7e+46) {
		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 <= (-1.62d+122)) then
        tmp = t
    else if (z <= (-3.9d-230)) then
        tmp = t_1
    else if (z <= 2.4d-257) then
        tmp = y / (a / t)
    else if (z <= 7d+46) 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 <= -1.62e+122) {
		tmp = t;
	} else if (z <= -3.9e-230) {
		tmp = t_1;
	} else if (z <= 2.4e-257) {
		tmp = y / (a / t);
	} else if (z <= 7e+46) {
		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 <= -1.62e+122:
		tmp = t
	elif z <= -3.9e-230:
		tmp = t_1
	elif z <= 2.4e-257:
		tmp = y / (a / t)
	elif z <= 7e+46:
		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 <= -1.62e+122)
		tmp = t;
	elseif (z <= -3.9e-230)
		tmp = t_1;
	elseif (z <= 2.4e-257)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 7e+46)
		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 <= -1.62e+122)
		tmp = t;
	elseif (z <= -3.9e-230)
		tmp = t_1;
	elseif (z <= 2.4e-257)
		tmp = y / (a / t);
	elseif (z <= 7e+46)
		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, -1.62e+122], t, If[LessEqual[z, -3.9e-230], t$95$1, If[LessEqual[z, 2.4e-257], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+46], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.61999999999999994e122 or 6.9999999999999997e46 < z

   1. Initial program 38.7%

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

      1. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in z around inf 60.0%

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

   if -1.61999999999999994e122 < z < -3.9000000000000002e-230 or 2.40000000000000017e-257 < z < 6.9999999999999997e46

   1. Initial program 84.1%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around 0 61.7%

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

   5. Taylor expanded in x around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

   7. Simplified 51.2%

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

   if -3.9000000000000002e-230 < z < 2.40000000000000017e-257

   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/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around 0 53.9%

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

   5. Taylor expanded in z around 0 53.9%

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

      1. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.8e+122)
     t
     (if (<= z -5.5e-193)
       t_1
       (if (<= z 2.8e-257) (* y (/ (- t x) a)) (if (<= z 9.5e+46) 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 <= -1.8e+122) {
		tmp = t;
	} else if (z <= -5.5e-193) {
		tmp = t_1;
	} else if (z <= 2.8e-257) {
		tmp = y * ((t - x) / a);
	} else if (z <= 9.5e+46) {
		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 <= (-1.8d+122)) then
        tmp = t
    else if (z <= (-5.5d-193)) then
        tmp = t_1
    else if (z <= 2.8d-257) then
        tmp = y * ((t - x) / a)
    else if (z <= 9.5d+46) 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 <= -1.8e+122) {
		tmp = t;
	} else if (z <= -5.5e-193) {
		tmp = t_1;
	} else if (z <= 2.8e-257) {
		tmp = y * ((t - x) / a);
	} else if (z <= 9.5e+46) {
		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 <= -1.8e+122:
		tmp = t
	elif z <= -5.5e-193:
		tmp = t_1
	elif z <= 2.8e-257:
		tmp = y * ((t - x) / a)
	elif z <= 9.5e+46:
		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 <= -1.8e+122)
		tmp = t;
	elseif (z <= -5.5e-193)
		tmp = t_1;
	elseif (z <= 2.8e-257)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 9.5e+46)
		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 <= -1.8e+122)
		tmp = t;
	elseif (z <= -5.5e-193)
		tmp = t_1;
	elseif (z <= 2.8e-257)
		tmp = y * ((t - x) / a);
	elseif (z <= 9.5e+46)
		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, -1.8e+122], t, If[LessEqual[z, -5.5e-193], t$95$1, If[LessEqual[z, 2.8e-257], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+46], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8000000000000001e122 or 9.5000000000000008e46 < z

   1. Initial program 38.7%

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

      1. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in z around inf 60.0%

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

   if -1.8000000000000001e122 < z < -5.50000000000000014e-193 or 2.80000000000000001e-257 < z < 9.5000000000000008e46

   1. Initial program 84.5%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around 0 60.9%

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

   5. Taylor expanded in x around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

   7. Simplified 50.8%

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

   if -5.50000000000000014e-193 < z < 2.80000000000000001e-257

   1. Initial program 86.4%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 96.5%

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

   5. Taylor expanded in y around inf 75.4%

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

      1. div-sub 79.0%

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

      2. *-commutative 79.0%

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

   7. Simplified 79.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+122)
   t
   (if (<= z -5.8e-24)
     (/ (- y) (/ z (- t x)))
     (if (<= z -1.25e-224)
       (* x (- 1.0 (/ y a)))
       (if (<= z 1.8e+43) (+ x (/ (* y t) a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+122) {
		tmp = t;
	} else if (z <= -5.8e-24) {
		tmp = -y / (z / (t - x));
	} else if (z <= -1.25e-224) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.8e+43) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.2d+122)) then
        tmp = t
    else if (z <= (-5.8d-24)) then
        tmp = -y / (z / (t - x))
    else if (z <= (-1.25d-224)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.8d+43) then
        tmp = x + ((y * t) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+122) {
		tmp = t;
	} else if (z <= -5.8e-24) {
		tmp = -y / (z / (t - x));
	} else if (z <= -1.25e-224) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.8e+43) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+122:
		tmp = t
	elif z <= -5.8e-24:
		tmp = -y / (z / (t - x))
	elif z <= -1.25e-224:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.8e+43:
		tmp = x + ((y * t) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+122)
		tmp = t;
	elseif (z <= -5.8e-24)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= -1.25e-224)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.8e+43)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+122)
		tmp = t;
	elseif (z <= -5.8e-24)
		tmp = -y / (z / (t - x));
	elseif (z <= -1.25e-224)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.8e+43)
		tmp = x + ((y * t) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+122], t, If[LessEqual[z, -5.8e-24], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-224], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+43], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1999999999999999e122 or 1.80000000000000005e43 < z

   1. Initial program 39.3%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in z around inf 59.4%

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

   if -2.1999999999999999e122 < z < -5.7999999999999997e-24

   1. Initial program 69.3%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in z around -inf 57.3%

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

      1. +-commutative 57.3%

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

      2. sub-neg 57.3%

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

      3. mul-1-neg 57.3%

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

      4. +-commutative 57.3%

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

      5. mul-1-neg 57.3%

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

      6. unsub-neg 57.3%

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

      7. +-commutative 57.3%

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

      8. mul-1-neg 57.3%

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

      9. sub-neg 57.3%

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

      10. distribute-rgt-out-- 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in y around -inf 35.3%

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

      1. mul-1-neg 35.3%

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

      2. associate-/l* 43.4%

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

   9. Simplified 43.4%

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

   if -5.7999999999999997e-24 < z < -1.25e-224

   1. Initial program 87.7%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in z around 0 72.4%

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

   5. Taylor expanded in x around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. unsub-neg 63.8%

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

   7. Simplified 63.8%

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

   if -1.25e-224 < z < 1.80000000000000005e43

   1. Initial program 89.3%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 79.0%

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

   5. Taylor expanded in t around inf 63.2%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 37.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+15)
   t
   (if (<= z -4.8e-193) x (if (<= z 7e+24) (* t (/ (- y z) a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+15) {
		tmp = t;
	} else if (z <= -4.8e-193) {
		tmp = x;
	} else if (z <= 7e+24) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.1d+15)) then
        tmp = t
    else if (z <= (-4.8d-193)) then
        tmp = x
    else if (z <= 7d+24) then
        tmp = t * ((y - z) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+15) {
		tmp = t;
	} else if (z <= -4.8e-193) {
		tmp = x;
	} else if (z <= 7e+24) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+15:
		tmp = t
	elif z <= -4.8e-193:
		tmp = x
	elif z <= 7e+24:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+15)
		tmp = t;
	elseif (z <= -4.8e-193)
		tmp = x;
	elseif (z <= 7e+24)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e+15)
		tmp = t;
	elseif (z <= -4.8e-193)
		tmp = x;
	elseif (z <= 7e+24)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+15], t, If[LessEqual[z, -4.8e-193], x, If[LessEqual[z, 7e+24], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e15 or 7.0000000000000004e24 < z

   1. Initial program 47.7%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 49.3%

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

   if -3.1e15 < z < -4.8e-193

   1. Initial program 86.0%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around inf 33.6%

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

   if -4.8e-193 < z < 7.0000000000000004e24

   1. Initial program 89.3%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 49.3%

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

      1. associate-*r/ 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in a around inf 46.8%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.62e+122)
   t
   (if (<= z -2.55e-228)
     (* x (- 1.0 (/ y a)))
     (if (<= z 7.9e+43) (+ x (/ (* y t) a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.62e+122) {
		tmp = t;
	} else if (z <= -2.55e-228) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 7.9e+43) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.62d+122)) then
        tmp = t
    else if (z <= (-2.55d-228)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 7.9d+43) then
        tmp = x + ((y * t) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.62e+122) {
		tmp = t;
	} else if (z <= -2.55e-228) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 7.9e+43) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.62e+122:
		tmp = t
	elif z <= -2.55e-228:
		tmp = x * (1.0 - (y / a))
	elif z <= 7.9e+43:
		tmp = x + ((y * t) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.62e+122)
		tmp = t;
	elseif (z <= -2.55e-228)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 7.9e+43)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.62e+122)
		tmp = t;
	elseif (z <= -2.55e-228)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 7.9e+43)
		tmp = x + ((y * t) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.62e+122], t, If[LessEqual[z, -2.55e-228], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.9e+43], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.61999999999999994e122 or 7.89999999999999963e43 < z

   1. Initial program 39.3%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in z around inf 59.4%

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

   if -1.61999999999999994e122 < z < -2.5500000000000001e-228

   1. Initial program 79.9%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in z around 0 54.1%

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

   5. Taylor expanded in x around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   7. Simplified 49.2%

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

   if -2.5500000000000001e-228 < z < 7.89999999999999963e43

   1. Initial program 89.3%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 79.0%

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

   5. Taylor expanded in t around inf 63.2%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+17)
   t
   (if (<= z -2.15e-193) x (if (<= z 1.95e+23) (* t (/ y a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+17) {
		tmp = t;
	} else if (z <= -2.15e-193) {
		tmp = x;
	} else if (z <= 1.95e+23) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.5d+17)) then
        tmp = t
    else if (z <= (-2.15d-193)) then
        tmp = x
    else if (z <= 1.95d+23) then
        tmp = t * (y / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+17) {
		tmp = t;
	} else if (z <= -2.15e-193) {
		tmp = x;
	} else if (z <= 1.95e+23) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+17:
		tmp = t
	elif z <= -2.15e-193:
		tmp = x
	elif z <= 1.95e+23:
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+17)
		tmp = t;
	elseif (z <= -2.15e-193)
		tmp = x;
	elseif (z <= 1.95e+23)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+17)
		tmp = t;
	elseif (z <= -2.15e-193)
		tmp = x;
	elseif (z <= 1.95e+23)
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+17], t, If[LessEqual[z, -2.15e-193], x, If[LessEqual[z, 1.95e+23], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5e17 or 1.95e23 < z

   1. Initial program 47.7%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 49.3%

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

   if -9.5e17 < z < -2.1500000000000001e-193

   1. Initial program 86.0%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around inf 33.6%

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

   if -2.1500000000000001e-193 < z < 1.95e23

   1. Initial program 89.3%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 49.3%

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

      1. associate-*r/ 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in z around 0 43.1%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 36.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+16)
   t
   (if (<= z -3.3e-193) x (if (<= z 2e+24) (/ y (/ a t)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+16) {
		tmp = t;
	} else if (z <= -3.3e-193) {
		tmp = x;
	} else if (z <= 2e+24) {
		tmp = y / (a / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+16)) then
        tmp = t
    else if (z <= (-3.3d-193)) then
        tmp = x
    else if (z <= 2d+24) then
        tmp = y / (a / t)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+16) {
		tmp = t;
	} else if (z <= -3.3e-193) {
		tmp = x;
	} else if (z <= 2e+24) {
		tmp = y / (a / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+16:
		tmp = t
	elif z <= -3.3e-193:
		tmp = x
	elif z <= 2e+24:
		tmp = y / (a / t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+16)
		tmp = t;
	elseif (z <= -3.3e-193)
		tmp = x;
	elseif (z <= 2e+24)
		tmp = Float64(y / Float64(a / t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+16)
		tmp = t;
	elseif (z <= -3.3e-193)
		tmp = x;
	elseif (z <= 2e+24)
		tmp = y / (a / t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+16], t, If[LessEqual[z, -3.3e-193], x, If[LessEqual[z, 2e+24], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5e16 or 2e24 < z

   1. Initial program 47.7%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 49.3%

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

   if -4.5e16 < z < -3.2999999999999999e-193

   1. Initial program 86.0%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around inf 33.6%

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

   if -3.2999999999999999e-193 < z < 2e24

   1. Initial program 89.3%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 49.3%

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

   5. Taylor expanded in z around 0 40.9%

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

      1. associate-/l* 43.2%

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

   7. Simplified 43.2%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 38.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+17) t (if (<= z 1.6e+43) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+17) {
		tmp = t;
	} else if (z <= 1.6e+43) {
		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 <= (-1d+17)) then
        tmp = t
    else if (z <= 1.6d+43) 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 <= -1e+17) {
		tmp = t;
	} else if (z <= 1.6e+43) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+17:
		tmp = t
	elif z <= 1.6e+43:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+17)
		tmp = t;
	elseif (z <= 1.6e+43)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+17)
		tmp = t;
	elseif (z <= 1.6e+43)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+17], t, If[LessEqual[z, 1.6e+43], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1e17 or 1.60000000000000007e43 < z

   1. Initial program 46.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 50.0%

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

   if -1e17 < z < 1.60000000000000007e43

   1. Initial program 87.7%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around inf 30.2%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 68.2%

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

   1. associate-*l/ 83.4%

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

3. Simplified 83.4%

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

4. Taylor expanded in t around 0 35.6%

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

   1. +-commutative 35.6%

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

   2. mul-1-neg 35.6%

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

   3. unsub-neg 35.6%

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

   4. associate-/l* 40.0%

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

6. Simplified 40.0%

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

7. Taylor expanded in y around 0 20.8%

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

   1. sub-neg 20.8%

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

   2. mul-1-neg 20.8%

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

   3. remove-double-neg 20.8%

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

   4. associate-/l* 22.4%

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

   5. associate-/r/ 21.6%

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

9. Simplified 21.6%

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

10. Taylor expanded in z around inf 2.7%

    \[\leadsto \color{blue}{-1 \cdot x + x} \]
11. Step-by-step derivation

    1. distribute-lft1-in 2.7%

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

    2. metadata-eval 2.7%

       \[\leadsto \color{blue}{0} \cdot x \]

    3. mul0-lft 2.7%

       \[\leadsto \color{blue}{0} \]

12. Simplified 2.7%

    \[\leadsto \color{blue}{0} \]

13. Final simplification 2.7%

    \[\leadsto 0 \]

Alternative 22: 25.1% 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 68.2%

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

   1. associate-*l/ 83.4%

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

3. Simplified 83.4%

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

4. Taylor expanded in z around inf 27.1%

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

5. Final simplification 27.1%

   \[\leadsto t \]

Developer target: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023185 
(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))))