Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.6% → 92.6%

Time: 19.8s

Alternatives: 17

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: 79.6% 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: 92.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\left(x - x \cdot \frac{y - z}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -4e-222)
     t_2
     (if (<= t_2 0.0)
       (+ t (/ (- x t) (/ z (- y a))))
       (if (<= t_2 5e+16)
         (+ (- x (* x (/ (- y z) (- a z)))) (/ (* (- y z) t) (- a z)))
         (fma (- y z) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -4e-222) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (t_2 <= 5e+16) {
		tmp = (x - (x * ((y - z) / (a - z)))) + (((y - z) * t) / (a - z));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -4e-222)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (t_2 <= 5e+16)
		tmp = Float64(Float64(x - Float64(x * Float64(Float64(y - z) / Float64(a - z)))) + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = fma(Float64(y - z), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-222], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+16], N[(N[(x - N[(x * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.00000000000000019e-222

   1. Initial program 88.1%

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

   if -4.00000000000000019e-222 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.1%

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

   2. Taylor expanded in z around inf 75.4%

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

      1. associate--l+ 75.4%

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

      2. distribute-lft-out-- 75.4%

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

      3. div-sub 75.4%

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

      4. mul-1-neg 75.4%

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

      5. unsub-neg 75.4%

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

      6. distribute-rgt-out-- 75.4%

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

      7. associate-/l* 96.3%

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

   4. Simplified 96.3%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e16

   1. Initial program 63.5%

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

   2. Taylor expanded in x around 0 93.5%

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

      1. distribute-rgt-in 93.6%

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

      2. *-un-lft-identity 93.6%

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

      3. mul-1-neg 93.6%

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

   4. Applied egg-rr 93.6%

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

   if 5e16 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. fma-def 98.7%

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

   3. Simplified 98.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-222}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\left(x - x \cdot \frac{y - z}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternative 2: 92.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\left(x - x \cdot \frac{y - z}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -4e-222)
     t_1
     (if (<= t_1 0.0)
       (+ t (/ (- x t) (/ z (- y a))))
       (if (<= t_1 5e+16)
         (+ (- x (* x (/ (- y z) (- a z)))) (/ (* (- y z) t) (- a 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 <= -4e-222) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (t_1 <= 5e+16) {
		tmp = (x - (x * ((y - z) / (a - z)))) + (((y - z) * t) / (a - 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 <= (-4d-222)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t + ((x - t) / (z / (y - a)))
    else if (t_1 <= 5d+16) then
        tmp = (x - (x * ((y - z) / (a - z)))) + (((y - z) * t) / (a - 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 <= -4e-222) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (t_1 <= 5e+16) {
		tmp = (x - (x * ((y - z) / (a - z)))) + (((y - z) * t) / (a - 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 <= -4e-222:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + ((x - t) / (z / (y - a)))
	elif t_1 <= 5e+16:
		tmp = (x - (x * ((y - z) / (a - z)))) + (((y - z) * t) / (a - 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 <= -4e-222)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (t_1 <= 5e+16)
		tmp = Float64(Float64(x - Float64(x * Float64(Float64(y - z) / Float64(a - z)))) + Float64(Float64(Float64(y - z) * t) / Float64(a - 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 <= -4e-222)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + ((x - t) / (z / (y - a)));
	elseif (t_1 <= 5e+16)
		tmp = (x - (x * ((y - z) / (a - z)))) + (((y - z) * t) / (a - 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, -4e-222], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+16], N[(N[(x - N[(x * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $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)))) < -4.00000000000000019e-222 or 5e16 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.6%

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

   if -4.00000000000000019e-222 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.1%

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

   2. Taylor expanded in z around inf 75.4%

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

      1. associate--l+ 75.4%

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

      2. distribute-lft-out-- 75.4%

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

      3. div-sub 75.4%

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

      4. mul-1-neg 75.4%

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

      5. unsub-neg 75.4%

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

      6. distribute-rgt-out-- 75.4%

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

      7. associate-/l* 96.3%

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

   4. Simplified 96.3%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e16

   1. Initial program 63.5%

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

   2. Taylor expanded in x around 0 93.5%

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

      1. distribute-rgt-in 93.6%

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

      2. *-un-lft-identity 93.6%

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

      3. mul-1-neg 93.6%

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

   4. Applied egg-rr 93.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-222}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\left(x - x \cdot \frac{y - z}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 3: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-222} \lor \neg \left(t_1 \leq 10^{-114}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -4e-222) (not (<= t_1 1e-114)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-222) || !(t_1 <= 1e-114)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-4d-222)) .or. (.not. (t_1 <= 1d-114))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-222) || !(t_1 <= 1e-114)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	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-222) or not (t_1 <= 1e-114):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	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-222) || !(t_1 <= 1e-114))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -4e-222) || ~((t_1 <= 1e-114)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-222], N[Not[LessEqual[t$95$1, 1e-114]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.00000000000000019e-222 or 1.0000000000000001e-114 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.4%

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

   if -4.00000000000000019e-222 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.0000000000000001e-114

   1. Initial program 14.0%

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

   2. Taylor expanded in z around inf 72.9%

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

      1. associate--l+ 72.9%

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

      2. distribute-lft-out-- 72.9%

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

      3. div-sub 72.9%

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

      4. mul-1-neg 72.9%

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

      5. unsub-neg 72.9%

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

      6. distribute-rgt-out-- 72.9%

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

      7. associate-/l* 87.4%

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

   4. Simplified 87.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-222} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-114}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t a))))
   (if (<= z -3.2e+66)
     t
     (if (<= z -5.4e-166)
       x
       (if (<= z 6.2e-278)
         t_1
         (if (<= z 2.4e+28) x (if (<= z 8.5e+84) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / a);
	double tmp;
	if (z <= -3.2e+66) {
		tmp = t;
	} else if (z <= -5.4e-166) {
		tmp = x;
	} else if (z <= 6.2e-278) {
		tmp = t_1;
	} else if (z <= 2.4e+28) {
		tmp = x;
	} else if (z <= 8.5e+84) {
		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 = (y - z) * (t / a)
    if (z <= (-3.2d+66)) then
        tmp = t
    else if (z <= (-5.4d-166)) then
        tmp = x
    else if (z <= 6.2d-278) then
        tmp = t_1
    else if (z <= 2.4d+28) then
        tmp = x
    else if (z <= 8.5d+84) 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 = (y - z) * (t / a);
	double tmp;
	if (z <= -3.2e+66) {
		tmp = t;
	} else if (z <= -5.4e-166) {
		tmp = x;
	} else if (z <= 6.2e-278) {
		tmp = t_1;
	} else if (z <= 2.4e+28) {
		tmp = x;
	} else if (z <= 8.5e+84) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / a)
	tmp = 0
	if z <= -3.2e+66:
		tmp = t
	elif z <= -5.4e-166:
		tmp = x
	elif z <= 6.2e-278:
		tmp = t_1
	elif z <= 2.4e+28:
		tmp = x
	elif z <= 8.5e+84:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / a))
	tmp = 0.0
	if (z <= -3.2e+66)
		tmp = t;
	elseif (z <= -5.4e-166)
		tmp = x;
	elseif (z <= 6.2e-278)
		tmp = t_1;
	elseif (z <= 2.4e+28)
		tmp = x;
	elseif (z <= 8.5e+84)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / a);
	tmp = 0.0;
	if (z <= -3.2e+66)
		tmp = t;
	elseif (z <= -5.4e-166)
		tmp = x;
	elseif (z <= 6.2e-278)
		tmp = t_1;
	elseif (z <= 2.4e+28)
		tmp = x;
	elseif (z <= 8.5e+84)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+66], t, If[LessEqual[z, -5.4e-166], x, If[LessEqual[z, 6.2e-278], t$95$1, If[LessEqual[z, 2.4e+28], x, If[LessEqual[z, 8.5e+84], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e66 or 8.5000000000000008e84 < z

   1. Initial program 64.1%

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

   2. Taylor expanded in z around inf 50.4%

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

   if -3.2e66 < z < -5.40000000000000013e-166 or 6.19999999999999983e-278 < z < 2.39999999999999981e28

   1. Initial program 86.8%

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

   2. Taylor expanded in a around inf 37.2%

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

   if -5.40000000000000013e-166 < z < 6.19999999999999983e-278 or 2.39999999999999981e28 < z < 8.5000000000000008e84

   1. Initial program 92.3%

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

   2. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 48.6%

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

      2. associate-/r/ 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in a around inf 51.5%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-278}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+84}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 55.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t \leq -4 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-280}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))))
   (if (<= t -4e-26)
     t_1
     (if (<= t 7.5e-280)
       (+ t (* x (/ y z)))
       (if (<= t 8.5e-203) x (if (<= t 5.7e-8) (+ t (/ x (/ z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (t <= -4e-26) {
		tmp = t_1;
	} else if (t <= 7.5e-280) {
		tmp = t + (x * (y / z));
	} else if (t <= 8.5e-203) {
		tmp = x;
	} else if (t <= 5.7e-8) {
		tmp = t + (x / (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    if (t <= (-4d-26)) then
        tmp = t_1
    else if (t <= 7.5d-280) then
        tmp = t + (x * (y / z))
    else if (t <= 8.5d-203) then
        tmp = x
    else if (t <= 5.7d-8) then
        tmp = t + (x / (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (t <= -4e-26) {
		tmp = t_1;
	} else if (t <= 7.5e-280) {
		tmp = t + (x * (y / z));
	} else if (t <= 8.5e-203) {
		tmp = x;
	} else if (t <= 5.7e-8) {
		tmp = t + (x / (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	tmp = 0
	if t <= -4e-26:
		tmp = t_1
	elif t <= 7.5e-280:
		tmp = t + (x * (y / z))
	elif t <= 8.5e-203:
		tmp = x
	elif t <= 5.7e-8:
		tmp = t + (x / (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (t <= -4e-26)
		tmp = t_1;
	elseif (t <= 7.5e-280)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (t <= 8.5e-203)
		tmp = x;
	elseif (t <= 5.7e-8)
		tmp = Float64(t + Float64(x / Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (t <= -4e-26)
		tmp = t_1;
	elseif (t <= 7.5e-280)
		tmp = t + (x * (y / z));
	elseif (t <= 8.5e-203)
		tmp = x;
	elseif (t <= 5.7e-8)
		tmp = t + (x / (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e-26], t$95$1, If[LessEqual[t, 7.5e-280], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-203], x, If[LessEqual[t, 5.7e-8], N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.0000000000000002e-26 or 5.70000000000000009e-8 < t

   1. Initial program 90.9%

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

   2. Taylor expanded in x around 0 45.6%

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

      1. associate-/l* 68.8%

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

      2. associate-/r/ 66.6%

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

   4. Simplified 66.6%

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

   if -4.0000000000000002e-26 < t < 7.4999999999999999e-280

   1. Initial program 60.7%

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

   2. Taylor expanded in z around inf 55.5%

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

      1. associate--l+ 55.5%

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

      2. distribute-lft-out-- 55.5%

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

      3. div-sub 55.5%

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

      4. mul-1-neg 55.5%

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

      5. unsub-neg 55.5%

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

      6. distribute-rgt-out-- 55.7%

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

      7. associate-/l* 62.1%

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

   4. Simplified 62.1%

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

   5. Taylor expanded in t around 0 52.2%

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

      1. associate-*r/ 52.2%

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

      2. mul-1-neg 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in a around 0 48.9%

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

      1. sub-neg 48.9%

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

      2. mul-1-neg 48.9%

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

      3. remove-double-neg 48.9%

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

      4. associate-/l* 55.0%

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

   10. Simplified 55.0%

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

   11. Taylor expanded in x around 0 48.9%

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

       1. associate-*r/ 55.0%

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

   13. Simplified 55.0%

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

   if 7.4999999999999999e-280 < t < 8.50000000000000031e-203

   1. Initial program 76.5%

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

   2. Taylor expanded in a around inf 42.3%

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

   if 8.50000000000000031e-203 < t < 5.70000000000000009e-8

   1. Initial program 69.7%

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

   2. Taylor expanded in z around inf 52.0%

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

      1. associate--l+ 52.0%

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

      2. distribute-lft-out-- 52.0%

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

      3. div-sub 52.2%

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

      4. mul-1-neg 52.2%

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

      5. unsub-neg 52.2%

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

      6. distribute-rgt-out-- 52.2%

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

      7. associate-/l* 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in t around 0 47.3%

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

      1. associate-*r/ 47.3%

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

      2. mul-1-neg 47.3%

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

   7. Simplified 47.3%

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

   8. Taylor expanded in a around 0 42.2%

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

      1. sub-neg 42.2%

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

      2. mul-1-neg 42.2%

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

      3. remove-double-neg 42.2%

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

      4. associate-/l* 50.0%

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

   10. Simplified 50.0%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-26}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-280}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 6: 51.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+293}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+260}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-28}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.12e+293)
   x
   (if (<= x -1.4e+260)
     (+ t (/ x (/ z y)))
     (if (<= x -4.6e+58)
       x
       (if (<= x 6.6e-28)
         (* (- y z) (/ t (- a z)))
         (* (- t x) (/ y (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.12e+293) {
		tmp = x;
	} else if (x <= -1.4e+260) {
		tmp = t + (x / (z / y));
	} else if (x <= -4.6e+58) {
		tmp = x;
	} else if (x <= 6.6e-28) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.12d+293)) then
        tmp = x
    else if (x <= (-1.4d+260)) then
        tmp = t + (x / (z / y))
    else if (x <= (-4.6d+58)) then
        tmp = x
    else if (x <= 6.6d-28) then
        tmp = (y - z) * (t / (a - z))
    else
        tmp = (t - x) * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.12e+293) {
		tmp = x;
	} else if (x <= -1.4e+260) {
		tmp = t + (x / (z / y));
	} else if (x <= -4.6e+58) {
		tmp = x;
	} else if (x <= 6.6e-28) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.12e+293:
		tmp = x
	elif x <= -1.4e+260:
		tmp = t + (x / (z / y))
	elif x <= -4.6e+58:
		tmp = x
	elif x <= 6.6e-28:
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = (t - x) * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.12e+293)
		tmp = x;
	elseif (x <= -1.4e+260)
		tmp = Float64(t + Float64(x / Float64(z / y)));
	elseif (x <= -4.6e+58)
		tmp = x;
	elseif (x <= 6.6e-28)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.12e+293)
		tmp = x;
	elseif (x <= -1.4e+260)
		tmp = t + (x / (z / y));
	elseif (x <= -4.6e+58)
		tmp = x;
	elseif (x <= 6.6e-28)
		tmp = (y - z) * (t / (a - z));
	else
		tmp = (t - x) * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.12e+293], x, If[LessEqual[x, -1.4e+260], N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.6e+58], x, If[LessEqual[x, 6.6e-28], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.1200000000000001e293 or -1.3999999999999999e260 < x < -4.60000000000000005e58

   1. Initial program 80.8%

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

   2. Taylor expanded in a around inf 53.6%

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

   if -1.1200000000000001e293 < x < -1.3999999999999999e260

   1. Initial program 49.1%

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

   2. Taylor expanded in z around inf 52.7%

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

      1. associate--l+ 52.7%

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

      2. distribute-lft-out-- 52.7%

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

      3. div-sub 52.7%

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

      4. mul-1-neg 52.7%

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

      5. unsub-neg 52.7%

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

      6. distribute-rgt-out-- 62.7%

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

      7. associate-/l* 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in t around 0 62.7%

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

      1. associate-*r/ 62.7%

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

      2. mul-1-neg 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in a around 0 62.1%

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

      1. sub-neg 62.1%

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

      2. mul-1-neg 62.1%

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

      3. remove-double-neg 62.1%

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

      4. associate-/l* 89.8%

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

   10. Simplified 89.8%

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

   if -4.60000000000000005e58 < x < 6.6000000000000003e-28

   1. Initial program 81.4%

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

   2. Taylor expanded in x around 0 57.1%

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

      1. associate-/l* 73.1%

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

      2. associate-/r/ 64.3%

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

   4. Simplified 64.3%

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

   if 6.6000000000000003e-28 < x

   1. Initial program 79.9%

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

   2. Taylor expanded in y around inf 56.2%

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

      1. div-sub 56.2%

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

      2. associate-*r/ 46.9%

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

      3. associate-/l* 56.1%

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

      4. associate-/r/ 56.1%

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

   4. Simplified 56.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+293}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+260}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-28}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 7: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+89}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+191)
   x
   (if (<= a -8.5e+167)
     (/ t (/ (- a z) y))
     (if (<= a -2e+63) x (if (<= a 6.5e+89) (+ t (* x (/ y z))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+191) {
		tmp = x;
	} else if (a <= -8.5e+167) {
		tmp = t / ((a - z) / y);
	} else if (a <= -2e+63) {
		tmp = x;
	} else if (a <= 6.5e+89) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+191)) then
        tmp = x
    else if (a <= (-8.5d+167)) then
        tmp = t / ((a - z) / y)
    else if (a <= (-2d+63)) then
        tmp = x
    else if (a <= 6.5d+89) then
        tmp = t + (x * (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+191) {
		tmp = x;
	} else if (a <= -8.5e+167) {
		tmp = t / ((a - z) / y);
	} else if (a <= -2e+63) {
		tmp = x;
	} else if (a <= 6.5e+89) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+191:
		tmp = x
	elif a <= -8.5e+167:
		tmp = t / ((a - z) / y)
	elif a <= -2e+63:
		tmp = x
	elif a <= 6.5e+89:
		tmp = t + (x * (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+191)
		tmp = x;
	elseif (a <= -8.5e+167)
		tmp = Float64(t / Float64(Float64(a - z) / y));
	elseif (a <= -2e+63)
		tmp = x;
	elseif (a <= 6.5e+89)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+191)
		tmp = x;
	elseif (a <= -8.5e+167)
		tmp = t / ((a - z) / y);
	elseif (a <= -2e+63)
		tmp = x;
	elseif (a <= 6.5e+89)
		tmp = t + (x * (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+191], x, If[LessEqual[a, -8.5e+167], N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e+63], x, If[LessEqual[a, 6.5e+89], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.4999999999999998e191 or -8.50000000000000007e167 < a < -2.00000000000000012e63 or 6.4999999999999996e89 < a

   1. Initial program 89.8%

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

   2. Taylor expanded in a around inf 53.2%

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

   if -9.4999999999999998e191 < a < -8.50000000000000007e167

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 31.7%

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

      1. associate-/l* 77.9%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in y around inf 64.2%

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

   if -2.00000000000000012e63 < a < 6.4999999999999996e89

   1. Initial program 72.6%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 62.2%

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

      4. mul-1-neg 62.2%

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

      5. unsub-neg 62.2%

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

      6. distribute-rgt-out-- 63.0%

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

      7. associate-/l* 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in t around 0 55.0%

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

      1. associate-*r/ 55.0%

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

      2. mul-1-neg 55.0%

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

   7. Simplified 55.0%

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

   8. Taylor expanded in a around 0 52.0%

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

      1. sub-neg 52.0%

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

      2. mul-1-neg 52.0%

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

      3. remove-double-neg 52.0%

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

      4. associate-/l* 56.7%

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

   10. Simplified 56.7%

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

   11. Taylor expanded in x around 0 52.0%

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

       1. associate-*r/ 56.7%

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

   13. Simplified 56.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+89}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 52.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{+167}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+89}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+191)
   x
   (if (<= a -8.4e+167)
     (/ (- t x) (/ a y))
     (if (<= a -9.5e+63) x (if (<= a 9e+89) (+ t (* x (/ y z))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+191) {
		tmp = x;
	} else if (a <= -8.4e+167) {
		tmp = (t - x) / (a / y);
	} else if (a <= -9.5e+63) {
		tmp = x;
	} else if (a <= 9e+89) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+191)) then
        tmp = x
    else if (a <= (-8.4d+167)) then
        tmp = (t - x) / (a / y)
    else if (a <= (-9.5d+63)) then
        tmp = x
    else if (a <= 9d+89) then
        tmp = t + (x * (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+191) {
		tmp = x;
	} else if (a <= -8.4e+167) {
		tmp = (t - x) / (a / y);
	} else if (a <= -9.5e+63) {
		tmp = x;
	} else if (a <= 9e+89) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+191:
		tmp = x
	elif a <= -8.4e+167:
		tmp = (t - x) / (a / y)
	elif a <= -9.5e+63:
		tmp = x
	elif a <= 9e+89:
		tmp = t + (x * (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+191)
		tmp = x;
	elseif (a <= -8.4e+167)
		tmp = Float64(Float64(t - x) / Float64(a / y));
	elseif (a <= -9.5e+63)
		tmp = x;
	elseif (a <= 9e+89)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+191)
		tmp = x;
	elseif (a <= -8.4e+167)
		tmp = (t - x) / (a / y);
	elseif (a <= -9.5e+63)
		tmp = x;
	elseif (a <= 9e+89)
		tmp = t + (x * (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+191], x, If[LessEqual[a, -8.4e+167], N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e+63], x, If[LessEqual[a, 9e+89], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.4999999999999998e191 or -8.3999999999999997e167 < a < -9.5000000000000003e63 or 9e89 < a

   1. Initial program 89.8%

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

   2. Taylor expanded in a around inf 53.2%

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

   if -9.4999999999999998e191 < a < -8.3999999999999997e167

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around -inf 45.2%

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

      1. *-commutative 45.2%

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

      2. associate-/l* 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in a around inf 65.0%

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

   if -9.5000000000000003e63 < a < 9e89

   1. Initial program 72.6%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 62.2%

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

      4. mul-1-neg 62.2%

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

      5. unsub-neg 62.2%

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

      6. distribute-rgt-out-- 63.0%

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

      7. associate-/l* 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in t around 0 55.0%

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

      1. associate-*r/ 55.0%

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

      2. mul-1-neg 55.0%

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

   7. Simplified 55.0%

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

   8. Taylor expanded in a around 0 52.0%

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

      1. sub-neg 52.0%

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

      2. mul-1-neg 52.0%

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

      3. remove-double-neg 52.0%

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

      4. associate-/l* 56.7%

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

   10. Simplified 56.7%

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

   11. Taylor expanded in x around 0 52.0%

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

       1. associate-*r/ 56.7%

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

   13. Simplified 56.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{+167}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+89}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 70.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+21} \lor \neg \left(z \leq 3 \cdot 10^{+67}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+21) (not (<= z 3e+67)))
   (- t (/ (- t x) (/ z y)))
   (+ x (* (- y z) (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+21) || !(z <= 3e+67)) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.8d+21)) .or. (.not. (z <= 3d+67))) then
        tmp = t - ((t - x) / (z / y))
    else
        tmp = x + ((y - z) * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+21) || !(z <= 3e+67)) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+21) or not (z <= 3e+67):
		tmp = t - ((t - x) / (z / y))
	else:
		tmp = x + ((y - z) * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+21) || !(z <= 3e+67))
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e+21) || ~((z <= 3e+67)))
		tmp = t - ((t - x) / (z / y));
	else
		tmp = x + ((y - z) * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+21], N[Not[LessEqual[z, 3e+67]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e21 or 3.0000000000000001e67 < z

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 57.2%

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

      1. associate--l+ 57.2%

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

      2. distribute-lft-out-- 57.2%

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

      3. div-sub 57.2%

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

      4. mul-1-neg 57.2%

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

      5. unsub-neg 57.2%

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

      6. distribute-rgt-out-- 57.5%

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

      7. associate-/l* 78.0%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in y around inf 74.4%

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

   if -5.8e21 < z < 3.0000000000000001e67

   1. Initial program 88.4%

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

   2. Taylor expanded in a around inf 69.3%

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

      1. associate-/l* 74.4%

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

      2. associate-/r/ 75.0%

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

   4. Simplified 75.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+21} \lor \neg \left(z \leq 3 \cdot 10^{+67}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]

Alternative 10: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19} \lor \neg \left(z \leq 1.65 \cdot 10^{+66}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e+19) (not (<= z 1.65e+66)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (* (- y z) (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+19) || !(z <= 1.65e+66)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.3d+19)) .or. (.not. (z <= 1.65d+66))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((y - z) * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+19) || !(z <= 1.65e+66)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e+19) or not (z <= 1.65e+66):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((y - z) * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e+19) || !(z <= 1.65e+66))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e+19) || ~((z <= 1.65e+66)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((y - z) * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e+19], N[Not[LessEqual[z, 1.65e+66]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e19 or 1.6500000000000001e66 < z

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 57.2%

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

      1. associate--l+ 57.2%

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

      2. distribute-lft-out-- 57.2%

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

      3. div-sub 57.2%

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

      4. mul-1-neg 57.2%

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

      5. unsub-neg 57.2%

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

      6. distribute-rgt-out-- 57.5%

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

      7. associate-/l* 78.0%

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

   4. Simplified 78.0%

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

   if -2.3e19 < z < 1.6500000000000001e66

   1. Initial program 88.4%

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

   2. Taylor expanded in a around inf 69.3%

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

      1. associate-/l* 74.4%

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

      2. associate-/r/ 75.0%

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

   4. Simplified 75.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19} \lor \neg \left(z \leq 1.65 \cdot 10^{+66}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]

Alternative 11: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+21} \lor \neg \left(z \leq 3.7 \cdot 10^{-22}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e+21) (not (<= z 3.7e-22)))
   (- t (/ (- t x) (/ z y)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e+21) || !(z <= 3.7e-22)) {
		tmp = t - ((t - x) / (z / y));
	} 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 <= (-5d+21)) .or. (.not. (z <= 3.7d-22))) then
        tmp = t - ((t - x) / (z / y))
    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 <= -5e+21) || !(z <= 3.7e-22)) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e+21) or not (z <= 3.7e-22):
		tmp = t - ((t - x) / (z / y))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e+21) || !(z <= 3.7e-22))
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	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 <= -5e+21) || ~((z <= 3.7e-22)))
		tmp = t - ((t - x) / (z / y));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e+21], N[Not[LessEqual[z, 3.7e-22]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $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 < -5e21 or 3.7e-22 < z

   1. Initial program 70.5%

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

   2. Taylor expanded in z around inf 55.8%

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

      1. associate--l+ 55.8%

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

      2. distribute-lft-out-- 55.8%

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

      3. div-sub 55.8%

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

      4. mul-1-neg 55.8%

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

      5. unsub-neg 55.8%

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

      6. distribute-rgt-out-- 56.8%

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

      7. associate-/l* 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in y around inf 70.4%

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

   if -5e21 < z < 3.7e-22

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0 68.0%

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

      1. associate-/l* 73.8%

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

   4. Simplified 73.8%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+21} \lor \neg \left(z \leq 3.7 \cdot 10^{-22}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 12: 65.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+66}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+86)
   (+ t (/ x (/ z y)))
   (if (<= z 2.65e+66) (+ x (* (- t x) (/ y a))) (+ t (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+86) {
		tmp = t + (x / (z / y));
	} else if (z <= 2.65e+66) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (x * (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 <= (-2.6d+86)) then
        tmp = t + (x / (z / y))
    else if (z <= 2.65d+66) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + (x * (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 <= -2.6e+86) {
		tmp = t + (x / (z / y));
	} else if (z <= 2.65e+66) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+86:
		tmp = t + (x / (z / y))
	elif z <= 2.65e+66:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + (x * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+86)
		tmp = Float64(t + Float64(x / Float64(z / y)));
	elseif (z <= 2.65e+66)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+86)
		tmp = t + (x / (z / y));
	elseif (z <= 2.65e+66)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+86], N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e+66], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5999999999999998e86

   1. Initial program 62.3%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. associate--l+ 55.9%

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

      2. distribute-lft-out-- 55.9%

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

      3. div-sub 55.9%

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

      4. mul-1-neg 55.9%

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

      5. unsub-neg 55.9%

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

      6. distribute-rgt-out-- 56.4%

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

      7. associate-/l* 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in t around 0 64.7%

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

      1. associate-*r/ 64.7%

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

      2. mul-1-neg 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in a around 0 62.0%

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

      1. sub-neg 62.0%

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

      2. mul-1-neg 62.0%

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

      3. remove-double-neg 62.0%

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

      4. associate-/l* 75.1%

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

   10. Simplified 75.1%

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

   if -2.5999999999999998e86 < z < 2.6499999999999998e66

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 61.5%

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

      1. associate-/l* 67.7%

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

      2. associate-/r/ 67.2%

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

   4. Simplified 67.2%

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

   if 2.6499999999999998e66 < z

   1. Initial program 64.6%

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

   2. Taylor expanded in z around inf 58.0%

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

      1. associate--l+ 58.0%

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

      2. distribute-lft-out-- 58.0%

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

      3. div-sub 58.0%

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

      4. mul-1-neg 58.0%

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

      5. unsub-neg 58.0%

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

      6. distribute-rgt-out-- 58.4%

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

      7. associate-/l* 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in t around 0 60.0%

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

      1. associate-*r/ 60.0%

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

      2. mul-1-neg 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in a around 0 59.5%

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

      1. sub-neg 59.5%

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

      2. mul-1-neg 59.5%

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

      3. remove-double-neg 59.5%

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

      4. associate-/l* 66.4%

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

   10. Simplified 66.4%

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

   11. Taylor expanded in x around 0 59.5%

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

       1. associate-*r/ 66.4%

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

   13. Simplified 66.4%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+66}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 13: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+88}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+88)
   (+ t (/ x (/ z y)))
   (if (<= z 1.35e+68) (+ x (/ y (/ a (- t x)))) (+ t (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+88) {
		tmp = t + (x / (z / y));
	} else if (z <= 1.35e+68) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (x * (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 <= (-3.4d+88)) then
        tmp = t + (x / (z / y))
    else if (z <= 1.35d+68) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + (x * (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 <= -3.4e+88) {
		tmp = t + (x / (z / y));
	} else if (z <= 1.35e+68) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+88:
		tmp = t + (x / (z / y))
	elif z <= 1.35e+68:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + (x * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+88)
		tmp = Float64(t + Float64(x / Float64(z / y)));
	elseif (z <= 1.35e+68)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e+88)
		tmp = t + (x / (z / y));
	elseif (z <= 1.35e+68)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+88], N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+68], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.40000000000000004e88

   1. Initial program 62.3%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. associate--l+ 55.9%

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

      2. distribute-lft-out-- 55.9%

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

      3. div-sub 55.9%

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

      4. mul-1-neg 55.9%

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

      5. unsub-neg 55.9%

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

      6. distribute-rgt-out-- 56.4%

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

      7. associate-/l* 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in t around 0 64.7%

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

      1. associate-*r/ 64.7%

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

      2. mul-1-neg 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in a around 0 62.0%

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

      1. sub-neg 62.0%

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

      2. mul-1-neg 62.0%

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

      3. remove-double-neg 62.0%

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

      4. associate-/l* 75.1%

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

   10. Simplified 75.1%

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

   if -3.40000000000000004e88 < z < 1.34999999999999995e68

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 61.5%

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

      1. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   if 1.34999999999999995e68 < z

   1. Initial program 64.6%

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

   2. Taylor expanded in z around inf 58.0%

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

      1. associate--l+ 58.0%

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

      2. distribute-lft-out-- 58.0%

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

      3. div-sub 58.0%

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

      4. mul-1-neg 58.0%

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

      5. unsub-neg 58.0%

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

      6. distribute-rgt-out-- 58.4%

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

      7. associate-/l* 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in t around 0 60.0%

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

      1. associate-*r/ 60.0%

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

      2. mul-1-neg 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in a around 0 59.5%

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

      1. sub-neg 59.5%

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

      2. mul-1-neg 59.5%

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

      3. remove-double-neg 59.5%

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

      4. associate-/l* 66.4%

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

   10. Simplified 66.4%

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

   11. Taylor expanded in x around 0 59.5%

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

       1. associate-*r/ 66.4%

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

   13. Simplified 66.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+88}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 14: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+77)
   t
   (if (<= z -3.2e-166)
     x
     (if (<= z 1.12e-277) (* y (/ t a)) (if (<= z 1.66e+67) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+77) {
		tmp = t;
	} else if (z <= -3.2e-166) {
		tmp = x;
	} else if (z <= 1.12e-277) {
		tmp = y * (t / a);
	} else if (z <= 1.66e+67) {
		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 <= (-8.8d+77)) then
        tmp = t
    else if (z <= (-3.2d-166)) then
        tmp = x
    else if (z <= 1.12d-277) then
        tmp = y * (t / a)
    else if (z <= 1.66d+67) 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 <= -8.8e+77) {
		tmp = t;
	} else if (z <= -3.2e-166) {
		tmp = x;
	} else if (z <= 1.12e-277) {
		tmp = y * (t / a);
	} else if (z <= 1.66e+67) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+77:
		tmp = t
	elif z <= -3.2e-166:
		tmp = x
	elif z <= 1.12e-277:
		tmp = y * (t / a)
	elif z <= 1.66e+67:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+77)
		tmp = t;
	elseif (z <= -3.2e-166)
		tmp = x;
	elseif (z <= 1.12e-277)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 1.66e+67)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+77)
		tmp = t;
	elseif (z <= -3.2e-166)
		tmp = x;
	elseif (z <= 1.12e-277)
		tmp = y * (t / a);
	elseif (z <= 1.66e+67)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+77], t, If[LessEqual[z, -3.2e-166], x, If[LessEqual[z, 1.12e-277], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.66e+67], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.8000000000000002e77 or 1.66e67 < z

   1. Initial program 64.8%

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

   2. Taylor expanded in z around inf 49.4%

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

   if -8.8000000000000002e77 < z < -3.20000000000000001e-166 or 1.12000000000000003e-277 < z < 1.66e67

   1. Initial program 85.9%

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

   2. Taylor expanded in a around inf 35.2%

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

   if -3.20000000000000001e-166 < z < 1.12000000000000003e-277

   1. Initial program 97.2%

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

   2. Taylor expanded in x around 0 49.1%

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

      1. associate-/l* 50.2%

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

   4. Simplified 50.2%

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

   5. Taylor expanded in z around 0 44.0%

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

      1. associate-/l* 45.0%

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

   7. Simplified 45.0%

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

      1. associate-/r/ 51.8%

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

   9. Applied egg-rr 51.8%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 52.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+91}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e+63) x (if (<= a 1.35e+91) (+ t (* x (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+63) {
		tmp = x;
	} else if (a <= 1.35e+91) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.9d+63)) then
        tmp = x
    else if (a <= 1.35d+91) then
        tmp = t + (x * (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+63) {
		tmp = x;
	} else if (a <= 1.35e+91) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e+63:
		tmp = x
	elif a <= 1.35e+91:
		tmp = t + (x * (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e+63)
		tmp = x;
	elseif (a <= 1.35e+91)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e+63)
		tmp = x;
	elseif (a <= 1.35e+91)
		tmp = t + (x * (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e+63], x, If[LessEqual[a, 1.35e+91], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9e63 or 1.35e91 < a

   1. Initial program 90.4%

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

   2. Taylor expanded in a around inf 49.9%

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

   if -3.9e63 < a < 1.35e91

   1. Initial program 72.6%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 62.2%

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

      4. mul-1-neg 62.2%

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

      5. unsub-neg 62.2%

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

      6. distribute-rgt-out-- 63.0%

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

      7. associate-/l* 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in t around 0 55.0%

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

      1. associate-*r/ 55.0%

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

      2. mul-1-neg 55.0%

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

   7. Simplified 55.0%

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

   8. Taylor expanded in a around 0 52.0%

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

      1. sub-neg 52.0%

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

      2. mul-1-neg 52.0%

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

      3. remove-double-neg 52.0%

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

      4. associate-/l* 56.7%

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

   10. Simplified 56.7%

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

   11. Taylor expanded in x around 0 52.0%

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

       1. associate-*r/ 56.7%

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

   13. Simplified 56.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+91}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 38.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+75) t (if (<= z 1.28e+70) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+75) {
		tmp = t;
	} else if (z <= 1.28e+70) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+75)) then
        tmp = t
    else if (z <= 1.28d+70) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+75) {
		tmp = t;
	} else if (z <= 1.28e+70) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+75:
		tmp = t
	elif z <= 1.28e+70:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+75)
		tmp = t;
	elseif (z <= 1.28e+70)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+75)
		tmp = t;
	elseif (z <= 1.28e+70)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+75], t, If[LessEqual[z, 1.28e+70], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e75 or 1.27999999999999994e70 < z

   1. Initial program 64.8%

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

   2. Taylor expanded in z around inf 49.4%

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

   if -1.4499999999999999e75 < z < 1.27999999999999994e70

   1. Initial program 88.4%

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

   2. Taylor expanded in a around inf 33.0%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 25.0% 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 79.6%

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

2. Taylor expanded in z around inf 24.5%

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

3. Final simplification 24.5%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023310 
(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)))))