Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.8% → 93.3%

Time: 13.8s

Alternatives: 16

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: 80.8% 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: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -4e-279)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -4e-279) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -4e-279)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

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, -4e-279], 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[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.00000000000000022e-279

   1. Initial program 90.4%

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

      1. +-commutative 90.4%

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

      2. associate-*r/ 71.6%

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

      3. *-commutative 71.6%

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

      4. associate-*r/ 94.3%

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

      5. fma-def 94.4%

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

   3. Simplified 94.4%

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

   if -4.00000000000000022e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   2. Taylor expanded in z around inf 96.7%

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

      1. +-commutative 96.7%

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

      2. associate--l+ 96.7%

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

      3. associate-*r/ 96.7%

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

      4. associate-*r/ 96.7%

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

      5. div-sub 96.7%

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

      6. distribute-lft-out-- 96.7%

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

      7. mul-1-neg 96.7%

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

      8. distribute-neg-frac 96.7%

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

      9. unsub-neg 96.7%

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

      10. distribute-rgt-out-- 96.7%

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

   4. Simplified 96.7%

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

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

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 82.0%

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

      3. associate-*r/ 95.2%

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

      4. clear-num 95.1%

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

      5. un-div-inv 95.2%

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

   3. Applied egg-rr 95.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-209} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-209) (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 <= -1e-209) || !(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 <= (-1d-209)) .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 <= -1e-209) || !(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 <= -1e-209) 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 <= -1e-209) || !(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 <= -1e-209) || ~((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, -1e-209], 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)))) < -1e-209 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

   if -1e-209 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 9.2%

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

   2. Taylor expanded in z around inf 91.7%

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

      1. +-commutative 91.7%

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

      2. associate--l+ 91.7%

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

      3. associate-*r/ 91.7%

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

      4. associate-*r/ 91.7%

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

      5. div-sub 91.7%

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

      6. distribute-lft-out-- 91.7%

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

      7. mul-1-neg 91.7%

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

      8. distribute-neg-frac 91.7%

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

      9. unsub-neg 91.7%

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

      10. distribute-rgt-out-- 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-209} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 3: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-279} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -4e-279) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ 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 <= -4e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-4d-279)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} 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 <= -4e-279) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-279) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -4e-279) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(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)))) < -4.00000000000000022e-279 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   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/ 77.0%

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

      3. associate-*r/ 94.8%

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

      4. clear-num 94.6%

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

      5. un-div-inv 94.7%

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

   3. Applied egg-rr 94.7%

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

   if -4.00000000000000022e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   2. Taylor expanded in z around inf 96.7%

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

      1. +-commutative 96.7%

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

      2. associate--l+ 96.7%

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

      3. associate-*r/ 96.7%

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

      4. associate-*r/ 96.7%

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

      5. div-sub 96.7%

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

      6. distribute-lft-out-- 96.7%

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

      7. mul-1-neg 96.7%

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

      8. distribute-neg-frac 96.7%

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

      9. unsub-neg 96.7%

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

      10. distribute-rgt-out-- 96.7%

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

   4. Simplified 96.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-279} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 4: 40.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -2.05e+37)
     t
     (if (<= z -1.85e-25)
       t_1
       (if (<= z -1.3e-87)
         x
         (if (<= z -1.1e-283)
           t_1
           (if (<= z 1.7e-214)
             x
             (if (<= z 1.8e-172) t_1 (if (<= z 1.4e+18) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -2.05e+37) {
		tmp = t;
	} else if (z <= -1.85e-25) {
		tmp = t_1;
	} else if (z <= -1.3e-87) {
		tmp = x;
	} else if (z <= -1.1e-283) {
		tmp = t_1;
	} else if (z <= 1.7e-214) {
		tmp = x;
	} else if (z <= 1.8e-172) {
		tmp = t_1;
	} else if (z <= 1.4e+18) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (z <= (-2.05d+37)) then
        tmp = t
    else if (z <= (-1.85d-25)) then
        tmp = t_1
    else if (z <= (-1.3d-87)) then
        tmp = x
    else if (z <= (-1.1d-283)) then
        tmp = t_1
    else if (z <= 1.7d-214) then
        tmp = x
    else if (z <= 1.8d-172) then
        tmp = t_1
    else if (z <= 1.4d+18) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -2.05e+37) {
		tmp = t;
	} else if (z <= -1.85e-25) {
		tmp = t_1;
	} else if (z <= -1.3e-87) {
		tmp = x;
	} else if (z <= -1.1e-283) {
		tmp = t_1;
	} else if (z <= 1.7e-214) {
		tmp = x;
	} else if (z <= 1.8e-172) {
		tmp = t_1;
	} else if (z <= 1.4e+18) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -2.05e+37:
		tmp = t
	elif z <= -1.85e-25:
		tmp = t_1
	elif z <= -1.3e-87:
		tmp = x
	elif z <= -1.1e-283:
		tmp = t_1
	elif z <= 1.7e-214:
		tmp = x
	elif z <= 1.8e-172:
		tmp = t_1
	elif z <= 1.4e+18:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -2.05e+37)
		tmp = t;
	elseif (z <= -1.85e-25)
		tmp = t_1;
	elseif (z <= -1.3e-87)
		tmp = x;
	elseif (z <= -1.1e-283)
		tmp = t_1;
	elseif (z <= 1.7e-214)
		tmp = x;
	elseif (z <= 1.8e-172)
		tmp = t_1;
	elseif (z <= 1.4e+18)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -2.05e+37)
		tmp = t;
	elseif (z <= -1.85e-25)
		tmp = t_1;
	elseif (z <= -1.3e-87)
		tmp = x;
	elseif (z <= -1.1e-283)
		tmp = t_1;
	elseif (z <= 1.7e-214)
		tmp = x;
	elseif (z <= 1.8e-172)
		tmp = t_1;
	elseif (z <= 1.4e+18)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+37], t, If[LessEqual[z, -1.85e-25], t$95$1, If[LessEqual[z, -1.3e-87], x, If[LessEqual[z, -1.1e-283], t$95$1, If[LessEqual[z, 1.7e-214], x, If[LessEqual[z, 1.8e-172], t$95$1, If[LessEqual[z, 1.4e+18], x, t]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0499999999999999e37 or 1.4e18 < z

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf 51.9%

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

   if -2.0499999999999999e37 < z < -1.85000000000000004e-25 or -1.30000000000000001e-87 < z < -1.0999999999999999e-283 or 1.7e-214 < z < 1.80000000000000007e-172

   1. Initial program 87.1%

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

      1. +-commutative 87.1%

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

      2. fma-def 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in a around inf 76.6%

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

   5. Taylor expanded in y around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. div-sub 55.4%

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

   7. Simplified 55.4%

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

   if -1.85000000000000004e-25 < z < -1.30000000000000001e-87 or -1.0999999999999999e-283 < z < 1.7e-214 or 1.80000000000000007e-172 < z < 1.4e18

   1. Initial program 92.8%

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

   2. Taylor expanded in a around inf 48.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-283}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+43} \lor \neg \left(z \leq 1.95 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.8e+43) (not (<= z 1.95e+61)))
   (/ t (/ (- a z) (- y z)))
   (+ x (/ (- t x) (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.8e+43) || !(z <= 1.95e+61)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.8d+43)) .or. (.not. (z <= 1.95d+61))) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = x + ((t - x) / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.8e+43) || !(z <= 1.95e+61)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.8e+43) or not (z <= 1.95e+61):
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = x + ((t - x) / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.8e+43) || !(z <= 1.95e+61))
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.8e+43) || ~((z <= 1.95e+61)))
		tmp = t / ((a - z) / (y - z));
	else
		tmp = x + ((t - x) / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.8e+43], N[Not[LessEqual[z, 1.95e+61]], $MachinePrecision]], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000001e43 or 1.94999999999999994e61 < z

   1. Initial program 66.2%

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

   2. Taylor expanded in x around 0 47.8%

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

      1. associate-/l* 67.3%

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

   4. Simplified 67.3%

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

   if -7.8000000000000001e43 < z < 1.94999999999999994e61

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 87.0%

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

      3. associate-*r/ 93.3%

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

      4. clear-num 93.1%

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

      5. un-div-inv 93.2%

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

   3. Applied egg-rr 93.2%

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

   4. Taylor expanded in y around inf 82.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+43} \lor \neg \left(z \leq 1.95 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 6: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+42} \lor \neg \left(z \leq 1.85 \cdot 10^{+32}\right):\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e+42) (not (<= z 1.85e+32)))
   (+ t (/ (* (- t x) (- a y)) z))
   (+ x (/ (- t x) (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e+42) || !(z <= 1.85e+32)) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.6d+42)) .or. (.not. (z <= 1.85d+32))) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + ((t - x) / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e+42) || !(z <= 1.85e+32)) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e+42) or not (z <= 1.85e+32):
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((t - x) / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e+42) || !(z <= 1.85e+32))
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.6e+42) || ~((z <= 1.85e+32)))
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((t - x) / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e+42], N[Not[LessEqual[z, 1.85e+32]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6000000000000001e42 or 1.85e32 < z

   1. Initial program 68.6%

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

   2. Taylor expanded in z around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. associate--l+ 71.8%

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

      3. associate-*r/ 71.8%

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

      4. associate-*r/ 71.8%

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

      5. div-sub 71.8%

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

      6. distribute-lft-out-- 71.8%

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

      7. mul-1-neg 71.8%

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

      8. distribute-neg-frac 71.8%

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

      9. unsub-neg 71.8%

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

      10. distribute-rgt-out-- 72.0%

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

   4. Simplified 72.0%

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

   if -3.6000000000000001e42 < z < 1.85e32

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

      2. associate-*l/ 87.5%

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

      3. associate-*r/ 93.0%

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

      4. clear-num 92.7%

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

      5. un-div-inv 92.8%

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

   3. Applied egg-rr 92.8%

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

   4. Taylor expanded in y around inf 83.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+42} \lor \neg \left(z \leq 1.85 \cdot 10^{+32}\right):\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 7: 52.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (+ -1.0 (/ a z)))))
   (if (<= z -4.4e+38)
     t_1
     (if (<= z -6.4e-186)
       (* y (/ (- t x) (- a z)))
       (if (<= z 1.55e+18) (- x (/ y (/ a x))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (-1.0 + (a / z));
	double tmp;
	if (z <= -4.4e+38) {
		tmp = t_1;
	} else if (z <= -6.4e-186) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.55e+18) {
		tmp = x - (y / (a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / ((-1.0d0) + (a / z))
    if (z <= (-4.4d+38)) then
        tmp = t_1
    else if (z <= (-6.4d-186)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.55d+18) then
        tmp = x - (y / (a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (-1.0 + (a / z));
	double tmp;
	if (z <= -4.4e+38) {
		tmp = t_1;
	} else if (z <= -6.4e-186) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.55e+18) {
		tmp = x - (y / (a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (-1.0 + (a / z))
	tmp = 0
	if z <= -4.4e+38:
		tmp = t_1
	elif z <= -6.4e-186:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.55e+18:
		tmp = x - (y / (a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(-1.0 + Float64(a / z)))
	tmp = 0.0
	if (z <= -4.4e+38)
		tmp = t_1;
	elseif (z <= -6.4e-186)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.55e+18)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (-1.0 + (a / z));
	tmp = 0.0;
	if (z <= -4.4e+38)
		tmp = t_1;
	elseif (z <= -6.4e-186)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.55e+18)
		tmp = x - (y / (a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+38], t$95$1, If[LessEqual[z, -6.4e-186], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+18], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000013e38 or 1.55e18 < z

   1. Initial program 69.4%

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

   2. Taylor expanded in y around 0 37.6%

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

      1. mul-1-neg 37.6%

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

      2. unsub-neg 37.6%

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

      3. *-commutative 37.6%

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

      4. associate-/l* 58.5%

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

      5. div-sub 58.5%

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

      6. *-inverses 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in x around 0 59.0%

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

      1. sub-neg 59.0%

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

      2. metadata-eval 59.0%

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

      3. associate-*r/ 59.0%

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

      4. mul-1-neg 59.0%

         \[\leadsto \frac{\color{blue}{-t}}{\frac{a}{z} + -1} \]

      5. +-commutative 59.0%

         \[\leadsto \frac{-t}{\color{blue}{-1 + \frac{a}{z}}} \]

   7. Simplified 59.0%

      \[\leadsto \color{blue}{\frac{-t}{-1 + \frac{a}{z}}} \]

   if -4.40000000000000013e38 < z < -6.4000000000000001e-186

   1. Initial program 89.2%

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

      1. clear-num 89.3%

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

      2. associate-/r/ 89.2%

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

   3. Applied egg-rr 89.2%

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

   4. Taylor expanded in y around inf 59.3%

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

      1. div-sub 59.3%

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

      2. *-commutative 59.3%

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

   6. Simplified 59.3%

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

   if -6.4000000000000001e-186 < z < 1.55e18

   1. Initial program 90.9%

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

   2. Taylor expanded in t around 0 65.7%

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

      1. neg-mul-1 65.7%

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

      2. distribute-neg-frac 65.7%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in z around 0 61.3%

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

      1. +-commutative 61.3%

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

      2. mul-1-neg 61.3%

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

      3. unsub-neg 61.3%

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

      4. associate-/l* 60.6%

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

   7. Simplified 60.6%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \end{array} \]

Alternative 8: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+43} \lor \neg \left(z \leq 2.2 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+43) (not (<= z 2.2e+60)))
   (/ (- t) (+ -1.0 (/ a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+43) || !(z <= 2.2e+60)) {
		tmp = -t / (-1.0 + (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 <= (-3.5d+43)) .or. (.not. (z <= 2.2d+60))) then
        tmp = -t / ((-1.0d0) + (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 <= -3.5e+43) || !(z <= 2.2e+60)) {
		tmp = -t / (-1.0 + (a / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+43) or not (z <= 2.2e+60):
		tmp = -t / (-1.0 + (a / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+43) || !(z <= 2.2e+60))
		tmp = Float64(Float64(-t) / Float64(-1.0 + 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 <= -3.5e+43) || ~((z <= 2.2e+60)))
		tmp = -t / (-1.0 + (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, -3.5e+43], N[Not[LessEqual[z, 2.2e+60]], $MachinePrecision]], N[((-t) / N[(-1.0 + 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 < -3.5000000000000001e43 or 2.19999999999999996e60 < z

   1. Initial program 66.6%

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

   2. Taylor expanded in y around 0 37.2%

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

      1. mul-1-neg 37.2%

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

      2. unsub-neg 37.2%

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

      3. *-commutative 37.2%

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

      4. associate-/l* 58.8%

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

      5. div-sub 58.8%

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

      6. *-inverses 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in x around 0 62.1%

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

      1. sub-neg 62.1%

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

      2. metadata-eval 62.1%

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

      3. associate-*r/ 62.1%

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

      4. mul-1-neg 62.1%

         \[\leadsto \frac{\color{blue}{-t}}{\frac{a}{z} + -1} \]

      5. +-commutative 62.1%

         \[\leadsto \frac{-t}{\color{blue}{-1 + \frac{a}{z}}} \]

   7. Simplified 62.1%

      \[\leadsto \color{blue}{\frac{-t}{-1 + \frac{a}{z}}} \]

   if -3.5000000000000001e43 < z < 2.19999999999999996e60

   1. Initial program 90.5%

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

   2. Taylor expanded in z around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. associate-/l* 70.1%

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

   4. Simplified 70.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+43} \lor \neg \left(z \leq 2.2 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 9: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+42} \lor \neg \left(z \leq 1.5 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+42) (not (<= z 1.5e+61)))
   (/ (- t) (+ -1.0 (/ a z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+42) || !(z <= 1.5e+61)) {
		tmp = -t / (-1.0 + (a / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9d+42)) .or. (.not. (z <= 1.5d+61))) then
        tmp = -t / ((-1.0d0) + (a / z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+42) || !(z <= 1.5e+61)) {
		tmp = -t / (-1.0 + (a / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+42) or not (z <= 1.5e+61):
		tmp = -t / (-1.0 + (a / z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+42) || !(z <= 1.5e+61))
		tmp = Float64(Float64(-t) / Float64(-1.0 + Float64(a / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+42) || ~((z <= 1.5e+61)))
		tmp = -t / (-1.0 + (a / z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+42], N[Not[LessEqual[z, 1.5e+61]], $MachinePrecision]], N[((-t) / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000025e42 or 1.5e61 < z

   1. Initial program 66.6%

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

   2. Taylor expanded in y around 0 37.2%

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

      1. mul-1-neg 37.2%

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

      2. unsub-neg 37.2%

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

      3. *-commutative 37.2%

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

      4. associate-/l* 58.8%

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

      5. div-sub 58.8%

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

      6. *-inverses 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in x around 0 62.1%

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

      1. sub-neg 62.1%

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

      2. metadata-eval 62.1%

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

      3. associate-*r/ 62.1%

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

      4. mul-1-neg 62.1%

         \[\leadsto \frac{\color{blue}{-t}}{\frac{a}{z} + -1} \]

      5. +-commutative 62.1%

         \[\leadsto \frac{-t}{\color{blue}{-1 + \frac{a}{z}}} \]

   7. Simplified 62.1%

      \[\leadsto \color{blue}{\frac{-t}{-1 + \frac{a}{z}}} \]

   if -9.00000000000000025e42 < z < 1.5e61

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*l/ 86.9%

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

      3. associate-*r/ 93.3%

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

      4. clear-num 93.1%

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

      5. un-div-inv 93.1%

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

   3. Applied egg-rr 93.1%

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

   4. Taylor expanded in z around 0 71.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+42} \lor \neg \left(z \leq 1.5 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 67.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+41} \lor \neg \left(z \leq 1.45 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+41) (not (<= z 1.45e+18)))
   (/ t (/ (- a z) (- y z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+41) || !(z <= 1.45e+18)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d+41)) .or. (.not. (z <= 1.45d+18))) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+41) || !(z <= 1.45e+18)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+41) or not (z <= 1.45e+18):
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+41) || !(z <= 1.45e+18))
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+41) || ~((z <= 1.45e+18)))
		tmp = t / ((a - z) / (y - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+41], N[Not[LessEqual[z, 1.45e+18]], $MachinePrecision]], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000005e41 or 1.45e18 < z

   1. Initial program 68.9%

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

   2. Taylor expanded in x around 0 48.2%

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

      1. associate-/l* 65.6%

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

   4. Simplified 65.6%

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

   if -8.00000000000000005e41 < z < 1.45e18

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*l/ 87.9%

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

      3. associate-*r/ 93.4%

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

      4. clear-num 93.2%

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

      5. un-div-inv 93.3%

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

   3. Applied egg-rr 93.3%

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

   4. Taylor expanded in z around 0 73.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+41} \lor \neg \left(z \leq 1.45 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 50.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+44} \lor \neg \left(z \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+44) (not (<= z 1.5e+18)))
   (/ (- t) (+ -1.0 (/ a z)))
   (- x (/ y (/ a x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+44) || !(z <= 1.5e+18)) {
		tmp = -t / (-1.0 + (a / z));
	} else {
		tmp = x - (y / (a / 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 <= (-1.45d+44)) .or. (.not. (z <= 1.5d+18))) then
        tmp = -t / ((-1.0d0) + (a / z))
    else
        tmp = x - (y / (a / 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 <= -1.45e+44) || !(z <= 1.5e+18)) {
		tmp = -t / (-1.0 + (a / z));
	} else {
		tmp = x - (y / (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+44) or not (z <= 1.5e+18):
		tmp = -t / (-1.0 + (a / z))
	else:
		tmp = x - (y / (a / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+44) || !(z <= 1.5e+18))
		tmp = Float64(Float64(-t) / Float64(-1.0 + Float64(a / z)));
	else
		tmp = Float64(x - Float64(y / Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e+44) || ~((z <= 1.5e+18)))
		tmp = -t / (-1.0 + (a / z));
	else
		tmp = x - (y / (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+44], N[Not[LessEqual[z, 1.5e+18]], $MachinePrecision]], N[((-t) / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4500000000000001e44 or 1.5e18 < z

   1. Initial program 68.9%

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

   2. Taylor expanded in y around 0 36.6%

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

      1. mul-1-neg 36.6%

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

      2. unsub-neg 36.6%

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

      3. *-commutative 36.6%

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

      4. associate-/l* 57.7%

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

      5. div-sub 57.8%

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

      6. *-inverses 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in x around 0 60.0%

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

      1. sub-neg 60.0%

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

      2. metadata-eval 60.0%

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

      3. associate-*r/ 60.0%

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

      4. mul-1-neg 60.0%

         \[\leadsto \frac{\color{blue}{-t}}{\frac{a}{z} + -1} \]

      5. +-commutative 60.0%

         \[\leadsto \frac{-t}{\color{blue}{-1 + \frac{a}{z}}} \]

   7. Simplified 60.0%

      \[\leadsto \color{blue}{\frac{-t}{-1 + \frac{a}{z}}} \]

   if -1.4500000000000001e44 < z < 1.5e18

   1. Initial program 90.5%

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

   2. Taylor expanded in t around 0 61.1%

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

      1. neg-mul-1 61.1%

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

      2. distribute-neg-frac 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in z around 0 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

      4. associate-/l* 53.7%

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

   7. Simplified 53.7%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+44} \lor \neg \left(z \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 12: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+42} \lor \neg \left(z \leq 1.6 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+42) (not (<= z 1.6e+18)))
   (/ t (/ z (- z y)))
   (- x (/ y (/ a x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+42) || !(z <= 1.6e+18)) {
		tmp = t / (z / (z - y));
	} else {
		tmp = x - (y / (a / 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 <= (-1.25d+42)) .or. (.not. (z <= 1.6d+18))) then
        tmp = t / (z / (z - y))
    else
        tmp = x - (y / (a / 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 <= -1.25e+42) || !(z <= 1.6e+18)) {
		tmp = t / (z / (z - y));
	} else {
		tmp = x - (y / (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+42) or not (z <= 1.6e+18):
		tmp = t / (z / (z - y))
	else:
		tmp = x - (y / (a / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+42) || !(z <= 1.6e+18))
		tmp = Float64(t / Float64(z / Float64(z - y)));
	else
		tmp = Float64(x - Float64(y / Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e+42) || ~((z <= 1.6e+18)))
		tmp = t / (z / (z - y));
	else
		tmp = x - (y / (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e+42], N[Not[LessEqual[z, 1.6e+18]], $MachinePrecision]], N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000002e42 or 1.6e18 < z

   1. Initial program 68.9%

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

   2. Taylor expanded in x around 0 48.2%

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

   3. Taylor expanded in a around 0 42.9%

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

      1. associate-*r/ 42.9%

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

      2. neg-mul-1 42.9%

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

      3. distribute-rgt-neg-in 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in t around 0 42.9%

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

      1. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

   if -1.25000000000000002e42 < z < 1.6e18

   1. Initial program 90.5%

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

   2. Taylor expanded in t around 0 61.1%

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

      1. neg-mul-1 61.1%

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

      2. distribute-neg-frac 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in z around 0 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

      4. associate-/l* 53.7%

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

   7. Simplified 53.7%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+42} \lor \neg \left(z \leq 1.6 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 13: 48.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e+43) t (if (<= z 1.55e+18) (- x (/ y (/ a x))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+43) {
		tmp = t;
	} else if (z <= 1.55e+18) {
		tmp = x - (y / (a / x));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.55d+43)) then
        tmp = t
    else if (z <= 1.55d+18) then
        tmp = x - (y / (a / x))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+43) {
		tmp = t;
	} else if (z <= 1.55e+18) {
		tmp = x - (y / (a / x));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e+43:
		tmp = t
	elif z <= 1.55e+18:
		tmp = x - (y / (a / x))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e+43)
		tmp = t;
	elseif (z <= 1.55e+18)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.55e+43)
		tmp = t;
	elseif (z <= 1.55e+18)
		tmp = x - (y / (a / x));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e+43], t, If[LessEqual[z, 1.55e+18], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5500000000000001e43 or 1.55e18 < z

   1. Initial program 68.9%

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

   2. Taylor expanded in z around inf 52.6%

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

   if -1.5500000000000001e43 < z < 1.55e18

   1. Initial program 90.5%

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

   2. Taylor expanded in t around 0 61.1%

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

      1. neg-mul-1 61.1%

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

      2. distribute-neg-frac 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in z around 0 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

      4. associate-/l* 53.7%

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

   7. Simplified 53.7%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 39.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+42) t (if (<= z 1.4e+18) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+42) {
		tmp = t;
	} else if (z <= 1.4e+18) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+42)) then
        tmp = t
    else if (z <= 1.4d+18) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+42) {
		tmp = t;
	} else if (z <= 1.4e+18) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+42:
		tmp = t
	elif z <= 1.4e+18:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+42)
		tmp = t;
	elseif (z <= 1.4e+18)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+42)
		tmp = t;
	elseif (z <= 1.4e+18)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+42], t, If[LessEqual[z, 1.4e+18], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000052e42 or 1.4e18 < z

   1. Initial program 68.9%

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

   2. Taylor expanded in z around inf 52.6%

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

   if -6.50000000000000052e42 < z < 1.4e18

   1. Initial program 90.5%

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

   2. Taylor expanded in a around inf 37.1%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 80.5%

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

2. Taylor expanded in t around 0 43.0%

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

   1. neg-mul-1 43.0%

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

   2. distribute-neg-frac 43.0%

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

4. Simplified 43.0%

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

5. Taylor expanded in z around inf 2.9%

   \[\leadsto \color{blue}{-1 \cdot x + x} \]
6. Step-by-step derivation

   1. distribute-lft1-in 2.9%

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

   2. metadata-eval 2.9%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.9%

      \[\leadsto \color{blue}{0} \]

7. Simplified 2.9%

   \[\leadsto \color{blue}{0} \]

8. Final simplification 2.9%

   \[\leadsto 0 \]

Alternative 16: 25.1% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 80.5%

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

2. Taylor expanded in z around inf 28.9%

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

3. Final simplification 28.9%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023200 
(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)))))