Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 81.5% → 93.4%

Time: 16.6s

Alternatives: 19

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 81.5% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))) (t_2 (/ z (- t x))))
   (if (<= t_1 -5e-273)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0) (+ (- t (/ y t_2)) (/ a t_2)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if (t_1 <= -5e-273) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = (t - (y / t_2)) + (a / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if (t_1 <= -5e-273)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-273], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(t - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999965e-273

   1. Initial program 91.1%

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

      1. +-commutative 91.1%

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

      2. associate-*r/ 76.2%

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

      3. *-commutative 76.2%

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

      4. associate-*r/ 95.7%

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

      5. fma-def 95.8%

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

   3. Simplified 95.8%

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

   if -4.99999999999999965e-273 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

      1. *-commutative 3.7%

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

      2. associate-*l/ 9.1%

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

      3. associate-*r/ 9.6%

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

      4. clear-num 9.6%

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

      5. un-div-inv 9.6%

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

   3. Applied egg-rr 9.6%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. sub-neg 87.3%

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

      2. +-commutative 87.3%

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

      3. mul-1-neg 87.3%

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

      4. unsub-neg 87.3%

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

      5. associate-/l* 93.4%

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

      6. mul-1-neg 93.4%

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

      7. remove-double-neg 93.4%

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

      8. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 95.1%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-273}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 2: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))) (t_2 (/ z (- t x))))
   (if (<= t_1 -5e-273)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0) (+ (- t (/ y t_2)) (/ a t_2)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if (t_1 <= -5e-273) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = (t - (y / t_2)) + (a / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    t_2 = z / (t - x)
    if (t_1 <= (-5d-273)) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else if (t_1 <= 0.0d0) then
        tmp = (t - (y / t_2)) + (a / t_2)
    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 + ((y - z) * ((t - x) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if (t_1 <= -5e-273) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = (t - (y / t_2)) + (a / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = z / (t - x)
	tmp = 0
	if t_1 <= -5e-273:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	elif t_1 <= 0.0:
		tmp = (t - (y / t_2)) + (a / t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if (t_1 <= -5e-273)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = z / (t - x);
	tmp = 0.0;
	if (t_1 <= -5e-273)
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	elseif (t_1 <= 0.0)
		tmp = (t - (y / t_2)) + (a / t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-273], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(t - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999965e-273

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*l/ 76.2%

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

      3. associate-*r/ 95.7%

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

      4. clear-num 95.7%

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

      5. un-div-inv 95.8%

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

   3. Applied egg-rr 95.8%

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

   if -4.99999999999999965e-273 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

      1. *-commutative 3.7%

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

      2. associate-*l/ 9.1%

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

      3. associate-*r/ 9.6%

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

      4. clear-num 9.6%

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

      5. un-div-inv 9.6%

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

   3. Applied egg-rr 9.6%

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

   4. Taylor expanded in z around inf 87.3%

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

      1. sub-neg 87.3%

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

      2. +-commutative 87.3%

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

      3. mul-1-neg 87.3%

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

      4. unsub-neg 87.3%

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

      5. associate-/l* 93.4%

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

      6. mul-1-neg 93.4%

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

      7. remove-double-neg 93.4%

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

      8. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 95.1%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 3: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-153} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-153) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (* (- t x) (- a 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 <= -5e-153) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-153)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-153) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - 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 <= -5e-153) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-153) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-153) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-153], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000033e-153 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.6%

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

   if -5.00000000000000033e-153 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 17.1%

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

   2. Taylor expanded in z around inf 83.3%

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

      1. +-commutative 83.3%

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

      2. associate--l+ 83.3%

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

      3. associate-*r/ 83.3%

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

      4. associate-*r/ 83.3%

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

      5. div-sub 83.3%

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

      6. distribute-lft-out-- 83.3%

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

      7. mul-1-neg 83.3%

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

      8. distribute-neg-frac 83.3%

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

      9. unsub-neg 83.3%

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

      10. distribute-rgt-out-- 83.3%

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

   4. Simplified 83.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-153} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 4: 91.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-273)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0) (+ t (/ (* (- t x) (- a y)) z)) t_1))))

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 <= -5e-273) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-5d-273)) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else if (t_1 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-273) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -5e-273:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	elif t_1 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-273)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = t_1;
	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 <= -5e-273)
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-273], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999965e-273

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*l/ 76.2%

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

      3. associate-*r/ 95.7%

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

      4. clear-num 95.7%

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

      5. un-div-inv 95.8%

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

   3. Applied egg-rr 95.8%

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

   if -4.99999999999999965e-273 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. associate--l+ 87.3%

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

      3. associate-*r/ 87.3%

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

      4. associate-*r/ 87.3%

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

      5. div-sub 87.3%

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

      6. distribute-lft-out-- 87.3%

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

      7. mul-1-neg 87.3%

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

      8. distribute-neg-frac 87.3%

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

      9. unsub-neg 87.3%

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

      10. distribute-rgt-out-- 87.3%

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

   4. Simplified 87.3%

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

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

   1. Initial program 95.1%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 5: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+90} \lor \neg \left(z \leq 6.6 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z))))
   (if (<= z -4.6e-16)
     (* t t_1)
     (if (<= z 5.2e-34)
       (+ x (/ y (/ a (- t x))))
       (if (or (<= z 2.6e+90) (not (<= z 6.6e+120)))
         (/ t (/ (- a z) (- y z)))
         (* x (- 1.0 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double tmp;
	if (z <= -4.6e-16) {
		tmp = t * t_1;
	} else if (z <= 5.2e-34) {
		tmp = x + (y / (a / (t - x)));
	} else if ((z <= 2.6e+90) || !(z <= 6.6e+120)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x * (1.0 - 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 = (y - z) / (a - z)
    if (z <= (-4.6d-16)) then
        tmp = t * t_1
    else if (z <= 5.2d-34) then
        tmp = x + (y / (a / (t - x)))
    else if ((z <= 2.6d+90) .or. (.not. (z <= 6.6d+120))) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = x * (1.0d0 - 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 = (y - z) / (a - z);
	double tmp;
	if (z <= -4.6e-16) {
		tmp = t * t_1;
	} else if (z <= 5.2e-34) {
		tmp = x + (y / (a / (t - x)));
	} else if ((z <= 2.6e+90) || !(z <= 6.6e+120)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x * (1.0 - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) / (a - z)
	tmp = 0
	if z <= -4.6e-16:
		tmp = t * t_1
	elif z <= 5.2e-34:
		tmp = x + (y / (a / (t - x)))
	elif (z <= 2.6e+90) or not (z <= 6.6e+120):
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = x * (1.0 - t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(a - z))
	tmp = 0.0
	if (z <= -4.6e-16)
		tmp = Float64(t * t_1);
	elseif (z <= 5.2e-34)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif ((z <= 2.6e+90) || !(z <= 6.6e+120))
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = Float64(x * Float64(1.0 - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) / (a - z);
	tmp = 0.0;
	if (z <= -4.6e-16)
		tmp = t * t_1;
	elseif (z <= 5.2e-34)
		tmp = x + (y / (a / (t - x)));
	elseif ((z <= 2.6e+90) || ~((z <= 6.6e+120)))
		tmp = t / ((a - z) / (y - z));
	else
		tmp = x * (1.0 - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e-16], N[(t * t$95$1), $MachinePrecision], If[LessEqual[z, 5.2e-34], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.6e+90], N[Not[LessEqual[z, 6.6e+120]], $MachinePrecision]], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5999999999999998e-16

   1. Initial program 70.3%

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

   2. Taylor expanded in t around inf 60.7%

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

      1. div-sub 60.7%

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

   4. Simplified 60.7%

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

   if -4.5999999999999998e-16 < z < 5.1999999999999999e-34

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

   if 5.1999999999999999e-34 < z < 2.5999999999999998e90 or 6.59999999999999981e120 < z

   1. Initial program 70.5%

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

   2. Taylor expanded in x around 0 41.2%

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

      1. associate-/l* 66.9%

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

   4. Simplified 66.9%

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

   if 2.5999999999999998e90 < z < 6.59999999999999981e120

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   4. Simplified 81.3%

      \[\leadsto \color{blue}{\left(1 - \frac{y - z}{a - z}\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+90} \lor \neg \left(z \leq 6.6 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \end{array} \]

Alternative 6: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a - z}{y}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ (- a z) y)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.4e+18)
     t_2
     (if (<= z 8.6e+40)
       t_1
       (if (<= z 4.5e+89)
         t_2
         (if (<= z 4.8e+120) t_1 (/ t (/ (- a z) (- y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / ((a - z) / y));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.4e+18) {
		tmp = t_2;
	} else if (z <= 8.6e+40) {
		tmp = t_1;
	} else if (z <= 4.5e+89) {
		tmp = t_2;
	} else if (z <= 4.8e+120) {
		tmp = t_1;
	} else {
		tmp = t / ((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) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) / ((a - z) / y))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-4.4d+18)) then
        tmp = t_2
    else if (z <= 8.6d+40) then
        tmp = t_1
    else if (z <= 4.5d+89) then
        tmp = t_2
    else if (z <= 4.8d+120) then
        tmp = t_1
    else
        tmp = t / ((a - z) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / ((a - z) / y));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.4e+18) {
		tmp = t_2;
	} else if (z <= 8.6e+40) {
		tmp = t_1;
	} else if (z <= 4.5e+89) {
		tmp = t_2;
	} else if (z <= 4.8e+120) {
		tmp = t_1;
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / ((a - z) / y))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4.4e+18:
		tmp = t_2
	elif z <= 8.6e+40:
		tmp = t_1
	elif z <= 4.5e+89:
		tmp = t_2
	elif z <= 4.8e+120:
		tmp = t_1
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.4e+18)
		tmp = t_2;
	elseif (z <= 8.6e+40)
		tmp = t_1;
	elseif (z <= 4.5e+89)
		tmp = t_2;
	elseif (z <= 4.8e+120)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / ((a - z) / y));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4.4e+18)
		tmp = t_2;
	elseif (z <= 8.6e+40)
		tmp = t_1;
	elseif (z <= 4.5e+89)
		tmp = t_2;
	elseif (z <= 4.8e+120)
		tmp = t_1;
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+18], t$95$2, If[LessEqual[z, 8.6e+40], t$95$1, If[LessEqual[z, 4.5e+89], t$95$2, If[LessEqual[z, 4.8e+120], t$95$1, N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4e18 or 8.6000000000000005e40 < z < 4.5e89

   1. Initial program 69.1%

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

   2. Taylor expanded in t around inf 64.8%

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

      1. div-sub 64.8%

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

   4. Simplified 64.8%

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

   if -4.4e18 < z < 8.6000000000000005e40 or 4.5e89 < z < 4.80000000000000002e120

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-*l/ 92.4%

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

      3. associate-*r/ 96.3%

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

      4. clear-num 96.2%

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

      5. un-div-inv 96.2%

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

   3. Applied egg-rr 96.2%

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

   4. Taylor expanded in y around inf 88.8%

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

   if 4.80000000000000002e120 < z

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 0 29.8%

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

      1. associate-/l* 70.6%

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

   4. Simplified 70.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 7: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := \frac{t}{\frac{-z}{y - z}}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (/ t (/ (- z) (- y z)))))
   (if (<= z -4.2e+19)
     t_2
     (if (<= z -2.4e-257)
       t_1
       (if (<= z -1.9e-297) (/ y (/ a t)) (if (<= z 1.56e+35) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t / (-z / (y - z));
	double tmp;
	if (z <= -4.2e+19) {
		tmp = t_2;
	} else if (z <= -2.4e-257) {
		tmp = t_1;
	} else if (z <= -1.9e-297) {
		tmp = y / (a / t);
	} else if (z <= 1.56e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t / (-z / (y - z))
    if (z <= (-4.2d+19)) then
        tmp = t_2
    else if (z <= (-2.4d-257)) then
        tmp = t_1
    else if (z <= (-1.9d-297)) then
        tmp = y / (a / t)
    else if (z <= 1.56d+35) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t / (-z / (y - z));
	double tmp;
	if (z <= -4.2e+19) {
		tmp = t_2;
	} else if (z <= -2.4e-257) {
		tmp = t_1;
	} else if (z <= -1.9e-297) {
		tmp = y / (a / t);
	} else if (z <= 1.56e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t / (-z / (y - z))
	tmp = 0
	if z <= -4.2e+19:
		tmp = t_2
	elif z <= -2.4e-257:
		tmp = t_1
	elif z <= -1.9e-297:
		tmp = y / (a / t)
	elif z <= 1.56e+35:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t / Float64(Float64(-z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -4.2e+19)
		tmp = t_2;
	elseif (z <= -2.4e-257)
		tmp = t_1;
	elseif (z <= -1.9e-297)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 1.56e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t / (-z / (y - z));
	tmp = 0.0;
	if (z <= -4.2e+19)
		tmp = t_2;
	elseif (z <= -2.4e-257)
		tmp = t_1;
	elseif (z <= -1.9e-297)
		tmp = y / (a / t);
	elseif (z <= 1.56e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+19], t$95$2, If[LessEqual[z, -2.4e-257], t$95$1, If[LessEqual[z, -1.9e-297], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.56e+35], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e19 or 1.56000000000000008e35 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in x around 0 36.5%

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

      1. associate-/l* 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in a around 0 52.8%

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

      1. neg-mul-1 52.8%

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

      2. distribute-neg-frac 52.8%

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

   7. Simplified 52.8%

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

   if -4.2e19 < z < -2.40000000000000017e-257 or -1.90000000000000002e-297 < z < 1.56000000000000008e35

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in z around 0 60.3%

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

   if -2.40000000000000017e-257 < z < -1.90000000000000002e-297

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 76.0%

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

      1. associate-/l* 87.8%

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

   4. Simplified 87.8%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \end{array} \]

Alternative 8: 46.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-298}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -3.2e+19)
     t
     (if (<= z -2.4e-257)
       t_1
       (if (<= z -1.7e-298) (/ y (/ a t)) (if (<= z 2.6e+39) 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 <= -3.2e+19) {
		tmp = t;
	} else if (z <= -2.4e-257) {
		tmp = t_1;
	} else if (z <= -1.7e-298) {
		tmp = y / (a / t);
	} else if (z <= 2.6e+39) {
		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 <= (-3.2d+19)) then
        tmp = t
    else if (z <= (-2.4d-257)) then
        tmp = t_1
    else if (z <= (-1.7d-298)) then
        tmp = y / (a / t)
    else if (z <= 2.6d+39) 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 <= -3.2e+19) {
		tmp = t;
	} else if (z <= -2.4e-257) {
		tmp = t_1;
	} else if (z <= -1.7e-298) {
		tmp = y / (a / t);
	} else if (z <= 2.6e+39) {
		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 <= -3.2e+19:
		tmp = t
	elif z <= -2.4e-257:
		tmp = t_1
	elif z <= -1.7e-298:
		tmp = y / (a / t)
	elif z <= 2.6e+39:
		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 <= -3.2e+19)
		tmp = t;
	elseif (z <= -2.4e-257)
		tmp = t_1;
	elseif (z <= -1.7e-298)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 2.6e+39)
		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 <= -3.2e+19)
		tmp = t;
	elseif (z <= -2.4e-257)
		tmp = t_1;
	elseif (z <= -1.7e-298)
		tmp = y / (a / t);
	elseif (z <= 2.6e+39)
		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, -3.2e+19], t, If[LessEqual[z, -2.4e-257], t$95$1, If[LessEqual[z, -1.7e-298], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+39], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e19 or 2.6e39 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in z around inf 48.2%

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

   if -3.2e19 < z < -2.40000000000000017e-257 or -1.7e-298 < z < 2.6e39

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in z around 0 60.3%

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

   if -2.40000000000000017e-257 < z < -1.7e-298

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 76.0%

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

      1. associate-/l* 87.8%

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

   4. Simplified 87.8%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-298}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (/ t (/ (- z a) z))))
   (if (<= z -4.1e+18)
     t_2
     (if (<= z -2.4e-257)
       t_1
       (if (<= z -2.2e-297) (/ y (/ a t)) (if (<= z 4.1e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t / ((z - a) / z);
	double tmp;
	if (z <= -4.1e+18) {
		tmp = t_2;
	} else if (z <= -2.4e-257) {
		tmp = t_1;
	} else if (z <= -2.2e-297) {
		tmp = y / (a / t);
	} else if (z <= 4.1e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t / ((z - a) / z)
    if (z <= (-4.1d+18)) then
        tmp = t_2
    else if (z <= (-2.4d-257)) then
        tmp = t_1
    else if (z <= (-2.2d-297)) then
        tmp = y / (a / t)
    else if (z <= 4.1d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t / ((z - a) / z);
	double tmp;
	if (z <= -4.1e+18) {
		tmp = t_2;
	} else if (z <= -2.4e-257) {
		tmp = t_1;
	} else if (z <= -2.2e-297) {
		tmp = y / (a / t);
	} else if (z <= 4.1e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t / ((z - a) / z)
	tmp = 0
	if z <= -4.1e+18:
		tmp = t_2
	elif z <= -2.4e-257:
		tmp = t_1
	elif z <= -2.2e-297:
		tmp = y / (a / t)
	elif z <= 4.1e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t / Float64(Float64(z - a) / z))
	tmp = 0.0
	if (z <= -4.1e+18)
		tmp = t_2;
	elseif (z <= -2.4e-257)
		tmp = t_1;
	elseif (z <= -2.2e-297)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 4.1e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t / ((z - a) / z);
	tmp = 0.0;
	if (z <= -4.1e+18)
		tmp = t_2;
	elseif (z <= -2.4e-257)
		tmp = t_1;
	elseif (z <= -2.2e-297)
		tmp = y / (a / t);
	elseif (z <= 4.1e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+18], t$95$2, If[LessEqual[z, -2.4e-257], t$95$1, If[LessEqual[z, -2.2e-297], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e18 or 4.0999999999999998e37 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in x around 0 36.5%

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

      1. associate-/l* 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in y around 0 56.6%

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

      1. associate-*r/ 56.6%

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

      2. neg-mul-1 56.6%

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

   7. Simplified 56.6%

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

   if -4.1e18 < z < -2.40000000000000017e-257 or -2.1999999999999998e-297 < z < 4.0999999999999998e37

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in z around 0 60.3%

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

   if -2.40000000000000017e-257 < z < -2.1999999999999998e-297

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 76.0%

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

      1. associate-/l* 87.8%

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

   4. Simplified 87.8%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 10: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+37}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+37)
   (+ t (/ (* (- t x) (- a y)) z))
   (if (<= z 9.5e+40)
     (+ x (/ (- t x) (/ (- a z) y)))
     (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+37) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 9.5e+40) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t / ((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) :: tmp
    if (z <= (-3.6d+37)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= 9.5d+40) then
        tmp = x + ((t - x) / ((a - z) / y))
    else
        tmp = t / ((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 tmp;
	if (z <= -3.6e+37) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 9.5e+40) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+37:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= 9.5e+40:
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+37)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= 9.5e+40)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e+37)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= 9.5e+40)
		tmp = x + ((t - x) / ((a - z) / y));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+37], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+40], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.59999999999999998e37

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 63.6%

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

      1. +-commutative 63.6%

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

      2. associate--l+ 63.6%

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

      3. associate-*r/ 63.6%

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

      4. associate-*r/ 63.6%

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

      5. div-sub 63.6%

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

      6. distribute-lft-out-- 63.6%

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

      7. mul-1-neg 63.6%

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

      8. distribute-neg-frac 63.6%

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

      9. unsub-neg 63.6%

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

      10. distribute-rgt-out-- 65.6%

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

   4. Simplified 65.6%

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

   if -3.59999999999999998e37 < z < 9.5000000000000003e40

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l/ 92.4%

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

      3. associate-*r/ 95.7%

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

      4. clear-num 95.6%

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

      5. un-div-inv 95.7%

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

   3. Applied egg-rr 95.7%

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

   4. Taylor expanded in y around inf 88.4%

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

   if 9.5000000000000003e40 < z

   1. Initial program 66.4%

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

   2. Taylor expanded in x around 0 36.6%

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

      1. associate-/l* 65.6%

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

   4. Simplified 65.6%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+37}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 11: 35.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -64000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-181}:\\ \;\;\;\;-\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -64000.0)
   t
   (if (<= z -1.9e-58)
     x
     (if (<= z -1.6e-181)
       (- (/ y (/ a x)))
       (if (<= z 1.2e-191) (/ t (/ a y)) (if (<= z 4.5e+40) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -64000.0) {
		tmp = t;
	} else if (z <= -1.9e-58) {
		tmp = x;
	} else if (z <= -1.6e-181) {
		tmp = -(y / (a / x));
	} else if (z <= 1.2e-191) {
		tmp = t / (a / y);
	} else if (z <= 4.5e+40) {
		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 <= (-64000.0d0)) then
        tmp = t
    else if (z <= (-1.9d-58)) then
        tmp = x
    else if (z <= (-1.6d-181)) then
        tmp = -(y / (a / x))
    else if (z <= 1.2d-191) then
        tmp = t / (a / y)
    else if (z <= 4.5d+40) 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 <= -64000.0) {
		tmp = t;
	} else if (z <= -1.9e-58) {
		tmp = x;
	} else if (z <= -1.6e-181) {
		tmp = -(y / (a / x));
	} else if (z <= 1.2e-191) {
		tmp = t / (a / y);
	} else if (z <= 4.5e+40) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -64000.0:
		tmp = t
	elif z <= -1.9e-58:
		tmp = x
	elif z <= -1.6e-181:
		tmp = -(y / (a / x))
	elif z <= 1.2e-191:
		tmp = t / (a / y)
	elif z <= 4.5e+40:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -64000.0)
		tmp = t;
	elseif (z <= -1.9e-58)
		tmp = x;
	elseif (z <= -1.6e-181)
		tmp = Float64(-Float64(y / Float64(a / x)));
	elseif (z <= 1.2e-191)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 4.5e+40)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -64000.0)
		tmp = t;
	elseif (z <= -1.9e-58)
		tmp = x;
	elseif (z <= -1.6e-181)
		tmp = -(y / (a / x));
	elseif (z <= 1.2e-191)
		tmp = t / (a / y);
	elseif (z <= 4.5e+40)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -64000.0], t, If[LessEqual[z, -1.9e-58], x, If[LessEqual[z, -1.6e-181], (-N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 1.2e-191], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+40], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -64000 or 4.50000000000000032e40 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf 47.9%

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

   if -64000 < z < -1.8999999999999999e-58 or 1.2e-191 < z < 4.50000000000000032e40

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf 48.1%

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

   if -1.8999999999999999e-58 < z < -1.6000000000000001e-181

   1. Initial program 96.7%

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

   2. Taylor expanded in x around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in z around 0 61.4%

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

   6. Taylor expanded in y around inf 40.6%

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

      1. mul-1-neg 40.6%

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

      2. associate-/l* 40.5%

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

   8. Simplified 40.5%

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

   if -1.6000000000000001e-181 < z < 1.2e-191

   1. Initial program 93.8%

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

   2. Taylor expanded in x around 0 45.7%

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

      1. associate-/l* 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in z around 0 48.1%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -64000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-181}:\\ \;\;\;\;-\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 35.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00094:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-190}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00094)
   t
   (if (<= z -5.7e-56)
     x
     (if (<= z -5.6e-180)
       (* x (/ (- y) a))
       (if (<= z 9e-190) (/ t (/ a y)) (if (<= z 8e+40) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00094) {
		tmp = t;
	} else if (z <= -5.7e-56) {
		tmp = x;
	} else if (z <= -5.6e-180) {
		tmp = x * (-y / a);
	} else if (z <= 9e-190) {
		tmp = t / (a / y);
	} else if (z <= 8e+40) {
		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 <= (-0.00094d0)) then
        tmp = t
    else if (z <= (-5.7d-56)) then
        tmp = x
    else if (z <= (-5.6d-180)) then
        tmp = x * (-y / a)
    else if (z <= 9d-190) then
        tmp = t / (a / y)
    else if (z <= 8d+40) 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 <= -0.00094) {
		tmp = t;
	} else if (z <= -5.7e-56) {
		tmp = x;
	} else if (z <= -5.6e-180) {
		tmp = x * (-y / a);
	} else if (z <= 9e-190) {
		tmp = t / (a / y);
	} else if (z <= 8e+40) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.00094:
		tmp = t
	elif z <= -5.7e-56:
		tmp = x
	elif z <= -5.6e-180:
		tmp = x * (-y / a)
	elif z <= 9e-190:
		tmp = t / (a / y)
	elif z <= 8e+40:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00094)
		tmp = t;
	elseif (z <= -5.7e-56)
		tmp = x;
	elseif (z <= -5.6e-180)
		tmp = Float64(x * Float64(Float64(-y) / a));
	elseif (z <= 9e-190)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 8e+40)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.00094)
		tmp = t;
	elseif (z <= -5.7e-56)
		tmp = x;
	elseif (z <= -5.6e-180)
		tmp = x * (-y / a);
	elseif (z <= 9e-190)
		tmp = t / (a / y);
	elseif (z <= 8e+40)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00094], t, If[LessEqual[z, -5.7e-56], x, If[LessEqual[z, -5.6e-180], N[(x * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-190], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+40], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.39999999999999972e-4 or 8.00000000000000024e40 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf 47.9%

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

   if -9.39999999999999972e-4 < z < -5.6999999999999998e-56 or 9.00000000000000042e-190 < z < 8.00000000000000024e40

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf 48.1%

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

   if -5.6999999999999998e-56 < z < -5.59999999999999994e-180

   1. Initial program 96.7%

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

   2. Taylor expanded in x around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in z around 0 61.4%

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

   6. Taylor expanded in y around inf 40.6%

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

      1. mul-1-neg 40.6%

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

      2. distribute-neg-frac 40.6%

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

      3. distribute-lft-neg-out 40.6%

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

      4. associate-*l/ 40.6%

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

      5. *-commutative 40.6%

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

   8. Simplified 40.6%

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

   if -5.59999999999999994e-180 < z < 9.00000000000000042e-190

   1. Initial program 93.8%

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

   2. Taylor expanded in x around 0 45.7%

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

      1. associate-/l* 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in z around 0 48.1%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00094:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-190}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 35.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -25500:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{x \cdot y}{-a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-190}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -25500.0)
   t
   (if (<= z -2.7e-53)
     x
     (if (<= z -8.8e-181)
       (/ (* x y) (- a))
       (if (<= z 1.4e-190) (/ t (/ a y)) (if (<= z 8.2e+39) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -25500.0) {
		tmp = t;
	} else if (z <= -2.7e-53) {
		tmp = x;
	} else if (z <= -8.8e-181) {
		tmp = (x * y) / -a;
	} else if (z <= 1.4e-190) {
		tmp = t / (a / y);
	} else if (z <= 8.2e+39) {
		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 <= (-25500.0d0)) then
        tmp = t
    else if (z <= (-2.7d-53)) then
        tmp = x
    else if (z <= (-8.8d-181)) then
        tmp = (x * y) / -a
    else if (z <= 1.4d-190) then
        tmp = t / (a / y)
    else if (z <= 8.2d+39) 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 <= -25500.0) {
		tmp = t;
	} else if (z <= -2.7e-53) {
		tmp = x;
	} else if (z <= -8.8e-181) {
		tmp = (x * y) / -a;
	} else if (z <= 1.4e-190) {
		tmp = t / (a / y);
	} else if (z <= 8.2e+39) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -25500.0:
		tmp = t
	elif z <= -2.7e-53:
		tmp = x
	elif z <= -8.8e-181:
		tmp = (x * y) / -a
	elif z <= 1.4e-190:
		tmp = t / (a / y)
	elif z <= 8.2e+39:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -25500.0)
		tmp = t;
	elseif (z <= -2.7e-53)
		tmp = x;
	elseif (z <= -8.8e-181)
		tmp = Float64(Float64(x * y) / Float64(-a));
	elseif (z <= 1.4e-190)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 8.2e+39)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -25500.0)
		tmp = t;
	elseif (z <= -2.7e-53)
		tmp = x;
	elseif (z <= -8.8e-181)
		tmp = (x * y) / -a;
	elseif (z <= 1.4e-190)
		tmp = t / (a / y);
	elseif (z <= 8.2e+39)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -25500.0], t, If[LessEqual[z, -2.7e-53], x, If[LessEqual[z, -8.8e-181], N[(N[(x * y), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[z, 1.4e-190], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+39], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -25500 or 8.20000000000000008e39 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf 47.9%

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

   if -25500 < z < -2.6999999999999999e-53 or 1.40000000000000003e-190 < z < 8.20000000000000008e39

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf 48.1%

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

   if -2.6999999999999999e-53 < z < -8.79999999999999988e-181

   1. Initial program 96.7%

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

   2. Taylor expanded in x around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in z around 0 61.4%

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

   6. Taylor expanded in y around inf 40.6%

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

      1. mul-1-neg 40.6%

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

      2. distribute-neg-frac 40.6%

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

      3. distribute-lft-neg-out 40.6%

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

      4. associate-*l/ 40.6%

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

      5. *-commutative 40.6%

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

   8. Simplified 40.6%

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

      1. associate-*r/ 40.6%

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

      2. frac-2neg 40.6%

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

      3. add-sqr-sqrt 12.4%

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

      4. sqrt-unprod 16.4%

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

      5. sqr-neg 16.4%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 4.9%

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

      8. distribute-rgt-neg-out 4.9%

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

      9. add-sqr-sqrt 3.9%

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

      10. sqrt-unprod 26.4%

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

      11. sqr-neg 26.4%

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

      12. sqrt-unprod 28.2%

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

      13. add-sqr-sqrt 40.6%

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

   10. Applied egg-rr 40.6%

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

   if -8.79999999999999988e-181 < z < 1.40000000000000003e-190

   1. Initial program 93.8%

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

   2. Taylor expanded in x around 0 45.7%

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

      1. associate-/l* 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in z around 0 48.1%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -25500:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{x \cdot y}{-a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-190}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-168} \lor \neg \left(t \leq 8.6 \cdot 10^{-99}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e-168) (not (<= t 8.6e-99)))
   (* t (/ (- y z) (- a z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e-168) || !(t <= 8.6e-99)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3d-168)) .or. (.not. (t <= 8.6d-99))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e-168) || !(t <= 8.6e-99)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3e-168) or not (t <= 8.6e-99):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e-168) || !(t <= 8.6e-99))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3e-168) || ~((t <= 8.6e-99)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e-168], N[Not[LessEqual[t, 8.6e-99]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.99999999999999991e-168 or 8.5999999999999998e-99 < t

   1. Initial program 85.9%

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

   2. Taylor expanded in t around inf 66.6%

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

      1. div-sub 66.6%

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

   4. Simplified 66.6%

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

   if -2.99999999999999991e-168 < t < 8.5999999999999998e-99

   1. Initial program 73.7%

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

   2. Taylor expanded in x around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in z around 0 57.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-168} \lor \neg \left(t \leq 8.6 \cdot 10^{-99}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 15: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-16} \lor \neg \left(z \leq 1.55 \cdot 10^{-39}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e-16) (not (<= z 1.55e-39)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-16) || !(z <= 1.55e-39)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.5d-16)) .or. (.not. (z <= 1.55d-39))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-16) || !(z <= 1.55e-39)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e-16) or not (z <= 1.55e-39):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e-16) || !(z <= 1.55e-39))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e-16) || ~((z <= 1.55e-39)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e-16], N[Not[LessEqual[z, 1.55e-39]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000002e-16 or 1.54999999999999985e-39 < z

   1. Initial program 71.6%

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

   2. Taylor expanded in t around inf 61.7%

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

      1. div-sub 61.7%

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

   4. Simplified 61.7%

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

   if -2.5000000000000002e-16 < z < 1.54999999999999985e-39

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-16} \lor \neg \left(z \leq 1.55 \cdot 10^{-39}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 16: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e-15)
   (* t (/ (- y z) (- a z)))
   (if (<= z 7.7e-38) (+ x (/ y (/ a (- t x)))) (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e-15) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 7.7e-38) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((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) :: tmp
    if (z <= (-1.45d-15)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 7.7d-38) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t / ((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 tmp;
	if (z <= -1.45e-15) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 7.7e-38) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e-15:
		tmp = t * ((y - z) / (a - z))
	elif z <= 7.7e-38:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e-15)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 7.7e-38)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e-15)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 7.7e-38)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e-15], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.7e-38], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000009e-15

   1. Initial program 70.3%

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

   2. Taylor expanded in t around inf 60.7%

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

      1. div-sub 60.7%

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

   4. Simplified 60.7%

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

   if -1.45000000000000009e-15 < z < 7.6999999999999999e-38

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

   if 7.6999999999999999e-38 < z

   1. Initial program 72.7%

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

   2. Taylor expanded in x around 0 39.1%

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

      1. associate-/l* 62.6%

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

   4. Simplified 62.6%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 17: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.0)
   t
   (if (<= z -9e-99)
     x
     (if (<= z 1.9e-191) (/ t (/ a y)) (if (<= z 1.25e+40) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.0) {
		tmp = t;
	} else if (z <= -9e-99) {
		tmp = x;
	} else if (z <= 1.9e-191) {
		tmp = t / (a / y);
	} else if (z <= 1.25e+40) {
		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 <= (-6.0d0)) then
        tmp = t
    else if (z <= (-9d-99)) then
        tmp = x
    else if (z <= 1.9d-191) then
        tmp = t / (a / y)
    else if (z <= 1.25d+40) 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 <= -6.0) {
		tmp = t;
	} else if (z <= -9e-99) {
		tmp = x;
	} else if (z <= 1.9e-191) {
		tmp = t / (a / y);
	} else if (z <= 1.25e+40) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.0:
		tmp = t
	elif z <= -9e-99:
		tmp = x
	elif z <= 1.9e-191:
		tmp = t / (a / y)
	elif z <= 1.25e+40:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.0)
		tmp = t;
	elseif (z <= -9e-99)
		tmp = x;
	elseif (z <= 1.9e-191)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 1.25e+40)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.0)
		tmp = t;
	elseif (z <= -9e-99)
		tmp = x;
	elseif (z <= 1.9e-191)
		tmp = t / (a / y);
	elseif (z <= 1.25e+40)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.0], t, If[LessEqual[z, -9e-99], x, If[LessEqual[z, 1.9e-191], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+40], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6 or 1.25000000000000001e40 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf 47.9%

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

   if -6 < z < -9.0000000000000006e-99 or 1.8999999999999999e-191 < z < 1.25000000000000001e40

   1. Initial program 95.4%

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

   2. Taylor expanded in a around inf 44.3%

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

   if -9.0000000000000006e-99 < z < 1.8999999999999999e-191

   1. Initial program 95.5%

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

   2. Taylor expanded in x around 0 38.0%

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

      1. associate-/l* 43.0%

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

   4. Simplified 43.0%

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

   5. Taylor expanded in z around 0 41.1%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 38.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -510000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -510000.0) t (if (<= z 1.6e+40) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -510000.0) {
		tmp = t;
	} else if (z <= 1.6e+40) {
		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 <= (-510000.0d0)) then
        tmp = t
    else if (z <= 1.6d+40) 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 <= -510000.0) {
		tmp = t;
	} else if (z <= 1.6e+40) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -510000.0:
		tmp = t
	elif z <= 1.6e+40:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -510000.0)
		tmp = t;
	elseif (z <= 1.6e+40)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -510000.0)
		tmp = t;
	elseif (z <= 1.6e+40)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -510000.0], t, If[LessEqual[z, 1.6e+40], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1e5 or 1.5999999999999999e40 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf 47.9%

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

   if -5.1e5 < z < 1.5999999999999999e40

   1. Initial program 95.4%

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

   2. Taylor expanded in a around inf 36.2%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -510000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 24.5% 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 81.9%

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

2. Taylor expanded in z around inf 27.7%

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

3. Final simplification 27.7%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023181 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))