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

Percentage Accurate: 67.7% → 90.2%

Time: 24.1s

Alternatives: 20

Speedup: 0.9×

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: 67.7% 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: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -1e-280)
     (fma (/ (- y z) (- a z)) (- t x) x)
     (if (<= t_1 0.0)
       (- t (/ (* (- t x) (- y a)) z))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -1e-280) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else if (t_1 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-280)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-280], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999996e-281

   1. Initial program 74.9%

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

      1. +-commutative 74.9%

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

      2. associate-*l/ 93.3%

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

      3. fma-def 93.3%

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

   3. Simplified 93.3%

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

   if -9.9999999999999996e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.9%

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

      1. associate-*l/ 4.9%

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

   3. Simplified 4.9%

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

   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. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-*l/ 91.6%

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

      3. fma-def 91.6%

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

   3. Simplified 91.6%

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

      1. fma-udef 91.6%

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

      2. *-commutative 91.6%

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

      3. clear-num 91.6%

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

      4. un-div-inv 91.9%

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

   5. Applied egg-rr 91.9%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2: 90.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-280} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-280) (not (<= t_1 0.0)))
     (+ x (* (- x t) (/ (- z y) (- a z))))
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-280)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - t) * ((z - y) / (a - z)))
    else
        tmp = t - (((t - x) * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-280) or not (t_1 <= 0.0):
		tmp = x + ((x - t) * ((z - y) / (a - z)))
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-280) || ~((t_1 <= 0.0)))
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	else
		tmp = t - (((t - x) * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-280], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999996e-281 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.4%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   if -9.9999999999999996e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.9%

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

      1. associate-*l/ 4.9%

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

   3. Simplified 4.9%

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

   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. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-280} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]

Alternative 3: 90.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-280}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -1e-280)
     (+ x (* (- x t) (/ (- z y) (- a z))))
     (if (<= t_1 0.0)
       (- t (/ (* (- t x) (- y a)) z))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -1e-280) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if (t_1 <= (-1d-280)) then
        tmp = x + ((x - t) * ((z - y) / (a - z)))
    else if (t_1 <= 0.0d0) then
        tmp = t - (((t - x) * (y - a)) / z)
    else
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -1e-280) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_1 <= -1e-280:
		tmp = x + ((x - t) * ((z - y) / (a - z)))
	elif t_1 <= 0.0:
		tmp = t - (((t - x) * (y - a)) / z)
	else:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-280)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -1e-280)
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	elseif (t_1 <= 0.0)
		tmp = t - (((t - x) * (y - a)) / z);
	else
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-280], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999996e-281

   1. Initial program 74.9%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   if -9.9999999999999996e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.9%

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

      1. associate-*l/ 4.9%

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

   3. Simplified 4.9%

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

   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. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-*l/ 91.6%

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

      3. fma-def 91.6%

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

   3. Simplified 91.6%

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

      1. fma-udef 91.6%

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

      2. *-commutative 91.6%

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

      3. clear-num 91.6%

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

      4. un-div-inv 91.9%

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

   5. Applied egg-rr 91.9%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-280}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 4: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-200}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-70}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t (- z y)) z)))
   (if (<= a -9.8e+19)
     (+ x (/ (* y t) a))
     (if (<= a -9.2e-113)
       t
       (if (<= a -1.35e-200)
         (* (- y a) (/ x z))
         (if (<= a 4.6e-175)
           t_1
           (if (<= a 4.5e-162)
             (/ (- y) (/ (- a z) x))
             (if (<= a 1.32e-70)
               (/ (* y t) (- a z))
               (if (<= a 5.5e-22) t_1 (+ x (/ y (/ a t))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (z - y)) / z;
	double tmp;
	if (a <= -9.8e+19) {
		tmp = x + ((y * t) / a);
	} else if (a <= -9.2e-113) {
		tmp = t;
	} else if (a <= -1.35e-200) {
		tmp = (y - a) * (x / z);
	} else if (a <= 4.6e-175) {
		tmp = t_1;
	} else if (a <= 4.5e-162) {
		tmp = -y / ((a - z) / x);
	} else if (a <= 1.32e-70) {
		tmp = (y * t) / (a - z);
	} else if (a <= 5.5e-22) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (z - y)) / z
    if (a <= (-9.8d+19)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-9.2d-113)) then
        tmp = t
    else if (a <= (-1.35d-200)) then
        tmp = (y - a) * (x / z)
    else if (a <= 4.6d-175) then
        tmp = t_1
    else if (a <= 4.5d-162) then
        tmp = -y / ((a - z) / x)
    else if (a <= 1.32d-70) then
        tmp = (y * t) / (a - z)
    else if (a <= 5.5d-22) then
        tmp = t_1
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * (z - y)) / z;
	double tmp;
	if (a <= -9.8e+19) {
		tmp = x + ((y * t) / a);
	} else if (a <= -9.2e-113) {
		tmp = t;
	} else if (a <= -1.35e-200) {
		tmp = (y - a) * (x / z);
	} else if (a <= 4.6e-175) {
		tmp = t_1;
	} else if (a <= 4.5e-162) {
		tmp = -y / ((a - z) / x);
	} else if (a <= 1.32e-70) {
		tmp = (y * t) / (a - z);
	} else if (a <= 5.5e-22) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * (z - y)) / z
	tmp = 0
	if a <= -9.8e+19:
		tmp = x + ((y * t) / a)
	elif a <= -9.2e-113:
		tmp = t
	elif a <= -1.35e-200:
		tmp = (y - a) * (x / z)
	elif a <= 4.6e-175:
		tmp = t_1
	elif a <= 4.5e-162:
		tmp = -y / ((a - z) / x)
	elif a <= 1.32e-70:
		tmp = (y * t) / (a - z)
	elif a <= 5.5e-22:
		tmp = t_1
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * Float64(z - y)) / z)
	tmp = 0.0
	if (a <= -9.8e+19)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -9.2e-113)
		tmp = t;
	elseif (a <= -1.35e-200)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (a <= 4.6e-175)
		tmp = t_1;
	elseif (a <= 4.5e-162)
		tmp = Float64(Float64(-y) / Float64(Float64(a - z) / x));
	elseif (a <= 1.32e-70)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (a <= 5.5e-22)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * (z - y)) / z;
	tmp = 0.0;
	if (a <= -9.8e+19)
		tmp = x + ((y * t) / a);
	elseif (a <= -9.2e-113)
		tmp = t;
	elseif (a <= -1.35e-200)
		tmp = (y - a) * (x / z);
	elseif (a <= 4.6e-175)
		tmp = t_1;
	elseif (a <= 4.5e-162)
		tmp = -y / ((a - z) / x);
	elseif (a <= 1.32e-70)
		tmp = (y * t) / (a - z);
	elseif (a <= 5.5e-22)
		tmp = t_1;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[a, -9.8e+19], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.2e-113], t, If[LessEqual[a, -1.35e-200], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-175], t$95$1, If[LessEqual[a, 4.5e-162], N[((-y) / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.32e-70], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-22], t$95$1, N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -9.8e19

   1. Initial program 65.9%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 79.8%

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

   5. Taylor expanded in t around inf 67.5%

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

   if -9.8e19 < a < -9.20000000000000032e-113

   1. Initial program 63.2%

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

      1. associate-*l/ 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in z around inf 55.1%

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

   if -9.20000000000000032e-113 < a < -1.3500000000000001e-200

   1. Initial program 81.5%

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

      1. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in x around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in z around inf 49.5%

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

      1. associate-*r/ 49.5%

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

      2. neg-mul-1 49.5%

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

      3. +-commutative 49.5%

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

      4. distribute-lft-in 49.5%

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

      5. neg-mul-1 49.5%

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

      6. remove-double-neg 49.5%

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

      7. neg-mul-1 49.5%

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

      8. sub-neg 49.5%

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

   9. Simplified 49.5%

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

       1. *-commutative 49.5%

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

       2. clear-num 49.5%

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

       3. un-div-inv 49.5%

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

   11. Applied egg-rr 49.5%

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

       1. associate-/r/ 53.7%

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

   13. Simplified 53.7%

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

   if -1.3500000000000001e-200 < a < 4.6e-175 or 1.3200000000000001e-70 < a < 5.5000000000000001e-22

   1. Initial program 60.3%

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

      1. associate-*l/ 76.8%

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

   3. Simplified 76.8%

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

   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 a around 0 52.5%

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

      1. mul-1-neg 52.5%

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

   7. Simplified 52.5%

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

   if 4.6e-175 < a < 4.50000000000000023e-162

   1. Initial program 50.9%

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

      1. associate-*l/ 51.5%

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

   3. Simplified 51.5%

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

   4. Taylor expanded in x around inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in y around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in y around 0 100.0%

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

       1. mul-1-neg 100.0%

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

       2. associate-/l* 100.0%

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

   12. Simplified 100.0%

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

   if 4.50000000000000023e-162 < a < 1.3200000000000001e-70

   1. Initial program 84.6%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around 0 65.2%

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

   5. Taylor expanded in y around inf 52.7%

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

   if 5.5000000000000001e-22 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around 0 69.6%

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

   5. Taylor expanded in t around inf 57.0%

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

      1. associate-/l* 63.3%

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

   7. Simplified 63.3%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-200}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-175}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-70}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 5: 38.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-304}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-177}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= a -5.1e+113)
     x
     (if (<= a -9.2e+21)
       t_1
       (if (<= a -1.2e-113)
         t
         (if (<= a -3.4e-304)
           (/ y (/ z x))
           (if (<= a 2.05e-177) t (if (<= a 3.1e+31) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -5.1e+113) {
		tmp = x;
	} else if (a <= -9.2e+21) {
		tmp = t_1;
	} else if (a <= -1.2e-113) {
		tmp = t;
	} else if (a <= -3.4e-304) {
		tmp = y / (z / x);
	} else if (a <= 2.05e-177) {
		tmp = t;
	} else if (a <= 3.1e+31) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (a <= (-5.1d+113)) then
        tmp = x
    else if (a <= (-9.2d+21)) then
        tmp = t_1
    else if (a <= (-1.2d-113)) then
        tmp = t
    else if (a <= (-3.4d-304)) then
        tmp = y / (z / x)
    else if (a <= 2.05d-177) then
        tmp = t
    else if (a <= 3.1d+31) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -5.1e+113) {
		tmp = x;
	} else if (a <= -9.2e+21) {
		tmp = t_1;
	} else if (a <= -1.2e-113) {
		tmp = t;
	} else if (a <= -3.4e-304) {
		tmp = y / (z / x);
	} else if (a <= 2.05e-177) {
		tmp = t;
	} else if (a <= 3.1e+31) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if a <= -5.1e+113:
		tmp = x
	elif a <= -9.2e+21:
		tmp = t_1
	elif a <= -1.2e-113:
		tmp = t
	elif a <= -3.4e-304:
		tmp = y / (z / x)
	elif a <= 2.05e-177:
		tmp = t
	elif a <= 3.1e+31:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -5.1e+113)
		tmp = x;
	elseif (a <= -9.2e+21)
		tmp = t_1;
	elseif (a <= -1.2e-113)
		tmp = t;
	elseif (a <= -3.4e-304)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 2.05e-177)
		tmp = t;
	elseif (a <= 3.1e+31)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -5.1e+113)
		tmp = x;
	elseif (a <= -9.2e+21)
		tmp = t_1;
	elseif (a <= -1.2e-113)
		tmp = t;
	elseif (a <= -3.4e-304)
		tmp = y / (z / x);
	elseif (a <= 2.05e-177)
		tmp = t;
	elseif (a <= 3.1e+31)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+113], x, If[LessEqual[a, -9.2e+21], t$95$1, If[LessEqual[a, -1.2e-113], t, If[LessEqual[a, -3.4e-304], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-177], t, If[LessEqual[a, 3.1e+31], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.09999999999999994e113 or 3.1000000000000002e31 < a

   1. Initial program 69.0%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in a around inf 57.3%

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

   if -5.09999999999999994e113 < a < -9.2e21 or 2.05e-177 < a < 3.1000000000000002e31

   1. Initial program 74.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around 0 49.2%

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

   5. Taylor expanded in y around inf 41.1%

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

      1. div-sub 41.1%

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

      2. *-commutative 41.1%

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

   7. Simplified 41.1%

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

   if -9.2e21 < a < -1.20000000000000006e-113 or -3.3999999999999999e-304 < a < 2.05e-177

   1. Initial program 56.3%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 54.4%

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

   if -1.20000000000000006e-113 < a < -3.3999999999999999e-304

   1. Initial program 73.7%

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

      1. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in x around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

   6. Simplified 46.2%

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

   7. Taylor expanded in a around 0 41.3%

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

      1. associate-/l* 44.8%

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

   9. Simplified 44.8%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-304}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-177}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 44.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-305}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-181}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-8}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e+18)
   (+ x (/ (* y t) a))
   (if (<= a -4.1e-114)
     t
     (if (<= a -1.85e-305)
       (* (- y a) (/ x z))
       (if (<= a 1.95e-181)
         t
         (if (<= a 7.6e-157)
           (/ (- y) (/ (- a z) x))
           (if (<= a 3e-8) (/ (* y t) (- a z)) (+ x (/ y (/ a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+18) {
		tmp = x + ((y * t) / a);
	} else if (a <= -4.1e-114) {
		tmp = t;
	} else if (a <= -1.85e-305) {
		tmp = (y - a) * (x / z);
	} else if (a <= 1.95e-181) {
		tmp = t;
	} else if (a <= 7.6e-157) {
		tmp = -y / ((a - z) / x);
	} else if (a <= 3e-8) {
		tmp = (y * t) / (a - z);
	} else {
		tmp = x + (y / (a / 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 (a <= (-4.8d+18)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-4.1d-114)) then
        tmp = t
    else if (a <= (-1.85d-305)) then
        tmp = (y - a) * (x / z)
    else if (a <= 1.95d-181) then
        tmp = t
    else if (a <= 7.6d-157) then
        tmp = -y / ((a - z) / x)
    else if (a <= 3d-8) then
        tmp = (y * t) / (a - z)
    else
        tmp = x + (y / (a / 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 (a <= -4.8e+18) {
		tmp = x + ((y * t) / a);
	} else if (a <= -4.1e-114) {
		tmp = t;
	} else if (a <= -1.85e-305) {
		tmp = (y - a) * (x / z);
	} else if (a <= 1.95e-181) {
		tmp = t;
	} else if (a <= 7.6e-157) {
		tmp = -y / ((a - z) / x);
	} else if (a <= 3e-8) {
		tmp = (y * t) / (a - z);
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e+18:
		tmp = x + ((y * t) / a)
	elif a <= -4.1e-114:
		tmp = t
	elif a <= -1.85e-305:
		tmp = (y - a) * (x / z)
	elif a <= 1.95e-181:
		tmp = t
	elif a <= 7.6e-157:
		tmp = -y / ((a - z) / x)
	elif a <= 3e-8:
		tmp = (y * t) / (a - z)
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e+18)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -4.1e-114)
		tmp = t;
	elseif (a <= -1.85e-305)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (a <= 1.95e-181)
		tmp = t;
	elseif (a <= 7.6e-157)
		tmp = Float64(Float64(-y) / Float64(Float64(a - z) / x));
	elseif (a <= 3e-8)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e+18)
		tmp = x + ((y * t) / a);
	elseif (a <= -4.1e-114)
		tmp = t;
	elseif (a <= -1.85e-305)
		tmp = (y - a) * (x / z);
	elseif (a <= 1.95e-181)
		tmp = t;
	elseif (a <= 7.6e-157)
		tmp = -y / ((a - z) / x);
	elseif (a <= 3e-8)
		tmp = (y * t) / (a - z);
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e+18], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.1e-114], t, If[LessEqual[a, -1.85e-305], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e-181], t, If[LessEqual[a, 7.6e-157], N[((-y) / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-8], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.8e18

   1. Initial program 65.9%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 79.8%

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

   5. Taylor expanded in t around inf 67.5%

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

   if -4.8e18 < a < -4.0999999999999997e-114 or -1.84999999999999989e-305 < a < 1.95e-181

   1. Initial program 54.5%

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

      1. associate-*l/ 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in z around inf 54.5%

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

   if -4.0999999999999997e-114 < a < -1.84999999999999989e-305

   1. Initial program 73.7%

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

      1. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in x around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

   6. Simplified 46.2%

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

   7. Taylor expanded in z around inf 45.8%

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

      1. associate-*r/ 45.8%

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

      2. neg-mul-1 45.8%

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

      3. +-commutative 45.8%

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

      4. distribute-lft-in 45.8%

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

      5. neg-mul-1 45.8%

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

      6. remove-double-neg 45.8%

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

      7. neg-mul-1 45.8%

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

      8. sub-neg 45.8%

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

   9. Simplified 45.8%

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

       1. *-commutative 45.8%

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

       2. clear-num 45.8%

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

       3. un-div-inv 45.9%

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

   11. Applied egg-rr 45.9%

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

       1. associate-/r/ 48.1%

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

   13. Simplified 48.1%

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

   if 1.95e-181 < a < 7.60000000000000041e-157

   1. Initial program 58.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. unsub-neg 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in y around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

   9. Simplified 72.4%

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

   10. Taylor expanded in y around 0 72.4%

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

       1. mul-1-neg 72.4%

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

       2. associate-/l* 72.3%

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

   12. Simplified 72.3%

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

   if 7.60000000000000041e-157 < a < 2.99999999999999973e-8

   1. Initial program 81.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 67.7%

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

   5. Taylor expanded in y around inf 48.2%

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

   if 2.99999999999999973e-8 < a

   1. Initial program 72.6%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in z around 0 70.9%

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

   5. Taylor expanded in t around inf 57.4%

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

      1. associate-/l* 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-305}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-181}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-8}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 7: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-144}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 40000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -7.2e+18)
     t_1
     (if (<= a 9.5e-144)
       (- t (/ y (/ z (- t x))))
       (if (<= a 40000000000.0)
         (* t (/ (- y z) (- a z)))
         (if (<= a 6.5e+37) (/ x (/ z (- y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -7.2e+18) {
		tmp = t_1;
	} else if (a <= 9.5e-144) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 40000000000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 6.5e+37) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (a <= (-7.2d+18)) then
        tmp = t_1
    else if (a <= 9.5d-144) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= 40000000000.0d0) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 6.5d+37) then
        tmp = x / (z / (y - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -7.2e+18) {
		tmp = t_1;
	} else if (a <= 9.5e-144) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 40000000000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 6.5e+37) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -7.2e+18:
		tmp = t_1
	elif a <= 9.5e-144:
		tmp = t - (y / (z / (t - x)))
	elif a <= 40000000000.0:
		tmp = t * ((y - z) / (a - z))
	elif a <= 6.5e+37:
		tmp = x / (z / (y - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -7.2e+18)
		tmp = t_1;
	elseif (a <= 9.5e-144)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= 40000000000.0)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 6.5e+37)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -7.2e+18)
		tmp = t_1;
	elseif (a <= 9.5e-144)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= 40000000000.0)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 6.5e+37)
		tmp = x / (z / (y - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+18], t$95$1, If[LessEqual[a, 9.5e-144], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 40000000000.0], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+37], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.2e18 or 6.4999999999999998e37 < a

   1. Initial program 69.2%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 78.9%

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

   if -7.2e18 < a < 9.49999999999999953e-144

   1. Initial program 63.1%

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

      1. associate-*l/ 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in z around -inf 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. distribute-rgt-out-- 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 79.4%

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

   9. Simplified 79.4%

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

   if 9.49999999999999953e-144 < a < 4e10

   1. Initial program 83.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 65.4%

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

      1. associate-*r/ 69.8%

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

   6. Simplified 69.8%

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

   if 4e10 < a < 6.4999999999999998e37

   1. Initial program 52.0%

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

      1. associate-*l/ 51.6%

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

   3. Simplified 51.6%

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

   4. Taylor expanded in x around inf 19.3%

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

      1. mul-1-neg 19.3%

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

      2. unsub-neg 19.3%

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

   6. Simplified 19.3%

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

   7. Taylor expanded in z around inf 67.4%

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

      1. associate-*r/ 67.4%

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

      2. neg-mul-1 67.4%

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

      3. +-commutative 67.4%

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

      4. distribute-lft-in 67.4%

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

      5. neg-mul-1 67.4%

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

      6. remove-double-neg 67.4%

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

      7. neg-mul-1 67.4%

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

      8. sub-neg 67.4%

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

   9. Simplified 67.4%

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

       1. *-commutative 67.4%

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

       2. clear-num 67.4%

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

       3. un-div-inv 67.6%

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

   11. Applied egg-rr 67.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-144}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 40000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 195000000000:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -9.8e+23)
     t_1
     (if (<= a 5.8e-144)
       (- t (/ y (/ z (- t x))))
       (if (<= a 195000000000.0)
         (/ t (/ (- a z) (- y z)))
         (if (<= a 1.85e+37) (/ x (/ z (- y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -9.8e+23) {
		tmp = t_1;
	} else if (a <= 5.8e-144) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 195000000000.0) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1.85e+37) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (a <= (-9.8d+23)) then
        tmp = t_1
    else if (a <= 5.8d-144) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= 195000000000.0d0) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 1.85d+37) then
        tmp = x / (z / (y - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -9.8e+23) {
		tmp = t_1;
	} else if (a <= 5.8e-144) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 195000000000.0) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1.85e+37) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -9.8e+23:
		tmp = t_1
	elif a <= 5.8e-144:
		tmp = t - (y / (z / (t - x)))
	elif a <= 195000000000.0:
		tmp = t / ((a - z) / (y - z))
	elif a <= 1.85e+37:
		tmp = x / (z / (y - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -9.8e+23)
		tmp = t_1;
	elseif (a <= 5.8e-144)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= 195000000000.0)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 1.85e+37)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -9.8e+23)
		tmp = t_1;
	elseif (a <= 5.8e-144)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= 195000000000.0)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 1.85e+37)
		tmp = x / (z / (y - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.8e+23], t$95$1, If[LessEqual[a, 5.8e-144], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 195000000000.0], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+37], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.8000000000000006e23 or 1.85e37 < a

   1. Initial program 69.2%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 78.9%

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

   if -9.8000000000000006e23 < a < 5.8000000000000004e-144

   1. Initial program 63.1%

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

      1. associate-*l/ 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in z around -inf 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. distribute-rgt-out-- 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 79.4%

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

   9. Simplified 79.4%

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

   if 5.8000000000000004e-144 < a < 1.95e11

   1. Initial program 83.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 65.4%

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

      1. expm1-log1p-u 32.6%

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

      2. expm1-udef 21.1%

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

      3. associate-/l* 24.9%

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

   6. Applied egg-rr 24.9%

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

      1. expm1-def 36.5%

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

      2. expm1-log1p 69.9%

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

   8. Simplified 69.9%

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

   if 1.95e11 < a < 1.85e37

   1. Initial program 52.0%

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

      1. associate-*l/ 51.6%

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

   3. Simplified 51.6%

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

   4. Taylor expanded in x around inf 19.3%

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

      1. mul-1-neg 19.3%

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

      2. unsub-neg 19.3%

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

   6. Simplified 19.3%

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

   7. Taylor expanded in z around inf 67.4%

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

      1. associate-*r/ 67.4%

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

      2. neg-mul-1 67.4%

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

      3. +-commutative 67.4%

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

      4. distribute-lft-in 67.4%

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

      5. neg-mul-1 67.4%

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

      6. remove-double-neg 67.4%

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

      7. neg-mul-1 67.4%

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

      8. sub-neg 67.4%

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

   9. Simplified 67.4%

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

       1. *-commutative 67.4%

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

       2. clear-num 67.4%

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

       3. un-div-inv 67.6%

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

   11. Applied egg-rr 67.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 195000000000:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-144}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 155000000000:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+60}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -1.46e+23)
     t_1
     (if (<= a 9.5e-144)
       (- t (/ y (/ z (- t x))))
       (if (<= a 155000000000.0)
         (/ t (/ (- a z) (- y z)))
         (if (<= a 1.7e+60) (+ t (/ (- y a) (/ z x))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -1.46e+23) {
		tmp = t_1;
	} else if (a <= 9.5e-144) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 155000000000.0) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1.7e+60) {
		tmp = t + ((y - a) / (z / 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 = x + ((t - x) * (y / a))
    if (a <= (-1.46d+23)) then
        tmp = t_1
    else if (a <= 9.5d-144) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= 155000000000.0d0) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 1.7d+60) then
        tmp = t + ((y - a) / (z / 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 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -1.46e+23) {
		tmp = t_1;
	} else if (a <= 9.5e-144) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 155000000000.0) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 1.7e+60) {
		tmp = t + ((y - a) / (z / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -1.46e+23:
		tmp = t_1
	elif a <= 9.5e-144:
		tmp = t - (y / (z / (t - x)))
	elif a <= 155000000000.0:
		tmp = t / ((a - z) / (y - z))
	elif a <= 1.7e+60:
		tmp = t + ((y - a) / (z / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.46e+23)
		tmp = t_1;
	elseif (a <= 9.5e-144)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= 155000000000.0)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 1.7e+60)
		tmp = Float64(t + Float64(Float64(y - a) / Float64(z / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -1.46e+23)
		tmp = t_1;
	elseif (a <= 9.5e-144)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= 155000000000.0)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 1.7e+60)
		tmp = t + ((y - a) / (z / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e+23], t$95$1, If[LessEqual[a, 9.5e-144], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 155000000000.0], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+60], N[(t + N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45999999999999996e23 or 1.7e60 < a

   1. Initial program 69.5%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 79.5%

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

   if -1.45999999999999996e23 < a < 9.49999999999999953e-144

   1. Initial program 63.1%

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

      1. associate-*l/ 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in z around -inf 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. distribute-rgt-out-- 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 79.4%

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

   9. Simplified 79.4%

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

   if 9.49999999999999953e-144 < a < 1.55e11

   1. Initial program 83.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 65.4%

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

      1. expm1-log1p-u 32.6%

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

      2. expm1-udef 21.1%

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

      3. associate-/l* 24.9%

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

   6. Applied egg-rr 24.9%

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

      1. expm1-def 36.5%

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

      2. expm1-log1p 69.9%

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

   8. Simplified 69.9%

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

   if 1.55e11 < a < 1.7e60

   1. Initial program 52.2%

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

      1. associate-*l/ 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in z around -inf 87.7%

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

      1. +-commutative 87.7%

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

      2. mul-1-neg 87.7%

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

      3. unsub-neg 87.7%

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

      4. distribute-rgt-out-- 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in t around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-/l* 75.0%

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

   9. Simplified 75.0%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+23}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-144}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 155000000000:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+60}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-195}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))))
   (if (<= a -3.2e+24)
     (+ x (/ (* y t) a))
     (if (<= a -2e-115)
       t_1
       (if (<= a -6.8e-195)
         (* (- y a) (/ x z))
         (if (<= a 8.5e-23) t_1 (+ x (/ y (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -3.2e+24) {
		tmp = x + ((y * t) / a);
	} else if (a <= -2e-115) {
		tmp = t_1;
	} else if (a <= -6.8e-195) {
		tmp = (y - a) * (x / z);
	} else if (a <= 8.5e-23) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    if (a <= (-3.2d+24)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-2d-115)) then
        tmp = t_1
    else if (a <= (-6.8d-195)) then
        tmp = (y - a) * (x / z)
    else if (a <= 8.5d-23) then
        tmp = t_1
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -3.2e+24) {
		tmp = x + ((y * t) / a);
	} else if (a <= -2e-115) {
		tmp = t_1;
	} else if (a <= -6.8e-195) {
		tmp = (y - a) * (x / z);
	} else if (a <= 8.5e-23) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	tmp = 0
	if a <= -3.2e+24:
		tmp = x + ((y * t) / a)
	elif a <= -2e-115:
		tmp = t_1
	elif a <= -6.8e-195:
		tmp = (y - a) * (x / z)
	elif a <= 8.5e-23:
		tmp = t_1
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (a <= -3.2e+24)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -2e-115)
		tmp = t_1;
	elseif (a <= -6.8e-195)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (a <= 8.5e-23)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	tmp = 0.0;
	if (a <= -3.2e+24)
		tmp = x + ((y * t) / a);
	elseif (a <= -2e-115)
		tmp = t_1;
	elseif (a <= -6.8e-195)
		tmp = (y - a) * (x / z);
	elseif (a <= 8.5e-23)
		tmp = t_1;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+24], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e-115], t$95$1, If[LessEqual[a, -6.8e-195], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-23], t$95$1, N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.1999999999999997e24

   1. Initial program 65.9%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 79.8%

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

   5. Taylor expanded in t around inf 67.5%

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

   if -3.1999999999999997e24 < a < -2.0000000000000001e-115 or -6.80000000000000003e-195 < a < 8.4999999999999996e-23

   1. Initial program 65.9%

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

      1. associate-*l/ 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in x around 0 53.8%

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

   5. Taylor expanded in a around 0 46.8%

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

      1. mul-1-neg 46.8%

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

      2. associate-/l* 59.3%

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

      3. distribute-neg-frac 59.3%

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

   7. Simplified 59.3%

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

   if -2.0000000000000001e-115 < a < -6.80000000000000003e-195

   1. Initial program 81.5%

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

      1. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in x around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in z around inf 49.5%

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

      1. associate-*r/ 49.5%

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

      2. neg-mul-1 49.5%

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

      3. +-commutative 49.5%

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

      4. distribute-lft-in 49.5%

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

      5. neg-mul-1 49.5%

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

      6. remove-double-neg 49.5%

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

      7. neg-mul-1 49.5%

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

      8. sub-neg 49.5%

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

   9. Simplified 49.5%

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

       1. *-commutative 49.5%

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

       2. clear-num 49.5%

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

       3. un-div-inv 49.5%

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

   11. Applied egg-rr 49.5%

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

       1. associate-/r/ 53.7%

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

   13. Simplified 53.7%

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

   if 8.4999999999999996e-23 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around 0 69.6%

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

   5. Taylor expanded in t around inf 57.0%

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

      1. associate-/l* 63.3%

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

   7. Simplified 63.3%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-115}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-195}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 11: 37.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e-8)
   t
   (if (<= z -4.2e-228)
     x
     (if (<= z -3.4e-279)
       (/ y (/ a t))
       (if (<= z 4.2e-146)
         x
         (if (<= z 2.2e-60) (* x (/ y z)) (if (<= z 2.5e+130) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-8) {
		tmp = t;
	} else if (z <= -4.2e-228) {
		tmp = x;
	} else if (z <= -3.4e-279) {
		tmp = y / (a / t);
	} else if (z <= 4.2e-146) {
		tmp = x;
	} else if (z <= 2.2e-60) {
		tmp = x * (y / z);
	} else if (z <= 2.5e+130) {
		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 <= (-4.4d-8)) then
        tmp = t
    else if (z <= (-4.2d-228)) then
        tmp = x
    else if (z <= (-3.4d-279)) then
        tmp = y / (a / t)
    else if (z <= 4.2d-146) then
        tmp = x
    else if (z <= 2.2d-60) then
        tmp = x * (y / z)
    else if (z <= 2.5d+130) 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 <= -4.4e-8) {
		tmp = t;
	} else if (z <= -4.2e-228) {
		tmp = x;
	} else if (z <= -3.4e-279) {
		tmp = y / (a / t);
	} else if (z <= 4.2e-146) {
		tmp = x;
	} else if (z <= 2.2e-60) {
		tmp = x * (y / z);
	} else if (z <= 2.5e+130) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e-8:
		tmp = t
	elif z <= -4.2e-228:
		tmp = x
	elif z <= -3.4e-279:
		tmp = y / (a / t)
	elif z <= 4.2e-146:
		tmp = x
	elif z <= 2.2e-60:
		tmp = x * (y / z)
	elif z <= 2.5e+130:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e-8)
		tmp = t;
	elseif (z <= -4.2e-228)
		tmp = x;
	elseif (z <= -3.4e-279)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 4.2e-146)
		tmp = x;
	elseif (z <= 2.2e-60)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 2.5e+130)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e-8)
		tmp = t;
	elseif (z <= -4.2e-228)
		tmp = x;
	elseif (z <= -3.4e-279)
		tmp = y / (a / t);
	elseif (z <= 4.2e-146)
		tmp = x;
	elseif (z <= 2.2e-60)
		tmp = x * (y / z);
	elseif (z <= 2.5e+130)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e-8], t, If[LessEqual[z, -4.2e-228], x, If[LessEqual[z, -3.4e-279], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-146], x, If[LessEqual[z, 2.2e-60], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+130], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.3999999999999997e-8 or 2.4999999999999998e130 < z

   1. Initial program 41.0%

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

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in z around inf 46.1%

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

   if -4.3999999999999997e-8 < z < -4.19999999999999982e-228 or -3.40000000000000015e-279 < z < 4.1999999999999998e-146 or 2.1999999999999999e-60 < z < 2.4999999999999998e130

   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/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around inf 42.0%

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

   if -4.19999999999999982e-228 < z < -3.40000000000000015e-279

   1. Initial program 78.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.5%

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

   5. Taylor expanded in z around 0 78.5%

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

      1. associate-/l* 67.9%

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

   7. Simplified 67.9%

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

   if 4.1999999999999998e-146 < z < 2.1999999999999999e-60

   1. Initial program 99.8%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in a around 0 46.4%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 37.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.03:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-281}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.03)
   t
   (if (<= z -1e-228)
     x
     (if (<= z -3e-281)
       (/ (* y t) a)
       (if (<= z 4.6e-146)
         x
         (if (<= z 2.7e-65) (* x (/ y z)) (if (<= z 2.5e+130) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.03) {
		tmp = t;
	} else if (z <= -1e-228) {
		tmp = x;
	} else if (z <= -3e-281) {
		tmp = (y * t) / a;
	} else if (z <= 4.6e-146) {
		tmp = x;
	} else if (z <= 2.7e-65) {
		tmp = x * (y / z);
	} else if (z <= 2.5e+130) {
		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 <= (-0.03d0)) then
        tmp = t
    else if (z <= (-1d-228)) then
        tmp = x
    else if (z <= (-3d-281)) then
        tmp = (y * t) / a
    else if (z <= 4.6d-146) then
        tmp = x
    else if (z <= 2.7d-65) then
        tmp = x * (y / z)
    else if (z <= 2.5d+130) 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 <= -0.03) {
		tmp = t;
	} else if (z <= -1e-228) {
		tmp = x;
	} else if (z <= -3e-281) {
		tmp = (y * t) / a;
	} else if (z <= 4.6e-146) {
		tmp = x;
	} else if (z <= 2.7e-65) {
		tmp = x * (y / z);
	} else if (z <= 2.5e+130) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.03:
		tmp = t
	elif z <= -1e-228:
		tmp = x
	elif z <= -3e-281:
		tmp = (y * t) / a
	elif z <= 4.6e-146:
		tmp = x
	elif z <= 2.7e-65:
		tmp = x * (y / z)
	elif z <= 2.5e+130:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.03)
		tmp = t;
	elseif (z <= -1e-228)
		tmp = x;
	elseif (z <= -3e-281)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 4.6e-146)
		tmp = x;
	elseif (z <= 2.7e-65)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 2.5e+130)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.03)
		tmp = t;
	elseif (z <= -1e-228)
		tmp = x;
	elseif (z <= -3e-281)
		tmp = (y * t) / a;
	elseif (z <= 4.6e-146)
		tmp = x;
	elseif (z <= 2.7e-65)
		tmp = x * (y / z);
	elseif (z <= 2.5e+130)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.03], t, If[LessEqual[z, -1e-228], x, If[LessEqual[z, -3e-281], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 4.6e-146], x, If[LessEqual[z, 2.7e-65], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+130], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.029999999999999999 or 2.4999999999999998e130 < z

   1. Initial program 41.0%

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

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in z around inf 46.1%

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

   if -0.029999999999999999 < z < -1.00000000000000003e-228 or -2.99999999999999975e-281 < z < 4.6000000000000001e-146 or 2.6999999999999999e-65 < z < 2.4999999999999998e130

   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/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around inf 42.0%

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

   if -1.00000000000000003e-228 < z < -2.99999999999999975e-281

   1. Initial program 78.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.5%

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

   5. Taylor expanded in z around 0 78.5%

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

   if 4.6000000000000001e-146 < z < 2.6999999999999999e-65

   1. Initial program 99.8%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in a around 0 46.4%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.03:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-281}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 47.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -0.4:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-277}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -0.4)
     t
     (if (<= z -2.7e-229)
       t_1
       (if (<= z -1.12e-277) (/ (* y t) a) (if (<= z 4e+130) 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 <= -0.4) {
		tmp = t;
	} else if (z <= -2.7e-229) {
		tmp = t_1;
	} else if (z <= -1.12e-277) {
		tmp = (y * t) / a;
	} else if (z <= 4e+130) {
		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 <= (-0.4d0)) then
        tmp = t
    else if (z <= (-2.7d-229)) then
        tmp = t_1
    else if (z <= (-1.12d-277)) then
        tmp = (y * t) / a
    else if (z <= 4d+130) 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 <= -0.4) {
		tmp = t;
	} else if (z <= -2.7e-229) {
		tmp = t_1;
	} else if (z <= -1.12e-277) {
		tmp = (y * t) / a;
	} else if (z <= 4e+130) {
		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 <= -0.4:
		tmp = t
	elif z <= -2.7e-229:
		tmp = t_1
	elif z <= -1.12e-277:
		tmp = (y * t) / a
	elif z <= 4e+130:
		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 <= -0.4)
		tmp = t;
	elseif (z <= -2.7e-229)
		tmp = t_1;
	elseif (z <= -1.12e-277)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 4e+130)
		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 <= -0.4)
		tmp = t;
	elseif (z <= -2.7e-229)
		tmp = t_1;
	elseif (z <= -1.12e-277)
		tmp = (y * t) / a;
	elseif (z <= 4e+130)
		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, -0.4], t, If[LessEqual[z, -2.7e-229], t$95$1, If[LessEqual[z, -1.12e-277], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 4e+130], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.40000000000000002 or 4.0000000000000002e130 < z

   1. Initial program 41.0%

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

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in z around inf 46.1%

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

   if -0.40000000000000002 < z < -2.6999999999999998e-229 or -1.12000000000000003e-277 < z < 4.0000000000000002e130

   1. Initial program 86.2%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in z around 0 54.7%

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

   if -2.6999999999999998e-229 < z < -1.12000000000000003e-277

   1. Initial program 78.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.5%

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

   5. Taylor expanded in z around 0 78.5%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.4:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-277}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 77.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+106}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8)
   (- t (/ y (/ z (- t x))))
   (if (<= z 9e+106)
     (+ x (/ (- t x) (/ (- a z) y)))
     (+ t (/ (- y a) (/ z x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8) {
		tmp = t - (y / (z / (t - x)));
	} else if (z <= 9e+106) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t + ((y - a) / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.8d0)) then
        tmp = t - (y / (z / (t - x)))
    else if (z <= 9d+106) then
        tmp = x + ((t - x) / ((a - z) / y))
    else
        tmp = t + ((y - a) / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8) {
		tmp = t - (y / (z / (t - x)));
	} else if (z <= 9e+106) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t + ((y - a) / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8:
		tmp = t - (y / (z / (t - x)))
	elif z <= 9e+106:
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = t + ((y - a) / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (z <= 9e+106)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(t + Float64(Float64(y - a) / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8)
		tmp = t - (y / (z / (t - x)));
	elseif (z <= 9e+106)
		tmp = x + ((t - x) / ((a - z) / y));
	else
		tmp = t + ((y - a) / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+106], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999998

   1. Initial program 47.9%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in z around -inf 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. distribute-rgt-out-- 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in y around inf 64.6%

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

      1. associate-/l* 72.4%

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

   9. Simplified 72.4%

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

   if -2.7999999999999998 < z < 8.9999999999999994e106

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*l/ 96.2%

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

      3. fma-def 96.2%

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

   3. Simplified 96.2%

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

      1. fma-udef 96.2%

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

      2. *-commutative 96.2%

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

      3. clear-num 95.8%

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

      4. un-div-inv 96.0%

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

   5. Applied egg-rr 96.0%

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

   6. Taylor expanded in y around inf 85.3%

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

   if 8.9999999999999994e106 < z

   1. Initial program 29.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

      4. distribute-rgt-out-- 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in t around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. associate-/l* 77.9%

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

   9. Simplified 77.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+106}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \end{array} \]

Alternative 15: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+43)
   t
   (if (<= z -5.5e-281)
     (+ x (/ y (/ a t)))
     (if (<= z 4e+130) (* x (- 1.0 (/ y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+43) {
		tmp = t;
	} else if (z <= -5.5e-281) {
		tmp = x + (y / (a / t));
	} else if (z <= 4e+130) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.8d+43)) then
        tmp = t
    else if (z <= (-5.5d-281)) then
        tmp = x + (y / (a / t))
    else if (z <= 4d+130) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+43) {
		tmp = t;
	} else if (z <= -5.5e-281) {
		tmp = x + (y / (a / t));
	} else if (z <= 4e+130) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+43:
		tmp = t
	elif z <= -5.5e-281:
		tmp = x + (y / (a / t))
	elif z <= 4e+130:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+43)
		tmp = t;
	elseif (z <= -5.5e-281)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 4e+130)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+43)
		tmp = t;
	elseif (z <= -5.5e-281)
		tmp = x + (y / (a / t));
	elseif (z <= 4e+130)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+43], t, If[LessEqual[z, -5.5e-281], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+130], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000008e43 or 4.0000000000000002e130 < z

   1. Initial program 37.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 48.2%

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

   if -3.80000000000000008e43 < z < -5.5000000000000003e-281

   1. Initial program 85.1%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 66.4%

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

   5. Taylor expanded in t around inf 56.6%

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

      1. associate-/l* 56.6%

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

   7. Simplified 56.6%

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

   if -5.5000000000000003e-281 < z < 4.0000000000000002e130

   1. Initial program 86.2%

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

      1. associate-*l/ 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 x around inf 65.6%

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

      1. mul-1-neg 65.6%

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

      2. unsub-neg 65.6%

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

   6. Simplified 65.6%

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

   7. Taylor expanded in z around 0 57.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+91} \lor \neg \left(x \leq 5.9 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -9e+91) (not (<= x 5.9e+82)))
   (* x (- 1.0 (/ y a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -9e+91) || !(x <= 5.9e+82)) {
		tmp = x * (1.0 - (y / a));
	} 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) :: tmp
    if ((x <= (-9d+91)) .or. (.not. (x <= 5.9d+82))) then
        tmp = x * (1.0d0 - (y / a))
    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 tmp;
	if ((x <= -9e+91) || !(x <= 5.9e+82)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -9e+91) or not (x <= 5.9e+82):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -9e+91) || !(x <= 5.9e+82))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	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)
	tmp = 0.0;
	if ((x <= -9e+91) || ~((x <= 5.9e+82)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -9e+91], N[Not[LessEqual[x, 5.9e+82]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9e91 or 5.8999999999999997e82 < x

   1. Initial program 60.8%

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

      1. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in x around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in z around 0 61.1%

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

   if -9e91 < x < 5.8999999999999997e82

   1. Initial program 73.9%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 57.3%

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

      1. associate-*r/ 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+91} \lor \neg \left(x \leq 5.9 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 17: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-14} \lor \neg \left(z \leq 3.2 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e-14) (not (<= z 3.2e+130)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e-14) || !(z <= 3.2e+130)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.5d-14)) .or. (.not. (z <= 3.2d+130))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e-14) || !(z <= 3.2e+130)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e-14) or not (z <= 3.2e+130):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e-14) || !(z <= 3.2e+130))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e-14) || ~((z <= 3.2e+130)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e-14], N[Not[LessEqual[z, 3.2e+130]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000002e-14 or 3.2e130 < z

   1. Initial program 41.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 45.1%

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

      1. associate-*r/ 66.2%

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

   6. Simplified 66.2%

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

   if -3.5000000000000002e-14 < z < 3.2e130

   1. Initial program 85.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Taylor expanded in z around 0 71.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-14} \lor \neg \left(z \leq 3.2 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 18: 37.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-9}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-9)
   t
   (if (<= z 3.7e-144)
     x
     (if (<= z 2.05e-64) (* x (/ y z)) (if (<= z 2.5e+130) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-9) {
		tmp = t;
	} else if (z <= 3.7e-144) {
		tmp = x;
	} else if (z <= 2.05e-64) {
		tmp = x * (y / z);
	} else if (z <= 2.5e+130) {
		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 <= (-1.35d-9)) then
        tmp = t
    else if (z <= 3.7d-144) then
        tmp = x
    else if (z <= 2.05d-64) then
        tmp = x * (y / z)
    else if (z <= 2.5d+130) 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 <= -1.35e-9) {
		tmp = t;
	} else if (z <= 3.7e-144) {
		tmp = x;
	} else if (z <= 2.05e-64) {
		tmp = x * (y / z);
	} else if (z <= 2.5e+130) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-9:
		tmp = t
	elif z <= 3.7e-144:
		tmp = x
	elif z <= 2.05e-64:
		tmp = x * (y / z)
	elif z <= 2.5e+130:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-9)
		tmp = t;
	elseif (z <= 3.7e-144)
		tmp = x;
	elseif (z <= 2.05e-64)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 2.5e+130)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e-9)
		tmp = t;
	elseif (z <= 3.7e-144)
		tmp = x;
	elseif (z <= 2.05e-64)
		tmp = x * (y / z);
	elseif (z <= 2.5e+130)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-9], t, If[LessEqual[z, 3.7e-144], x, If[LessEqual[z, 2.05e-64], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+130], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e-9 or 2.4999999999999998e130 < z

   1. Initial program 41.0%

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

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in z around inf 46.1%

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

   if -1.3500000000000001e-9 < z < 3.7000000000000003e-144 or 2.05e-64 < z < 2.4999999999999998e130

   1. Initial program 83.8%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in a around inf 40.2%

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

   if 3.7000000000000003e-144 < z < 2.05e-64

   1. Initial program 99.8%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in a around 0 46.4%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-9}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 38.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.03:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.03) t (if (<= z 7.4e+130) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.03) {
		tmp = t;
	} else if (z <= 7.4e+130) {
		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 <= (-0.03d0)) then
        tmp = t
    else if (z <= 7.4d+130) 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 <= -0.03) {
		tmp = t;
	} else if (z <= 7.4e+130) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.03:
		tmp = t
	elif z <= 7.4e+130:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.03)
		tmp = t;
	elseif (z <= 7.4e+130)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.03)
		tmp = t;
	elseif (z <= 7.4e+130)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.03], t, If[LessEqual[z, 7.4e+130], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -0.029999999999999999 or 7.4000000000000003e130 < z

   1. Initial program 41.0%

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

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in z around inf 46.1%

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

   if -0.029999999999999999 < z < 7.4000000000000003e130

   1. Initial program 85.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 a around inf 37.8%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.03:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 25.2% 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 68.8%

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

   1. associate-*l/ 86.7%

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

3. Simplified 86.7%

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

4. Taylor expanded in z around inf 23.1%

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

5. Final simplification 23.1%

   \[\leadsto t \]

Developer target: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023274 
(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))))